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GENESYS 2003 Enterprise
Examples
Eagleware Corporation owns both the GENESYS software program suite and its documentation. No part of this publication may be produced, transmitted, transcribed, stored in a retrieval system, or translated into any language in any form without the written permission of Eagleware Corporation.
Copyright © 1985-2003 Eagleware Corporation. All rights reserved
Eagleware Corporation 635 Pinnacle Court Norcross, GA 30071 USA Main Phone: 678-291-0995 Sales Phone: 678-291-0259 Support Phone: 678-291-0719 Fax: 678-291-0971 Printed in the United States of America.
Version 2003 first printing August 2003
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Table Of Contents
Chapter 1 Examples Organization........................................................................................1 Overview............................................................................................................................................1 Find Application Examples ............................................................................................................2
APPLICATION SPECIFIC EXAMPLES .......................................................................... 2
Chapter 2 Signal Control......................................................................................................5 Signal Control\Film Atten.WSP ....................................................................................................5 Signal Control\Xfmr Coupler.WSP ..............................................................................................7 Signal Control\Edge Coupler.WSP...............................................................................................8 Signal Control\ResistiveBroadband10dB.WSP...........................................................................9 Signal Control\ResistiveBroadband20dB.WSP.........................................................................10 Signal Control\Dual Mode Coupler.WSP..................................................................................12 Signal Control\8 Way.WSP ..........................................................................................................14 Signal Control\BSCouplerFinalRecomp.WSP...........................................................................17 Signal Control\BSCouplerFinalRecomp.WSP...........................................................................20 Signal Control\BSCouplerFinalWhole.WSP..............................................................................22
Chapter 3 Components ......................................................................................................25 Coaxial Cable\Coaxial_cable.wsp................................................................................................25 Negation Element \ Negation.wsp .............................................................................................26 Components\Model Extract.WSP ..............................................................................................29 Components\Microstrip Line.WSP ............................................................................................31 Components\Stripline Standard.WSP ........................................................................................36 Components\Spiral Inductor2.WSP ...........................................................................................38 Components\Box Modes.WSP....................................................................................................41 Components\User Model.WSP ...................................................................................................43 Components\BJT NL Model Fit.WSP.......................................................................................46
Chapter 4 Amplifiers ..........................................................................................................49 Amplifiers\Stability.WSP ..............................................................................................................49 Amplifiers\Balanced Amp.WSP ..................................................................................................52 Amplifiers\Amp Feedback.WSP .................................................................................................54 Amplifiers\Amp Noise.WSP........................................................................................................55 Amplifiers\Amplifier Tuned.WSP...............................................................................................57 Amplifiers\Amplifier.WSP ...........................................................................................................58 Amplifiers\SiGe BFP620 Amp.WSP..........................................................................................60
Chapter 5 Filters.................................................................................................................65
Table Of Contents
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Filters\Contiguous Diplexer.WSP...............................................................................................65 Filters\ComblineDesign\Final Lossy.WSP................................................................................66 Filters\Coupled Stepped Z.WSP .................................................................................................72 Filters\Edge Coupled.WSP ..........................................................................................................74 ResonanceElimination\EdgeCoupledWithFictivePorts.WSP.................................................77 Filters\Interdigital.WSP ................................................................................................................79 Filters\Tuned Bandpass.WSP ......................................................................................................81 Filters\Two Level.WSP.................................................................................................................83 Filters\Xtal Filter.WSP..................................................................................................................84 S/FILTER.......................................................................................................................................85
How To Design ......................................................................................................................85 Equal Termination Example.................................................................................................86 Maximum Realizability Example..........................................................................................87 All Series Resonators Example.............................................................................................89 All Parallel Resonators Example ..........................................................................................91 Response Symmetry Example ..............................................................................................94 Equal Inductor Example .......................................................................................................96 Physical Symmetry Example .................................................................................................97 Termination Coupling Example.........................................................................................102 Parametric Bandpass Example ...........................................................................................103 LP All Pole ............................................................................................................................106 LP All Pole ............................................................................................................................107 Coaxial Resonator Example................................................................................................109 BP Edge Coupled .................................................................................................................110 BP Edge Redundant.............................................................................................................112 BP Stub with Inverters ........................................................................................................114
A/FILTER....................................................................................................................................115 AFILTER\Lowpass Minimum Inductor.wsp..................................................................115 AFILTER\Lowpass Minimum Capacitor.wsp ................................................................117 AFILTER\Lowpass Single Feedback.wsp .......................................................................118 AFILTER\Lowpass Multiple Feedback.wsp...................................................................120 Bandpass Maximum Gain Dual Amplifier .......................................................................121
FILTER .........................................................................................................................................122 FILTER\Gaussian_12dB.wsp ...........................................................................................122
M/FILTER ...................................................................................................................................123 MFILTER\Chebyshev Bandpass.wsp ..............................................................................123
Chapter 6 Oscillators ...................................................................................................... 127 Oscillators\Bipolar Cavity Oscillator.WSP ..............................................................................127 Oscillators\NegR VCO.WSP.....................................................................................................131 Oscillators\Coaxial OSC.WSP...................................................................................................132
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Chapter 7 Matching .........................................................................................................135 Matching\Synthesis Comparison.wsp.......................................................................................135 Matching\Ill Behaved Load.WSP..............................................................................................137 Matching\Power Amp.wsp.........................................................................................................139 Matching\Unstable Device.wsp.................................................................................................140 Matching\Match and Stability.WSP ..........................................................................................142 Matching\Stability Selection.WSP .............................................................................................143
Chapter 8 Detectors.........................................................................................................147 Detectors\Simple Detector.WSP...............................................................................................147 Detectors\Diode Detector with Co-simulation.WSP.............................................................149
Chapter 9 Mixer ...............................................................................................................153 Mixer\Low Power Mixer.WSP ..................................................................................................153
Chapter 10 Antennas..........................................................................................................155 Antennas\Patch Antenna Impedance.WSP.............................................................................155 Antennas\Array Driver.WSP .....................................................................................................156 Antennas\Agile Antenna.WSP...................................................................................................158 Antennas\MAmmannPatch.WSP..............................................................................................160 Antennas\Simple Dipole.WSP...................................................................................................162 Antennas\Thin Loop.WSP.........................................................................................................164
Chapter 11 Resonance Elimination ....................................................................................167 ResonanceElimination\LowPassWithFictivePorts.WSP .......................................................167 ResonanceElimination\MicrostripLineWithFictivePort.WSP ..............................................168 ResonanceElimination\MicrostripLineWithFictivePort2.WSP ............................................169 ResonanceElimination\ResonantStubFictivePort.WSP.........................................................171 ResonanceElimination\TwoLevelBPwithFictivePorts.WSP.................................................172
Chapter 12 SPECTRASYS....................................................................................................175 SPECTRASYS\Getting Started\GS1_Setup.WSP.................................................................175 SPECTRASYS\Getting Started\GS2_Spec_Prop.WSP .......................................................177 SPECTRASYS\Getting Started\GS3_Sources.WSP.............................................................180 SPECTRASYS\Getting Started\GS4_Chan_Meas.WSP......................................................184 SPECTRASYS\Getting Started\GS5_Paths.WSP.................................................................186 SPECTRASYS\Getting Started\GS6_Noise.WSP ................................................................189 SPECTRASYS\Getting Started\GS7_Coherent.WSP ..........................................................192 SPECTRASYS\Getting Started\GS8_Intermods.WSP ........................................................194 SPECTRASYS\Getting Started\GS9_Mixers.WSP...............................................................199
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SPECTRASYS\Amplifiers\Feed Forward Amplifier.WSP ..................................................202 SPECTRASYS\Amplifiers\Quad Hybrid Matrix Amp.WSP...............................................206 SPECTRASYS\TX & RX\TX and RX Chain.WSP..............................................................209 SPECTRASYS\Noise\TX Noise in RX Band.WSP..............................................................212 SPECTRASYS\Transmitters\Diversity TX and Hybrid Amp.WSP...................................216
Index............................................................................................................... 221
1
Chapter 1 Examples Organization
Overview These examples can be found in the EXAMPLES subdirectory of your Eagleware installation (commonly C:\Eagle or C:\Program Files\GENESYS). The header of each example section is the filename. The required RAM is the value estimated by EMPOWER. They are approximate and are determined by algorithm rather than a test of memory used. The execution times are for a 266 MHz Pentium II with 256Mbytes of RAM operating under Windows 98. In most cases execution time is for the discontinuity mode. When different run options are used during the example the time and RAM listed are for exercise options with the longest time and largest memory requirement.
The following extra examples are provided for your reference, but are not included in the Examples manual. Examples\Benchmarks BulkConductivityTest.wsp LossyGroundPlane.wsp MicrostripStandard.wsp ShortLengthVia.wsp Stripline Standard.wsp Stripline3Ddiscretisation.wsp UltraThinDielectric.wsp ZeroLengthThrough.wsp ZoDefinition.wsp Examples\Components ApertureCoupledMicrostrips.wsp BigPlanarInductor.wsp CrisscrossDecomp.wsp InductorDecmposition.wsp Microstrip Line ND.wsp RfilmInLine.wsp RfilmInTjunction.wsp SpiralInductor.wsp TeeAndCrossModels.wsp TeeModel.wsp ThickResonatorThickLine.wsp ThickResonatorThinLine.wsp TransistorConnection.wsp TwoStubs.wsp ViaTroughGround.wsp Examples 7.5\Components\Bondwires CompensatedCrossover1.wsp
Examples
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CompensatedCrossover2.wsp Simple3Dbondwire1.wsp Simple3Dbondwire2.wsp SimpleCrossover.wsp Examples\Components\Lines Zdefinition2unsim.wsp Zdefinition3sim.wsp Zdefinition3unsim.wsp Examples\Filters HybridCoplanarBandstop.wsp TwoLevelBPdecomp.wsp TwoLevelBPdecompThinning.wsp
Find Application Examples The following indexes have the examples organized by Application. Examples have also been organized by How To.
APPLICATION SPECIFIC EXAMPLES Components
EM Box Modes (EMPower, Metal Box with and without Top Cover)
Model Extraction (Parameter Extraction, Post-Processing, Optimization, Link to Data File)
User Model (Tuning, User Models)
Spiral Inductor (EMPower: Decomposition, Co-Simulation: Linear and EM)
Microstrip (EMPower: Introduction, Microstrip Impedance, Extrapolating Line Impedance, and Deembedding)
Stripline (EMPower: Accuracy vs Cell Size, Extrapolating Line Impedance)
BJT NL Model Fit (Optimization, SPICE Model, S-Parameters)
Coaxial Cable (Parameter Extraction)
Signal Control
Film Attenutor (EMPower, Deembedding)
Transformer Coupler (Lumped Elements, Equations)
Edge Coupler (Microstrip, Substrates, Layout)
Microstrip 3 dB Directional Coupler (EMPower, Tuning, Decomposition)
Resistive 10 dB Attenuator (EMPower)
Resistive 20 dB Attenuator (EMPower)
Examples Organization
3
Dual Mode Coupler (EMPower: Viewer and Thinning)
8 Way Power Divider (EMPower, Microstrip, Lumped Elements)
Amplifiers
Stability (Amplifier Stability Circles)
Balanced Amplifier (Microstrip, NET Component, Layout)
Amplifier Feedback Topologies (Multiple Schematics)
Amplifier Noise (Microstrip, Noise Circles, Layout)
Transmission Line Amplifier (EMPower, Lumped Elements)
Optimized Tuned Transmission Line Amplifier (EMPower, Lumped Elements, Optimization)
SiGe BFP620 Amplifier (Harbec, Linear Simulation, NonLinear Simulation, User Model, Multiple Schematics, Parameter Sweep)
Filters
Contiguous Diplexer (FILTER: Basic, Lumped Elements)
Combline Filter (FILTER: Walkthrough, EMPower)
Coupled Stepped Z (EMPower: Viewer)
Edge Coupled (EMPower: Grid Fitting)
Interdigital (M/FILTER: EMPower: Wall Grounding)
Tuned Bandpass (EMPower, Lumped Elements, Tunable Filter, Co-Simulation: Linear and EM)
Two Metal Layer Filter (EMPower)
Xtal Filter (FILTER, Lumped Elements)
Oscillators
Negative Resistance (OSCILLATOR, Post Processing, Negative Resistance)
Coaxial (OSCILLATOR, Post Processing, Loaded-Q, Phase Noise)
Bipolar Cavity Oscillator (OSCILLATOR, Harbec, Linear Simulation, Optimization)
LC Colpitts (OSCILLATOR)
Phase Noise (Phase Noise Template)
Matching
Ill Behaved Load (MATCH, Port Impedance Data File)
Match and Stability (Match, Stability, Optimization)
Stability Selection (Stability, Optimization)
Examples
4
Detectors
Simple Detector (Harbec, Linear Simulation, Parameter Sweeps)
Diode Detector with Co-Simulation (EMPower, Harbec, Co-Simulation)
Mixers
Lower Power Mixer (Harbec, Linear Simulation, Non-Linear Simulation, Data File, Parameter Sweep, Multiple User Models, Multiple Schematics)
Antennas
Patch Antenna Impedance (EMPower, Patch Antenna Impedance and Resonance)
Array Driver (Linear Simulation)
Frequency Agile Antenna (EMPower, Linear Simulation, Lumped Elements)
Patch Antenna (EMPower)
Simple Dipole (EMPower)
Thin Loop (EMPower)
Resonance Elimination
Low Pass with Fictive Ports (EMPower)
Microstrip Line with Fictive Port Wide Width (EMPower)
Microstrip Line with Fictive Port Narrow Width (EMPower)
Resonant Stub Fictive Port (EMPower)
Two Level Bandpass Filter with Fictive Port (EMPower)
Edge Coupled Filter with Fictive Port (EMPower)
Advanced TLINE
Hairpin 2 Pole (Advanced TLINE, EMPower)
5
Chapter 2 Signal Control
Signal Control\Film Atten.WSP RAM: 31.7Mbytes Time: 3324s/freq Illustrates: Resistive films, deembedding, benchmark
Given below is a broad bandwidth resistive film 20dB attenuator developed by Res-Net Microwave Inc., of Largo, Florida, which offers a number of high performance resistive microwave products.
This attenuator works well through 12GHz and benchmark data is available through 20GHz. Metal is the darkest color and the mid-tone sections are 50 ohm/square resistive films on a 40mil thick BeO 100 by 200mil substrate with a relative dielectric constant of 6.70.
Examples
6
A much larger grid than 1.25 by 1.25mils could have been used except it was desired to match the dimensions of the attenuator closely. Had an electromagnetic simulation been anticipated the original dimensions could have been fit to a larger grid and the desired DC resistance of the films could still have been achieved. This example would then run quickly.
The launching connectors have a strip width of approximately 25mils while the input and output lines are 70mils. To simulate this discontinuity, the 70 mil lines were not brought to the edge of the board. In addition, deembedding was turned off in this EMPOWER run to include stray capacitance from the line to the face of the launching connector. The net capacitance is 0.24pF as computed from the 0.003024mhos 2GHz susceptance reported in the listing file line analysis. These careful precautions would be unnecessary were it not for the desire to compare EMPOWER results with measured data to 20GHz.
EMPOWER results are given as the traces below and the circles and squares are measured data.
For the resistive film dimensions from the constructed attenuator, the series DC resistance is 43.905 / 53.175 * 50 = 41.283ohms and for the shunt resistors are 10.669 / 27.675 * 50 = 19.276 for each shunt half. This results in a DC attenuation and return loss of 20.4 and 109 dB. The on-grid EMPOWER values are 20.4 and 30 dB.
At low frequencies it is difficult to rationalize the measured 20 dB measured attenuation with the predicted 20.4 dB value other than dimensional errors or film resistivity. The on-grid return loss of 30 dB in combination with the dimensional or resistivity error are potential sources for the disagreement in the return loss.
Signal Control
7
When ports are not deembedded the normalizing impedance is defined as 1 ohm. Therefore the S-parameter data displayed in the EMPOWER log window will not indicate good return loss and 20 dB attenuation during the EM run. The ports can be set at 50 ohms normalizing impedance by adding the option -NI50 in the Cmd Line cell in the EMPOWER setup dialog box.
Signal Control\Xfmr Coupler.WSP Illustrates: Transformers/MUI, Equations
Common but puzzling components used in HF through UHF circuits are broadband transformers and couplers. They are hybrid mode devices which operate as magnetic transformers at low frequencies and as coupled transmission lines at high frequencies.
In this example, the coupler is simulated assuming the magnetic transformer mode. The equations are used to tune the coupling value. We specify the primary turns and the equation block calculates the closest integer secondary turns. The analysis provides insight which is elusive without simulation; the optimum unused port termination resistance isn’t equal to Zo and capacitance improves the return loss.
In the figure below, the solid curves are with R1=39 ohms and C1=1.2 pF. Using tune, you will discover the optimum R and C are functions of the coupling value and whether the through or coupled port is optimized.
Examples
8
Signal Control\Edge Coupler.WSP Illustrates: Microstrip, substrates, LAYOUT
This example illustrates a 10dB microstrip coupler with three sections for improved bandwidth. Coupled-line couplers in microstrip do not achieve 3 dB coupling without exceptionally close lines. Therefore Wilkinson and branch-line networks are often used when equal splits are needed.
Signal Control
9
In the layout below, the rubber band lines which connect the three coupled microstrip sections were left unresolved. It is not absolutely neccesary to resolve rubber band lines if the metal is connected by a footprint or by a polygon of metal which you may add. In this case the lumped element capacitors, which improve the directivity, were used to close the natural gap between line sections caused by different line spacing.
Signal Control\ResistiveBroadband10dB.WSP EMPOWER Example: Thin Film Attenuator
Illustrates: Analysis of a structure with thin resistive film and comparison with measured data.
10 dB Broadband Resistive Attenuator, developed by Res-Net Microwave Inc., of Largo, Florida, which offers a number of high performance resistive microwave products.
Examples
10
Simulation details: The structure is simulated with the solid thinning out (because of large areas of metal and film).
Signal Control\ResistiveBroadband20dB.WSP EMPOWER Example: Thin Film Attenuator
Illustrates: Analysis of a structure with thin resistive film, simulation without de-embedding, and comparison with measured data.
20 dB Broadband Resistive Attenuator, developed by Res-Net Microwave Inc., of Largo, Florida, which offers a number of high performance resistive microwave products.
Signal Control
11
Simulation details: The structure is simulated without thinning out (the most accurate analysis). Two external ports are marked as No Deembed to take into account actual reactance of the sidewalls. Option -ni50 sets normalization for the EMPOWER simulation.
Examples
12
Signal Control\Dual Mode Coupler.WSP RAM: 1.9Mbytes Time: 68s/freq Illustrates: Dual mode couplers, solid thinning, viewer
Given above is a directional coupler laid on a 25 X 25 mil grid centered at 3GHz which a first glance resembles a branchline coupler. Port 1 was placed at the lower left, port 2 at the upper left, port 3 at the lower right and port four at the upper right.
For reasons discussed momentarily we refer to this device as a dual mode coupler. The sides are roughly half wavelength. This results in undesirably large size at lower frequencies, but at the higher microwave frequencies the smaller size of a branch line coupler introduces difficulties. 3GHz is normally the lowest frequency indicated for the dual mode coupler [Kawai and Ohta, 1994].
This version was designed for equal splits at ports 3 and 4. Transmission and reflection responses including losses as computed by EMPOWER and displayed by GENESYS are given below.
Signal Control
13
Notice that unlike the conventional branch line coupler the dual mode coupler is solid in the center. The large metal area requires solid thinning which was specified in the EMPOWER Properties Dialog box. Fortunately, the dual mode coupler has symmetry in both the XZ and YZ planes which compensates for the slower execution of solid thinning.
In conventional pseudo-TEM mode microstrip, current is maximum at the edges of the strip. In this coupler energy launched at port 1 soon transitions to TE10 in the large patch area, thus the term dual mode. This is evident in the Viewer screen given below. Notice that the maximum current is located at the center of the structure. The Viewer is particularly useful in designing structures of this type. In a preliminary run, it was observed
Examples
14
in the Viewer that the signal transferred to port 4 was significantly less than signal at port 3. The idea of placing an obstruction (notch) in the line between port 1 and port 3 immediately bore fruit. As an exercise, use the Viewer to observe the dynamic behavior of this coupler.
The previously cited reference gives additional information on these couplers including broadbanding techniques.
Signal Control\8 Way.WSP RAM: 124.3MB Time: 11067s/freq Illustrates: Power dividers, large EMPOWER runs, lumped elements
The task is an 8 way power divider. It will be based on the cascade of Wilkinson equal dividers. This divider was tested first to verify and optimize the performance of this building block before the much larger, and slower executing, 8 way divider is tested.
Signal Control
15
The input is on the left and the outputs are on the top and bottom walls. The Wilkinson operates by transforming the two 50ohm terminations to 100ohms through quarter wavelength sections of narrower 70.7ohm lines. The two 100ohm impedances in parallel at the junction provide a 50ohm match to the short 50ohm input line. After the test and optimization of this single Wilkinson they were assembled in the 8 way unit shown below.
Examples
16
This entire assemblage of 7 Wilkinsons and connecting lines was then run in EMPOWER. Initial runs indicated significant non-flatness near the center frequency due to box modes. The ports were spaced closer and the box size was reduced. The final design has what are believed to be box modes above and below the band of interest. Some of the initial runs were lossless to conserve execution time. The final runs were lossy and the required memory and time are for the lossy case.
Signal Control
17
The final transmission and selected isolation magnitudes are given here. Because EMPOWER generates all port data, the graphs in GENESYS may be modified to display data for any set of ports without rerunning EMPOWER.
Signal Control\BSCouplerFinalRecomp.WSP Illustrates: EMPOWER ML, Decomposition
EMPOWER Example: Development of a microstrip surface mount 3-dB directional coupler for Mike Giacalone from Americal Technical Ceramics. This example uses advanced EMPOWER techniques to allow easy tuning and optimization of circuit performance. Notice in the design that at the center of the coupler, the lines are separated for a small portion. Adjusting the length of this section allows fine adjustment of the coupling.
There are three files in this example:
Examples
18
• BSCouplerDevelopment.wsp - Implements coupler using tuned capacitors and decomposition. This allows a very quick analysis of the file, plus the coupler can be tuned.
• BSCouplerFinalRecomp.wsp - The coupler's capacitors have been replaced with patches. This file still uses recomposition, allowing line length adjustments.
• BSCouplerFinalWhole.wsp - In this final file, the coupler is simulated as a whole. This file confirms the validity of the decompositional simulation in the previous file.
The simulation results from the final coupler:
Specifications: Coupling: -3dB (S21 and S31) Return loss (S11): less then -20 dB. Isolation (S41): less then -20dB Simulation details: All elements are simulated with the solid thinning out technique to increase accuracy. CoupledLine: A segment of broadside coupled microstrip lines (conductors are in different levels) is simulated and optimized to get Ze=120, Zo=20 (see listing file). Inputs 1 and 2 are coupled as well as inputs 3 and 4. The program automatically goes to the mixed analysis mode (line+discontinuity). 50toCoupledJunction: A tee-like connection of two 50-Ohm microstrips in three-layered media with the coupled microstrip line (design CoupledLine). The inputs 3 and 4 on the right side form two-mode coupled input. CPJunction: A segment of coupled microstrip lines (design CoupledLine) is connected with a segment of a similar line with the same conductor widths but less coupled (to reduce overall coupling). The reference plane of the coupled inputs are shifted in the center.
Signal Control
19
Recomposition: The coupler is assembled from two tee-like junctions of 50-Ohm microstrip lines and coupled line segments (design 50toCoupledJunction), two coupled microstrip line segments (line empower.l3 from the design 50toCoupledJunction, length L1), two step-like junctions with less coupled line (design CPJunction), and the less coupled line segment in the middle (line empower.l2 from the design CPJunction, length L2). Descriptors of all segments must be precalculated. Run simulations EM2, EM3 to simulate the components. Goal coupling -3 dB (S21 and S31) and return loss and isolation below -20 dB could be achieved by tuning lengths (L1 and L2) of coupled line segments and capacitances AuxCap of capacitors Tuning Cap.
Design is not finished because capacitors are only circuit level solution and must be implemented physically (see possible solution in BSCouplerFinalRecomp.wsp).
Examples
20
Signal Control\BSCouplerFinalRecomp.WSP EMPOWER Example: Microstrip surface mount 3-dB directional coupler designed for Mike Giacalone from American Technical Ceramics. Illustrates: An advanced multilevel example with decomposition. Parts of the coupler are simulated with EMPOWER in one work space, then recomposed (coupled sections in the mode space) and optimized to achieve desired performances. Specifications: Coupling: -3dB (S21 and S31) Return loss (S11): less then -20 dB. Isolation (S41): less then -20dB Simulation details: All elements are simulated with the solid thinning out technique to increase accuracy. CoupledLine: A segment of coupled microstrip lines (conductors are in different levels) is simulated and optimized to get Ze=120, Zo=20 (see listing file). Inputs 1 and 2 are coupled as well as inputs 3 and 4. The program automatically goes to the mixed analysis mode (line+discontinuity). 50toCoupledJunction: A tee-like connection of two 50-Ohm microstrips in three-layered media with the coupled microstrip line (design CoupledLine). The inputs 3 and 4 on the right side form two-mode coupled input. A rectangular patch was added to achieve 3-dB coupling, and return loss and isolation below -20dB. The dimensions of the patch were
Signal Control
21
estimated using a couple of auxiliary capacitors hooked up at inputs 2 and 4 of the preliminary structure of the coupler (see BSCouplerDevelopment.wsp) CPJunction: A segment of coupled microstrip lines (design CoupledLine) is connected with a segment of a similar line with the same conductor widths but less coupled (to reduce coupling). The reference plane of the coupled inputs are shifted in the center. Recomposition: The coupler is assembled from two tee-like junctions of 50-Ohm microstrip lines and coupled line segments (design 50toCoupledJunction), two coupled microstrip line segments (line empower.l3 from the design 50toCoupledJunction, length L1), two step-like junctions with less coupled line (design CPJunction), and the less coupled line segment in the middle (line empower.l2 from the design CPJunction, length L2). Descriptors of all segments must be precalculated. Run simulations EM2, EM3 to simulate the components. Goal coupling -3 dB (S21 and S31) and return loss and isolation below -20 dB could be achieved by tuning lengths (L1 and L2) of coupled line segments.
Simulation details: Solid thinning out is used to increase accuracy. Option -O2 is used to reduce line simulation time. Simulation EM2VIEW contains data to visualize current flow at the central frequency.
For the final EM simulation of the whole structure, optimized with decomposition see BSCouplerFinalWhole.wsp).
Examples
22
Signal Control\BSCouplerFinalWhole.WSP EMPOWER Example: Microstrip surface mount 3-dB directional coupler designed for Mike Giacalone from American Technical Ceramics. Illustrates: An advanced multilevel example
Here is the final EM simulation of the whole structure, optimized with decomposition in the example BSCouplerFinalRecomp.wsp. Specifications: Coupling: -3dB (S21 and S31) Return loss (S11): less then -20 dB. Isolation (S41): less then -20dB
Signal Control
23
Simulation details: Solid thinning out is used to increase accuracy. Option -O2 is used to reduce line simulation time. Simulation EM2VIEW contains data to visualize current flow at the central frequency.
25
Chapter 3 Components
Coaxial Cable\Coaxial_cable.wsp Illustrates: Use manufacturer's data to compute parameters for model.
The following data was obtained from a manufacturer of RG-58 coaxial cable.
Data:
Cable Type = RG-58 Zo = characteristic impedance = 53.5 ohms dielectric constant = 2.26 (velocity factor = 0.67) attenuation data:
f (MHz) 100 200 300 400 500 600 700 800 900 1000 attn (db) 4.50 6.80 8.40 10.0 11.33 12.67 14.0 15.0 16.0 17.0 Note: attenuation in db per 100 feet of cable.
Approach:
GENESYS has a model for coaxial cable with the following parameters: length (L), characteristic impedance (Zo), dielectric constant (Er), and two parameters (Kdb1, Kdb2) to define the attenuation as a function of frequency. The optimization feature of GENESYS is used to drive the difference between the model and the manufacturer data toward zero. The model parameters Kdb1 and Kdb2 are the tuned parameters. The measured data is in the file RG58.s2p, which is repeated below. The frequency range for the optimization is 100 to 1000 MHz. Notice from the graph of error that the error is always less than +/- 0.25 db over this range.
The simulation data is compared to the measured data in graph "Data Match". The simulation data is scaled to units of db/100 ft. The resulting parameters Kdb1 and Kdb2
Examples
26
were equal to 0.0139 and 0.1225e-3, respectively. These parameters are part of the equation which determines the attenuation per 100 meters (attn) as:
attn = Kdb1 * sqrt[f] + Kdb2 * f
where: Kdb1: Attenuation per 100 meters, per square root of frequency (in MHz)
Kdb2: Attenuation per 100 meters, per MHz.
It is clear that for this data the model adequately represents the data.
Data file (RG58.S2p): [format: f s11_db s11_deg s21_db s21_deg s12_db s12_deg s22_db s22_deg ]
[ data entered as + values for ease of plotting]
# MHZ S DB R 50 100 0. 0. 4.50 0. 4.50 0. 0. 0. 200 0. 0. 6.80 0. 6.80 0. 0. 0. 300 0. 0. 8.40 0. 8.40 0. 0. 0. 400 0. 0. 10.0 0. 10.0 0. 0. 0. 500 0. 0. 11.33 0. 11.33 0. 0. 0. 600 0. 0. 12.67 0. 12.67 0. 0. 0. 700 0. 0. 14.00 0. 14.00 0. 0. 0. 800 0. 0. 15.00 0. 15.00 0. 0. 0. 900 0. 0. 16.00 0. 16.00 0. 0. 0. 1000 0. 0. 17.00 0. 17.00 0. 0. 0.
Negation Element \ Negation.wsp Illustrates: Use of the two port negation element NEG2 to remove the effect of an element defined by an s-parameter file.
Components
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The NEG2 element creates a two-port element by reading data from a disk file of the element to be negated. It is used to de-embed a port or network. When placed in series with the original network the overall effect is a short circuit. When placed in parallel with the original network the result is an open circuit. This symbol is available in SCHEMAX in the LINEAR Toolbar.
In this example a lumped element filter (Schematic: FILTER) is measured using a 6 meter length of coax (RG-58) between the circuit board and the test equipment. The s-parameter characteristics of the cable were measured and stored in the file: coax_6m.s2p. The goal is to remove the effect of the cable from the measured data. The result is the estimated filter characteristics.
Schematics:
FILTER - the model of the filter only (lumped elements)
Measured Circuit - combination of FILTER and coaxial cable model
Coax Model - GENESYS model of RG-58 cable
Estimated Filter - Measured Circuit with NEG2 element in series.
FILTER: The filter is a lumped element implementation of a third order Butterworth bandpass filter.
Measured Circuit: The schematic re-uses the filter schematic above and the coaxial cable model for cable model RG-58.
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Estimated Filter: The model for the cable was used to generate an s-parameter file "Coax_6m.s2p". The negation element uses this file to generate the inverse transfer function. Again re-using a previously defined schematic simplifies this new schematic. The cascade of these two elements removes the effect of the cable. The remainder is an estimate of the filter alone.
Observations:
1. In the "Estimated Filter" schematic, the effect of the coaxial cable is removed by the negation element. The file referred to by this element is the s-parameter file of the cable.
2. The graph "Estimated Filter Performance" compares the original filter model, the measured circuit, and the Estimated Filter. Notice that the measured circuit is considerably different than the others due to the effect of the cable. The negation element is effective in generating an accurate estimate of the filter. On this graph, the curves for the original filter and the estimate are overlays.
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Components\Model Extract.WSP Illustrates: Post-Processing, Parameter extraction, optimization, simulation/data overrides, Link to Data File.
This is a model for a VHF bipolar transistor with package parasitics. The parameters in the BIP model and the package parasitics are optimized to match the model to measured S-parameter data. This is often refered to as “parameter extraction”. The schematic for the model is shown below.
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The device data is loaded using a "Link to Data File". This example uses post processing, described in the Equation section of the Reference manual. The global equations subtract the device measured data (defined in the data file link "Data") from the model (defined in "BipModel", using sweep "Linear1"):
Using Linear1.bipModel Diff=abs(.RECT[S] - Data.Data.RECT[S]) errorS11=diff[1,1] errorS12=diff[1,2] errorS21=diff[2,1] errorS22=diff[2,2]
The variable "diff" contains a 2x2 matrix with each element containing the magnitude of the complex difference between the measured and calculated S-Parameters. The optimization targets specify that the difference of the s-parameters should be zero:
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It was empirically determined that S21 needed a smaller weight, allowing the optimizer to work harder on the other parameters. This example also illustrates the ability to plot different networks on one graph (note the Smith chart/Polar Chart properties which plot, for example, "S11" [from Linear1.BipModel] and "Data.Data.S11"):
Components\Microstrip Line.WSP RAM: 7.7Mbytes Time: 253s/freq Illustrates: Microstrip impedance, EMPOWER introductory concepts, effect of cell size, required wall and cover spacing for microstrip, extrapolating line impedance and deembedding.
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This example is simply a microstrip line in a box which is 400 mils long (in the x direction, the direction of propagation along the microstrip) by 855 mils wide ( y direction) with a cover 1000 mils above the microstrip metal layer. The line is 95 mils wide on a 31 mil thick substrate with a relative dielectric constant of 2.21. The characteristic impedance reported by T/LINE and the circuit simulator SUPERSTAR which uses analytical expressions from Jansen and Kirschning is 50.1 ohms at frequencies up to 6 GHz. Shown below is a plot from the LAYOUT module where the problem was defined.
The grid spacing in x=20 mils and in y=11.875 mils. There are 8 grids across the microstrip line for a width of 95 mils. The box contains 20 cells in the x direction and 72 cells in y. Also defined in the General tab of the Preferences dialog box are the x and y coordinates of the origin, units, and the LAYOUT drawing snap angle. Default dimensions for line widths, drill diameter, and drawing port sizes are also specified. You may select the General Layer and EMPOWER Layer tabs to view the layer setup for this problem:
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The return loss is generally good, suggesting a characteristic line impedance near 50 ohms. However, when a transmission line is 180o long the input impedance equals the terminating impedance regardless of the characteristic impedance of the line. To determine the line Zo, select Show Listing File from the right-click menu of EM1. Near the end of this file is a section labeled "Line parameters at 2.000e+009 Hz" where Zo is given as 47.746776 ohms. This is an error of 4.7% with respect to the analytical results of 50.1 ohms.
Zo vs. Cell Size If the "Grid Spacing Y" in the LAYOUT Preferences dialog box is changed from 11.875 to 5.9375 mils (increasing the number of cells across the line to 16), then recalculating EMPOWER yields a Zo of 48.810311 ohms.
Extrapolating Zo As the number of cells is increased the accuracy of the electromagnetic simulation improves but the simulation time increases. 128 cells only requires 7.8 Mbytes in this simple problem. But such a large number of cells for typical problems such as filters would require an unreasonable amount of computer memory and execution time. EMPOWER is asymptotically well behaved with respect to the number of cells and the following formula by Richardson allows for accurate extrapolation of Zo.
where Z(Nw) is the impedance calculated by EMPOWER with Nw cells across the line. For example, in the previous runs with 16 and 8 cells across the line, Z(16)=48.810 and Z(8)=47.747. From this we compute for Zo=49.873.
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Given in the table below are the direct and extrapolated line impedances for this example with Nw=2 to 128.
Nw Size (mils) Z(Nw) Zo
2 47.5 41.292 -
4 23.75 45.595 49.898
8 11.875 47.747 49.899
16 5.9375 48.810 49.873
32 2.96875 49.339 49.868
64 1.484375 49.602 49.865
128 0.7421875 49.733 49.864 Notice the well behaved convergence of this data. This is an inherent advantage of Method of lines electromagnetic simulation. From this table we conclude that the correct line impedance at 2 GHz is very close to 49.864 ohms.
Generalized S-Parameters One of the important features of EMPOWER and SUPERSTAR is the support of generalized S-parameters. Many electromagnetic simulators write S-parameter data with a fixed reference impedance, typically 50 ohms. In the above example we see that accurate line impedances require a large number of cells. The 95 mil wide line has a Zo of 49.864 ohms, very close to 50 ohms. But electromagnetic simulation with 4 cells yields a Zo of 45.595 ohms, an error of approximately 8.6%.
EMPOWER writes and GENESYS reads generalized S-parameter data. Generalized S-parameter data is normalized not to a fixed impedance such as 50 ohms, but to an impedance which matches the deembedded line impedance of the electromagnetic simulation. This reference impedance is generally a function of frequency. EMPOWER writes files with the extension .R1,.R2, etc., which GENESYS reads when Generalized is checked in the EMPOWER simulation properties dialog.
This technique substantially improves the accuracy of simulations with a minimum number of cells, vastly improving the economy of electromagnetic simulation.
The following example illustrates this point. In the LAYOUT Preferences dialog box, change the Grid Spacing Y to 23.75 mils which is 4 cells across the line. Next, right-click EM1 in the workspace window and select Properties. Click the "Generalized" check box and press "Recalculate Now". This uses generalized S-parameter data from the EMPOWER run. The results using conventional and generalized S-parameter data are off the bottom of the graph, at around -160 dB.
When circuit subsections are added together the generalized S-parameter technique will result in significantly improved accuracy. To understand why this is so, consider the case of simply cascading true 50 ohm lines. If the lines are under discretized, the resulting lower impedances may strongly interact at quarter wavelength frequencies and cause significant error, even though all lines are equal width and no discontinuities exist.
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De-Embedding When EMPOWER computes the electromagnetic fields of the microstrip line in a box, the simulation emulates a true physical configuration including side walls, end walls and the cover. Many of the circuits that EMPOWER simulates will be used within other circuits away from walls. The sidewalls and cover may be set at an adequate distance such that they do not significantly impact the results. However, the lines must approach the end walls to be launched. For this reason, EMPOWER includes deembedding routines to remove the effect of the end walls before reporting results. This is the normal operating mode. On the other hand, if the circuit being simulated is the entire circuit in a box and the effects on end walls are desired, then deembedding may be turned off. To do this, double-click on all ports of the circuit in the LAYOUT module and select "No Deembed" in the Port Type option.
Given below are the return loss responses of the line with 16 cells across. The line impedance at 2GHz with deembedded ports is 48.8103 ohms. The plots below are with a normalizing impedance of 48.8103 ohms and the trace which dips to over 100 dB return loss at 2 GHz is the deembedded line. The second trace is the same line but with non-deembedded ports. As can be seen the capacitance to the end walls degrades the return loss. Although it may not be not obvious through 6GHz, at higher frequencies this problem becomes more severe.
Zo vs. Wall Spacing and Cover Height Given below are Z(16), Z(8) and Zo for various box widths and cover heights. The original box width of 855 mils is (855-95)/2 or 380 mils spacing between the edge of the microstrip and the sidewalls of the box.
When the cover is well removed, Zo drops 0.5% at a box width of 475 mils, and with well removed sidewalls Zo drops 0.5% at a cover spacing of 310 mils. These spacings represent an edge to wall spacing of 6X the substrate thickness and a cover spacing of 10X substrate thickness.
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Width Cover Z(16) Z(8) Zo
855 1000 48.810 47.747 49.874
475 1000 48.537 47.473 49.602
285 1000 47.712 46.641 48.783
166.25 1000 44.304 43.134 45.475
855 310 48.554 47.491 49.617
855 133 47.573 46.512 48.634
475 310 48.537 47.473 49.601
Components\Stripline Standard.WSP RAM: 18.2Mbytes Time: 776s/freq Illustrates: Benchmark, extrapolating line impedance, accuracy vs. cell size.
It would seem that benchmarking the accuracy of electromagnetic simulation is simply a matter of comparing measured results to computed results. Several examples of this form of benchmarking are given in other examples. However, the difficulty here is the identification and extraction of measurement errors.
An effective method of eliminating this difficulty is to compare electromagnetic simulation results for a system for which an exact solution is known. This is the basis of a benchmark proposed by Rautio [1994]. It consists of a zero metal thickness stripline of width 1.4423896mm in a box with a ground to ground spacing of 1mm and length in the direction of propagation (x) of 4.99654097mm which is 90 degrees at 15GHz. The filling material has a relative dielectric constant of exactly 1 (the relative dielectric constant of air is 1.0006). The sidewall spacing is 10X the strip width which is sufficiently removed to not impact the line Zo to several significant digits.
Even this "simple" test configuration is not a pure first principle system. To launch a signal the line must approach the end walls which increases the capacitance of the line to ground. The process of removing this effect is deembedding and in the following results the automatic deembedding routines in EMPOWER have been utilized.
The line Zo and transmission phase are taken from the EMPOWER listing file. In each case the cell size in the x direction is 0.156142mm which is 128 per wavelength at 15GHz. The following table gives the computed Zo and transmission phase vs. the number of cells across the line.
Ny Zo(ohms) Error(%) ANG[S21] (o)
Time (sec)
2 39.969 20.06 90.0094 <1
4 45.059 9.88 90.0094 <1
8 47.575 4.85 90.0094 1
16 48.806 2.39 90.0094 7
32 49.413 1.17 90.0094 39
64 49.715 0.57 90.0094 202
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128 49.865 0.27 90.0094 1455To enhance accuracy, thinning is turned off. Execution time includes line and deembed modes on a 266 MHz Pentium II with 256 Mbytes of RAM.
Increasing the number of y cells improves accuracy at the expense of execution time. A sufficient number of cells for good accuracy is practical in this small problem. For larger systems, a small cell size results in unacceptable execution time. There are several methods available for improving accuracy while using moderately large cell size.
Richardson's Extrapolation This technique was introduced in the Microstrip Line example. The results for this benchmark are given below. This significantly improves accuracy and large cell size provides small errors. Successful application of Richardson's extrapolation requires well behaved asymptotic results from the EM simulator, which is one of the advantages of EMPOWER's MOL technique. While this technique may be used to determine more accurately the Zo of a line, it requires two runs and it has little direct impact on the precision of an EM analysis of a compound circuit.
Ny Zo(ohms) Error(%) Zo (ohms)
Error (%)
2 39.969 20.06 - -
4 45.059 9.88 50.149 0.30
8 47.575 4.85 50.091 0.18
16 48.806 2.39 50.037 0.074
32 49.413 1.17 50.020 0.040
64 49.715 0.57 50.017 0.034
128 49.865 0.27 50.015 0.030
Edge Positioning Singularities exist at the edge of metal strips. When the EM solution is well behaved as it is with the MOL, improved accuracy can be obtained by modifying the position of the edge [Schulz, 1981]. Significantly improved accuracy will result if the line is analyzed with the edge moved toward the center of the line by 25% of the cell size. Alternatively, the system can be analyzed with a given line width and later constructed with edges moved away from the line center by 25% of the cell size.
In the table below the line was analyzed with reduced width lines. The accuracy is significantly improved for relatively large cell size. In fact, increasingly smaller cell size results in little improvement and may even increase the error although the error at this point is small. The difficulty with this method is that adjusting cell size and line widths is tedious for circuits with arbitrary metal. Although it is not mathematically pleasing, the circuit may be analyzed and when the layout artwork is generated from LAYOUT an etch factor is entered to widen the lines by 25% of the cell size. This method works well and is simple to implement when the x and y cell sizes are similar.
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Ny y cell size Zo(ohms) Error (%)
2 0.5408961 50.749 1.50
4 0.3155227 50.074 0.15
8 0.1690300 50.014 .03
16 0.087332218 50.013 .03
32 0.044370383 50.014 .03
64 0.022361265 50.015 .03
128 0.011224651 50.015 .03
Generalized S-Parameters Generalized S-parameters are perhaps the most user transparent method for improving accuracy while using larger cell size. It is easily implemented using EMPOWER and GENESYS Version 7.0 and later because they support generalized parameters. Few competitive EM/circuit simulator environments support these parameters. For additional details on the theory please refer to the Deembed section of the EMPOWER manual and for an illustration refer to the Microstrip Line example.
Components\Spiral Inductor2.WSP RAM: 12.9Mbytes Time: 380s/freq Illustrates: Spiral inductors, lumped elements, accuracy vs. cell size, co-simulation of circuit and EM simulation
Shown below is the layout on a 5 X 5 mil grid of a spiral inductor in series with the transmission system. The small squares near the center and on the left are landing pads for a bond wire to connect to the center of the spiral. The WIRE model in SUPERSTAR was used for this bond wire and in LAYOUT the BONDWIRE 100 X 20 mil footprint was selected. The bond wire is longer because it is a loop that must clear the spiral. This total system consists of an input microstrip line, the bond wire, the spiral, and an output microstrip line on a 62 mil thick substrate with a relative dielectric constant of 4.8.
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The graph below shows the S21 responses from GENESYS circuit theory (top trace) and S21 from EMPOWER. Metal loss was included in the EMPOWER run.
On the next graph are input reactances, IM[I1], using EMPOWER (peak trace) and circuit theory (smaller excursions). At 100 MHz, the circuit theory reactance of 13.07 ohms corresponds to an inductance of 20.8nH and an EMPOWER reactance of 15.52 ohms corresponds to 24.7nH.
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Spirals are notoriously difficult to model in circuit theory simulators and the EMPOWER data is assumed more accurate. Notice that near resonance (1400MHz) the reactances are more divergent. In general, the accuracy of spirals in a circuit theory simulator is useful at low frequencies, but expecting these models to be accurate at higher frequencies where the capacitance is significant is risky at best. Fortunately, EMPOWER runs for spirals generally do not require more than one or two cells across the lines and simulations are relatively fast.
To illustrate this given next are the same responses with only one cell across the line for the EMPOWER run. You may duplicate these results by running EMPOWER after changing the cell size from 5 mils to 10 mils. Notice that the reactance at 100 MHz is now 14.19 ohms corresponding to an inductance of 22.58nH. This is within 13% of the value with 2 cells across each line. Considering the excellent convergence properties of MOL electromagnetic simulation, we can assume the results with 2 cells are more accurate and is closer to the actual inductance than the 8.6% difference determined with 1 versus 2 cells. Those of you with sufficient memory (about 100Mbytes) could run this problem with 4 cells and compare results.
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The inductances reported above are the effective inductances of the entire systems including the two microstrip lines, the bond wire and the spiral. The inductance of the microstrip lines could be removed by moving the reference planes in LAYOUT. The inductance of the bond wire could be manually removed by finding the inductance of just a bond wire in SUPERSTAR.
Components\Box Modes.WSP RAM: 0.35Mbytes Time: <1s/freq Illustrates: Box modes, surface modes
Have you ever designed an amplifier, paying careful attention to the stability factor, only to have it oscillate despite all your precautions? Have you fought poor ultimate rejection in filter stopbands? Have you been unable to obtain flat gain in your amplifier? Have you fought large spurious signals in your system? A common cause of these problems is often box modes. These effects are often poorly understood but they are easily studied using EMPOWER.
Shown below is the simple system of a 3.6" by 1.96" box with a cover 0.250 inches above 50 ohm microstrip lines 1 inch long on a 62 mil thick substrate with a dielectric constant of 4.5. The grid is 40 X 40mils. The input and output lines are broken by a gap of 1.6 inches, far too large for any significant transfer from input to output. So it would seem.
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Given next is the forward transmission, dB[S21], for this system with the box cover on (the top trace) and the top cover off (the bottom trace).
Notice three peaks of transmission in the covered case at 3150, 4125 and 5250MHz. The peaks at 3150 and 5250MHz illustrate almost no attenuation from the input and output! These transmission peaks occur at the resonant frequencies of the box acting as a cavity. The first peak is the dominant (k101) mode of a 3.6 by 1.96 inch cavity partially loaded with the substrate dielectric. The remaining peaks result from higher order modes and additional peaks would exist if the sweep were extended. The transmission zero near 4500MHz is the result of two equal magnitude components from different modes vector adding out of phase.
How is a transfer attenuation of nearly zero decibels possible? Consider this LC circuit:
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Without the two parallel LC components the effective series capacitance is 0.005pF and the transmission in a 50 ohm system would be approximately -40 dB at 3150MHz. The addition of the resonant lossless LC pair reduces the attenuation to zero decibels. The ends of the microstrip lines in the original box radiate sufficiently to couple fully into the resonant cavity.
Clearly, the consequences of packaging circuitry in an enclosure are significant. First of all, even at a frequency as low as 1500MHz, it is unreasonable to expect stopband performance to exceed 60dB rejection. At higher frequencies, stopband rejection is totally destroyed. Poor stopband performance can devastate filter performance. When an amplifier is placed in a box, feedback near resonant frequencies may result in oscillation. When subsystems are enclosed in a box, spurious signals generated at one location may appear at another location with little attenuation, completely bypassing a filter designed to remove the spurs.
The lower response trace in the responses displayed by is with the cover removed. Actually, a layer with 377 ohms impedance was used for the cover. Sufficiently thick absorbent material on the cover would approach this condition. The Q is destroyed by energy lost from the cavity and fortunately the resonant peaks are removed. However, notice that the stop band performance remains less than -60dB across the sweep range and it worsens with increasing frequency.
The most effective weapon against these problems is a smaller box. Shielding of subsections within one enclosure is notoriously ineffective and careers have been wrecked by confident attempts.
For additional information on Box modes please refer to the Box Modes section.
Components\User Model.WSP Illustrates: Tuning, User Models
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The crystal oscillator shown above was synthesized using the OSCILLATOR program. To pull the oscillation frequency the varactor network to the right of the crystal was added. We created a model for a varactor diode so that the frequency versus tuning voltage can be studied.
The capacitance of the varactor versus the tuning voltage is given by the expression: Cv=Co/(1+Vt/0.7)^Gamma
Vt is the varactor reverse tuning voltage. Co is the capacitance at Vt=0. Gamma is the power of the C vs V curve which is controlled by the varactor doping profile. It is typically 0.5 for abrupt varactors.
There are parasitics associated with the varactor. The schematic shown below depicts the series loss resistance which results in finite varactor Q. Package capacitance and package inductance are shown as Cp and Lp.
To create a new user model:
1. Right-click on Designs in the Workspace Window and select "Add User Model (Schematic)". Enter the global name for the model ("Varactor" for our example.. You can choose to save this model into the MODEL directory.
2. Enter the parameters which will be passed to the model:
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3. The opening screen looks like a regular SCHEMAX screen. Use the same
techniques you would use to draw a circuit schematic to draw a schematic of the model. If a component value is a constant, simply enter the value in that component’s dialog box. If a value is computed by equations or is to be passed as a parameter in the model, choose and enter a variable name in the dialog box field.
4. If equations are used in a model, right-click the model icon in the Workspace Window and select "Edit Model Equations". For the varactor example, enter equations in the Equation Text Editor window shown here:
Cv=Co/(1+Vt/0.7)^Gamma C4=Co/(1+4/0.7)^Gamma Rs=1/(3.1416E8*C4*1E-12*Q)
Here the series resistance, Rs, is computed from the varactor Q which is typically specified at 4 volts bias and 50 MHz. In this way the model finds the effective Q at the desired tuning voltage and operating frequencies. The oscillator open loop cascade gain and phase are shown in the sample GENESYS screen for a tuning voltage of 2.64 volts.
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Components\BJT NL Model Fit.WSP Illustrates: How to compare and optimize a nonlinear SPICE model to measured S-parameters.
As nonlinear models are complex, it is always a good practice to compare S-parameters derived from the nonlinear model to actual measured S-parameters. In this way, you can be sure that you have good parameters and that they have been entered properly. In addition, nonlinear models characterize devices over all frequencies and all bias levels. To improve accuracy, it is usually a good idea to optimize the parameters of the model for the particular bias condition a designer has selected for a given application.
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In this workspace are three schematics, "Meas MMBR," "Test MMBR," and "MMBR Before Opt" Meas MMBR is a simple circuit that uses measured S-parameters for a Motorola MMBR941. Test MMBR contains the SPICE model for the intrinsic device and a set of parasitic inductors and capacitors, the values of which have already been optimized to fit the measured data. MMBR Before Opt contains the nonlinear SPICE model, before optimization has been run on the parasitic elements. In the Equations window, the difference between Meas MMBR and Test MMBR is calculated. Then, optimization targets were defined that drives the differences to zero. Note that the S21 target weighting is set to 0.1 so that minimizing the errors of this large number will not overwhelm the errors in match. Weighting can be adjusted depending on a given design's requirements. The initial model for the device is shown in MMBR Before Opt. Inductances and capacitances were included to bond wires inside the package and lead inductances from the package itself. Capacitances were added between each junction. Initial values were estimates based on the modeling engineer's experience. As the optimization was run, values for several of the parasitics became very small. So small, in fact, that inductor L6 and capacitors C3, C5, and C7 were removed in the final model. As the plots of match and transmission show, the simpler model, using the optimized values, results in a much better fit.
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To experiment with this example, tune some of the parasitic values to move the curves from ideal. then use Actions/Optimize/Automatic to have the optimizer adjust the values back to improve the performance.
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Chapter 4 Amplifiers
Amplifiers\Stability.WSP This example illustrates stability circles and designing an amplifier for stability. The first step is to examine the stability characteristics of the selected active device before adding additional circuitry. Stability should be examined over as broad a frequency range as possible, and not just over the range desired for the amplifier.
Shown above are the input and output plane stability circles for an HP/Avantek AT41586 bipolar transistor biased at 8 volts and 25 mA. The shaded regions of the Smith chart represent regions of instability. To insure stability, the impedance presented to the device at its input terminal should avoid the shaded region of the input plane stability circles. Similar conditions should be satisfied at the output. In this case, since the circles above represent the lowest frequency and since the top half of the Smith chart is inductive, stability is enhanced by insuring that the device is capacitively terminated at low frequencies. Therefore, we will use a series capacitor at the input and output with the smallest value which does not disturb the desired amplifier. To further enhance stability, resistors to RF ground are added at the input and output. These will also be a part of the bias scheme.
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These capacitors and resistors are evident in the schematic shown above. The microstrip tee and transmission line models are added to account for the physical structure which is necessary to add the resistors to the amplifier. The remaining microstrip models comprise the matching networks which were optimized for 10dB of gain and best flatness.
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The results after optimization of the lengths of lines in the input and output matching networks are shown in the GENESYS screen shown above. Notice that the entire Smith chart region, which represents any possible passive load, is stable for both the input and output. Also notice that the sweep range for the amplifier gain and match is from 2000 to 2800 MHz, but the sweep range for the stability analysis is from 100 to 6000 MHz, the entire range for which S-parameter data was available. The layout after resolution of the rubber band lines is given below.
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Amplifiers\Balanced Amp.WSP Illustrates: Microstrip design, the branch line coupler, the NET component, using two different networks in a workspace, and the LAYOUT module
This example is 2100-2900 MHz balanced amplifier. The single-ended (SE) amplifier used in this balanced circuit is shown at below. It is given the name AMP at its input. The return loss of the SE amp is shown on the Smith chart below. Notice the poor return loss.
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The balanced amplifier shown below is built using branch line couplers to split the input signal and later to combine the signals. The SE amp is duplicated in the balanced amplifier using the NET component. NET is given the designator AMP. As components in the SE amp are optimized they effect both amps in the balanced circuit. The branch line couplers deliver reflected signals to the terminating resistors so the return loss of the balanced circuit is improved, as shown in the response below.
Shown below is a finished layout of the balanced amplifier. This layout was created by selecting “Edit Layout” from the Layout menu in SCHEMAX. Footprints for the lumped elements and dimensioned metals are automatically placed on the layout page. You then select objects and snap nodes together to resolve rubber band lines.
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To duplicate the single ended amplifier in the layout, a few extra steps are required:
1. Initially, the single-ended amplifier components and two NET objects are placed in the layout. First, return to SCHEMAX and double-click on each NET object. In the dialog box, select the LAYOUT button and then choose Replace with Open Circuit. This removes NET objects from the layout.
2. Next, finish laying out the one SE amp. Draw a box around the SE amp portion of the layout and select Copy and Paste from the Edit menu in LAYOUT. Move these duplicated components to the desired position.
Amplifiers\Amp Feedback.WSP
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This example illustrates four feedback amplifier topologies. It is interesting to compare their gain, reverse isolation and match. Properly placed inductors and capacitors can typically improve the responses. This is also a good example of using multiple schematics on multiple graphs.
Amplifiers\Amp Noise.WSP Illustrates: Noise Figure, Microstrip, Circles, Layout of Microwave Circuits
This example of low-noise amplifier design is based on an article by Rob Lefebvre published in the March/April 1997 issue of Applied Microwave and Wireless magazine. It is a 9.5 to 10 GHz LNA using an HP/Avantek 10135 GaAs FET.
The amplifier schematic includes an extra FET with only the viaholes to ground the FET source leads. This portion of the schematic was added to display the noise circles of the FET alone. The center of the device noise circles is the impedance which should be
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presented to the device to achieve the best noise figure for the amplifier. This is the impedance seen looking toward the source at the input to the device.
Narrowband low-noise amplifier design is more straightforward than broadband design: 1) The device is stabilized with source inductance and or shunt resistors at the device input and output, 2) the input network is designed to present the correct impedance to the device and 3) the output network is designed for maximum gain.
For broadband design the concept is the same. However, presenting the correct impedance to the device across the band and a flat gain requires balancing multiple goals. This is best accomplished using a modern simulator such as GENESYS to optimize all of the requirements simultaneously. The short arc inside the first noise circle is the locus of impedances versus frequency which should be presented to the FET. For even broader bandwidth, the MATCH synthesis program can be used to find a network which presents near optimum impedance to the device over the entire band.
Shown on the left above are the noise circles of the amplifier with the input network present. Notice that the center of the optimum noise arc passes through the center of the Smith chart. This indicates that the input network has been optimized so that at the middle of the frequency band a 50 ohm source will provide the optimum noise performance. This is verified by examining the noise figure versus frequency plot on the left in the SUPERSTAR output screen. The gain flatness was acheived by optimization of the output matching network. Better output return loss could have been acheived by optimizing for match instead of gain flatness. The match at the input falls where it must because the input network is optimized for best noise and not best match.
The layout below was generated for the completed amplifier. The microstrip lines and discontinuities were automatically generated in LAYOUT.
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Amplifiers\Amplifier Tuned.WSP Illustrates: Automatic integration of lumped elements into the electromagnetic simulation and combined EM and circuit co-simulation.
This example is an optimized variant of Amplifier.wsp, a 2.3-2.5 GHz Bipolar Common Emitter amplifier.
Simulation details: EM frequency sweep has four points, co-simulation sweep is the same as the circuit one. External ports are de-embedded to remove sidewall reactances and normalized to 50 Ohm.
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Other parameters are default, including the following: Planar internal ports are used to hook up capacitor and resistors. Tree Z-directed internal ports are used to simulate transistor connection.
Amplifiers\Amplifier.WSP Illustrates: Automatic integration of lumped elements into the electromagnetic simulation and combined EM and circuit co-simulation.
This example is a 2.3-2.5 GHz Bipolar Common Emitter amplifier.
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Simulation details: EM frequency sweep has four points, co-simulation sweep is the same as the circuit one. External ports are de-embedded to remove sidewall reactances and normalized to 50 Ohm. Other parameters are default, including the following: Planar internal ports are used to hook up capacitor and resistors. Tree Z-directed internal ports are used to simulate transistor connection.
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Amplifiers\SiGe BFP620 Amp.WSP Illustrates: The analysis of an amplifier designed, built, and measured by Gerard Weaver using Infineon's new BFP620 Silicon-Germanium bipolar transistor. This device is a high performance, low cost device housed in a 4-lead ultra miniature SOT-343 surface mount package. With a transition frequency (Ft) in excess of 70 GHz, the device is ideal for high performance applications such as portable wireless communications products.
The amplifier was designed to operate between 1930 to 1990 MHz. Design goals included 15dB of gain, unconditional stability, and an input referenced third order intercept of +10dBm. Low part count and PCB area were also desired.
The schematics "Dev NL Test" and "Dev Lin Test" were used to verify the nonlinear model. The nonlinear device was biased at 2V and 8mA, and S-parameters of the device were simulated. The outputs "Dev Refl" and "Dev Trans" compare the S-parameters of the nonlinear device to the measured S-parameters. Excellent correlation is seen, indicating that the model was well extracted for the device (model parameters were supplied directly from Infineon).
Once the model parameters were verified, the device was entered as a User Model in "BFP620," allowing for easy reuse in future designs. The user model was then placed in the overall design found in schematic "Amp NL." Mr. Weaver took extra care in his simulation model to include parasitics as part of his lumped components. He also included transmission line segments to model the parasitics of the PC board. The S-parameters of the overall amplifier were simulated and graphed on output "S-params." At
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1960MHz, the gain is 15.4 dB, slightly better than the design goal. The overall response shape was very close to the measured results (available from Infineon).
Large signal analysis was then completed on the circuit. "Spect 1-tone" shows the output spectrum of the amplifier when driven with -20 dBm of available power. Note that the power measured at Port 1 (P1) is less than -20 dBm due to the mismatch of the port. The output spectrum is quite clean.
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"Compression" plots the gain compression of the amplifier as it is driven from -20 dBm to 0 dBm. The blue trace shows the gain compression. The 1dB compression point is approximately -5 dBm. The red and green traces show the output and input power versus drive level.
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"Wave 1-tone" shows the output waveforms at each point in the power sweep.
"Spect 2-tone" shows the output spectrum around the center frequency when the amplifier is driven with two -20 dBm signals. This spectrum was used to calculate the input referenced TOI level, shown to be +9.3 dBm, very close to the 10.3 dBm measured on the built circuit.
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Convergence controls were adjusted for this circuit. Full Jacobian calculation was set to "always" which speeds convergence as is typical when analyzing BJT circuits. In addition, the number of harmonics in "HB 1-tone" was increased to 16 so that the signals were adequately sampled during the power sweep.
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Chapter 5 Filters
Filters\Contiguous Diplexer.WSP This example illustrates the design of a contiguous diplex filter. It was designed by the following steps:
1. Design a 7th order singly-terminated Butterworth highpass filter using the synthesis program FILTER and write a file named CONTIGUS.SCH.
2. Return to FILTER. Design a 7th order singly-terminated Butterworth lowpass and write a file named LP.SCH. Then run GENESYS and display the lowpass response.
3. Open the schematic and draw a box around the entire lowpass schematic. Selecting “Cut” and “Paste” from the Edit menu places the lowpass schematic in the buffer and back in the schematic.
4. Next, load CONTIGUS.SCH, open the schematic, and select Paste from the Edit menu which drops the lowpass over the highpass. Drag the lowpass schematic off of the highpass schematic using the mouse.
5. Connect together the two filters at the singly-terminated, zero-impedance ends and modify the port impedances and graph properties to display the desired information. The resulting schematic is shown below:
The responses, isolation, and return loss are shown on the graph below. Notice that the RL is excellent through the entire crossover region. This is a natural and desirable consequence of designing diplexers by connecting together singly-terminated filters with
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identical cutoff frequencies (contiguous). With lossless, ideal components, the RL is theoretically infinite at all frequencies. Similar results are acheived using Chebyshev filters with contiguous 3 dB corner frequencies.
Filters\ComblineDesign\Final Lossy.WSP Illustrates: EMPOWER Example - Design of combline filter.
This is a multi-step example and starts with ComblineDesign\Step 1.wsp.
Filter specifications: Type: 5-resonator combline on a PTFE substrate. Center frequency: 1800 MHz Passband: 1700-1900 MHz.
Step1: Optimization of the synthesized filter - Step 1.wsp
Simulation details: The filter was synthesized with the M/FILTER. Capacitors values and resonator lengths where specified as tunable variables and optimized to get proper passband and return loss. There is no EM simulation yet, because the layout of the filter fits only a grid with excessively fine grid (1x1 mils).
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Step 2: Initial EM simulation - Step 2.wsp
Features: Fitting results of the synthesis to a grid and subsequent interactive optimization.
Filter specifications: Type: 5-resonator combline on a PTFE substrate.
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Center frequency: 1800 MHz Passband: 1700-1900 MHz.
Simulation details: The filter optimized in the Step 1 example is adjusted to a grid with cell size 6x6 mils. All microstrip line widths and spacings are rounded off to be multiples of 6 mils. It made the passband of the circuit theory model a bit wider and shifted it a bit. The values of the capacitances adjusted to get the center frequency back.
EM analysis results: The passband is shifted to lower frequencies about 8% and 10% wider then expected. The return loss are also no good.
Step 3: Shifting the center frequency - Step 3.wsp
Features: Fitting results of the synthesis to a grid and subsequent interactive optimization.
Simulation details: The filter adjusted to the grid in the Step 2 example. The lengths of the coupled line segments are made shorter by direct shifting them up and down in the layout. The input line segments are completed by tapered line segments.
Results: The center frequency is shifted.
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Step 4: Narrowing down the passband - Step 4.wsp
This step illustrates the fitting results of the synthesis to a grid and subsequent interactiveoptimization. To make the passband narrower, the spacings of the coupled line segments are increased.
Results: The passband is adjusted.
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Step 5: Improving matching - Step 5.wsp
Features: Fitting results of the synthesis to a grid and subsequent interactive optimization.
Simulation details: The tap point is moved up a little bit to improve matching.
Results: The return losses is improved.
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Last Step: Final simulation and tuning with losses - Final Lossy.wsp
Features: Fitting results of the synthesis to a grid and subsequent interactive optimization.
Simulation details: Only the capacitances where adjusted a little bit to tune passband of the filter.
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Notes: The structure is very sensitive to the capacitances values. So, it will be necessary to tune a fabricated filter.
Filters\Coupled Stepped Z.WSP RAM: 1.0Mbytes Time: 7s/freq Illustrates: Filters, EMPOWER thinning, stopbands, multiple EMPOWER runs
This filter illustrates filter design techniques which would not be feasible using conventional circuit theory simulation because it involves coupling between complex shaped resonators. The final filter design is shown below.
The filter is a bandpass centered at 2950MHz which utilizes three stepped impedance resonators (SIR). SIRs are physically shorter than uniform impedance resonators. The
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inductance is increased in the narrow sections near the viahole ground and the capacitance is increased at the open end. Both effects decrease the resonant frequency for a given physical length. With uniform impedance resonators this structure would be interdigital.
The filter was originally designed also using EMPOWER and the general technique described beginning on page 379 of the book "HF Filter Design and Computer Simulation". The resonant frequency and external Q vs. tap point were first determined using EMPOWER with a single resonator. Next, the internal coupling coefficient vs. resonator spacing was determined using two resonators. The filter was designed from this data and the technique described in the reference. The input and output taps reduce the frequency of the end resonators. The center resonator frequency is reduced by the addition of loading metal at the open end. This compensation was determined empirically.
Adequate resolution in the passband in combination with a wide sweep to observe the stopband requires a large number of frequencies. To conserve execution time, EMPOWER was first run from 2500 to 3400MHz with 31 points ("EM Passband"). Next, an EMPOWER simulation ("EM Stopband") was run from 1150 to 10500 MHz with 61 points. The final GENESYS screen after this second run is given below. The critical frequency was set at 4000 MHz for accuracy through the passband but precision was not required in the stopband. A critical frequency of 4GHz allowed thinning with accurate passband results.
To further reduce execution time, the above data was taken without Viewer data. One simulation was then modified, requesting three frequencies from 1000 to 5000 with "Generate Viewer Data" checked. The top view of the current magnitude at 3000 MHz is given below.
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Notice that the lines leading to the input and output taps appear as thin lines in the Viewer. This line was one cell across and the edges were not aligned with the edges of the cell. It mapped and displayed onto one grid line. EMPOWER calculates current along lines and not the space between lines. In this case, the results are useful but improved precision would have resulted from a more careful grid alignment. The input and output lines also are not exactly aligned with the grid. This inexact alignment has caused a nonsymmetrical mapping. This is due to the edge of the line being exactly centered in a cell.
Filters\Edge Coupled.WSP Files: EdgeCoupledOpened.WSP and EdgeCoupledBenchmark.WSP RAM: 2.0Mbytes Time: 15s/freq Illustrates: Benchmark, filter loss, phase, fitting grid to existing design, reference planes
This 3-section edge-coupled 12 GHz bandpass filter is analyzed in EMPOWER and compared to measured results [Wolff and Gronau, 1989]. This paper presented a practical method for deembedding the effect of connectors from measured data and it presented measured results for the 3-section edge-coupled bandpass filter of interest in this example. Since the connectors were deembedded from the presented data we will run EMPOWER with the automatic deembedding routines invoked.
This paper was selected because the authors have an record of reliable work. The circuit of interest was only a portion of the paper and a description of this circuit was brief. We chose appropriate box dimensions to complete the description for the EMPOWER run.
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The filter dimensions were fit to a grid of dx=0.105 and dy=0.105mm. For a definition of these dimensions please refer to the original paper. The original and on-grid values are given here to illustrate the dimensional errors introduced by placing the filter on grid.
Parameter Original On Grid
L1 4.612 4.620
L2 4.519 4.515
L3 4.502 4.515
L4 4.599 4.620
S1 0.100 0.105
S2 0.340 0.315
S3 0.325 0.315
S4 0.100 0.105
H 0.508 0.508
Wa1 0.815 0.840
Wb1 0.331 0.315
Wa2 0.387 0.420
Wb2 0.381 0.420
Wa3 0.380 0.420
Wb3 0.393 0.420
Wa4 0.329 0.315
Wb4 0.806 0.840
Hbox 5.080 5.080 The largest percentage errors are with the microstrip widths. In bandpass filter structures there is a large sensitivity of the responses to the resonant frequency of the resonators. This is predominantly determined by the resonator length and the percentage errors in length associated with placing the metal on the grid were small. The width of resonators has only a small impact on the resonant frequency but they impact filter bandwidth.
In this example the reference planes were shifted from the edge of the box to the edge of the input and output coupling lines. They are shifted by selecting the port and dragging the reference line in the desired direction. The shifted reference lines may be observed in the LAYOUT module for this example.
Given below are plots of S21 and S11 linear magnitudes and phases as computed by EMPOWER and displayed by GENESYS.
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Excellent agreement with measured data (not shown, see the reference above for measured data) was achieved. As stated earlier, the choice of grids introduced small percentage errors in the length of metal but width errors were significant. While the center frequency appears to be slightly higher in the simulation this is possibly the result of bandwidth shrinkage with most of the shift occurring on the lower side of the passband. An interesting exercise for those with adequate memory would be to run this filter with gridding closer to the original dimensions.
Edge coupled filters are susceptible to radiation loss. Given below are responses of the previous this filter in an enclosure with the height (y direction) doubled to 18.9mm and with the cover removed. Notice that the insertion loss on the low side of the passband has increased. This is due to radiation. Can you predict why radiation increases the loss primarily below the center frequency? Notice the non-monotonic response in the lower transition region. This is probably due to box modes. Would you expect radiation to occur in the original width enclosure with the cover removed? Answers to these questions are given in Section 5.9 of HF Filter Design and Computer Simulation.
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ResonanceElimination\EdgeCoupledWithFictivePorts.WSP EMPOWER Example: Edge-Coupled Filter - Resonance Elimination Technique.
Illustrates: EM simulation of a filter with edge-coupled microstrip resonators and comparison with published results of simulation and measurement [1]. Also demonstrates a resonance elimination technique that uses fictive loaded internal ports to expand and interpolate S-matrices of the filter and then reduces the expanded descriptor matrix to the initial one. Description of the problem: The three-resonator edge coupled filter is described in [1]. Transverse dimensions of the coupled line sections were rounded to the nearest integer number of discretisation distances. The discretisation distances along and across lines were 0.105 mm. Dimensions of the Grounau and Wolff filter and (rounded) values are:
l1 = 4.612 (4.62) l2 = 4.519 (4.515) l3 = 4.502 (4.515) l4 = 4.599 (4.62) Wa1 = 0.815 (0.840) Wb1 = 0.331 (0.315) Wa2 = 0.387 (0.420) Wb2 = 0.381 (0.420) Wa3 = 0.380 (0.420) Wb3 = 0.393 (0.420) Wa4 = 0.329 (0.315) Wb4 = 0.806 (0.840) s1 = 0.100 (0.105) s2 = 0.340 (0.315)
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s3 = 0.325 (0.315) s4 = 0.101 (0.105) w = 1.580 (1.575)
Simulation details: Design Layout1 describes the whole filter that is simulated in EM1 at 49 frequency points (about 20 min per frequency point). S-parameters are generalized. Design plus4ports is the same filter but with 4 additional internal ports breaking resonators in halves and eliminating resonances when they are 50-Ohms loaded. Corresponding simulation EM2 is done only for 7 frequency points in the same frequency range as the initial filter (S-matrix is very smooth). Design short4ports takes 6-port data from the simulation EM2 and sets proper boundary conditions in fictive port areas (short circuit conditions). The external ports are normalized to impedances calculated in the EM2 simulation to have generalized parameters of the filter. Thinning out is off for both simulations. Option -O4 is used in all simulations to enforce de-embedding line segment to be shorter then default and to reduce de-embedding simulation time. Simulation results: The simulation results obtained by the resonance elimination technique is almost on the top of the en-block simulation results. 7 times acceleration is achieved with simple interpolation technique and without considerable loss of accuracy.
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Reference: 1) Gronau G., Wolff I. A simple broad-band device de-embedding method using an automatic network analyzer with time-domain option. - IEEE Trans., v. MTT-37, 1989, N 3, pp. 479-483. The filter shown in Fig.11 of the paper.
Filters\Interdigital.WSP RAM: 19.6Mbytes Time: 1227s/freq Illustrates: Low loss filters, non-resonant simulation, wall grounding
The requirement for this exercise is a low loss printed 5th order bandpass filter with a center frequency of 1178MHz and a bandwidth of approximately 50MHz. This is a bandwidth of 4.2% and a loaded Q of 23.6. Low insertion loss dictates a high unloaded Q so a suspended stripline structure with a large ground to ground spacing of 500 mils was selected. The metal is etched on a 32mil thick teflon PWB with a relative dielectric constant of 2.2. The metal is centered between the grounds and the teflon is below the metal. The layering setup may be viewed in the layer tabs of the LAYOUT Properties dialog box. The metal pattern is shown below.
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The lines terminate in ground at the sidewalls rather than through via holes. The filter may be designed using the technique referred to in the Coupled Stepped Z example, or in this case by designing a stripline filter in M/FILTER and entering a relative dielectric constant based on a filling factor, a dielectric constant of 1 + (32/500) * (Er-1)=1.08. This serves as a reasonable starting point.
The small 4.2% bandwidth increases the sensitivity of the response to small errors in the analysis. Therefore, a fine grid is necessary. In this case a grid of 24mils in x and 18mils in y was used. This results in 13 cells across the width of the lines which is generally more than necessary. However, this cell size was selected because the spacing to the input/output coupling lines is small. The small grid in y is required to satisfy the need in narrowband filters for precise control of resonator frequencies.
This problem contains 225 cells in x and 136 cells in y for a total of 30,600 cells. This in combination with the need for several frequencies in the passband and the probable need for several runs to iterate the design would result in a tedious and time consuming effort were it not for a number of tricks employed with this filter. Listed in order of importance they are:
TIP 1: The interdigital filter behaves simultaneously as multiple coupled lines and resonators. It is the resonant process which is frequency selective. The frequency dependence of the coupling coefficients is slow and monotonic. The lines were terminated in ports rather than ground so that they are nonresonant. GENESYS then reads this data and terminates all ports except the input and output with a direct connection to ground. This manifests in resonance and the filter bandpass behavior is observed. Because EMPOWER is analyzing a monotonic nonresonant structure only 5 frequencies were used. During the interactive design process 3 frequencies were used and then for the final plot given here a final EMPOWER run with 5 frequencies was used. The results for 3 and 5 frequencies in this example agree within hundredths of a decibel at every frequency in the 101 frequency GENESYS plot. The schematic to ground the nodes is shown below along with the circuit response. Notice the use of the NPO8 block with the filename "WSP:Simulations\EM1\EMPOWER.SS". This instructs the NPO to get it's data from the Current workspace (WSP:), "Simulations" Folder, Simulation "EM1", file EMPOWER.SS. This is the method to get raw EMPOWER data from a simulation. For more details on this method, see File Descriptions in your EMPOWER manual.
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TIP 2: Once the resonator grounds are replaced with ports it is possible to add a line model from the port to ground. If these line models are also stripline with a similar substrate description then the line lengths may be tuned or optimized with immediate GENESYS display of the results. Resonator length corrections for a new EMPOWER run are thus found quickly.
TIP 3: A similar circuit can be analyzed entirely as a circuit theory file in GENESYS to estimate the source of response errors in the EMPOWER run. For example, if GENESYS shows that end spacings which are narrowed match EMPOWER results then the spacings are increased for the next EMPOWER trial.
Filters\Tuned Bandpass.WSP RAM: 5.3Mbytes Time: 92s/freq Illustrates: Tunable filters, non-resonant simulation, lumped elements, correlation of lumped/EM simulation
Filters may be electronically tuned using voltage variable capacitors (varactors). While varactors may adjust the center frequency, the remaining element values are generally not optimum for the new center frequency. Adhering to the following principles mitigates these difficulties:
1. Use like-kind resonators for each section. Avoid the classic BP with alternating series and shunt resonators.
2. For constant bandwidth vs. frequency, internal coupling between resonators should decrease with increasing frequency. Series coupling capacitors are common in filters but are a very poor choice for tuned filters.
3. As above, external coupling should decrease with frequency. Series coupling inductors may be used for both internal and external coupling.
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The filter is a 2-section microstrip combline bandpass. Combline structures are grounded on one end and are capacitively loaded at the open end. If the lines are a quarter wavelength long, magnetic coupling near the grounded ends and electrostatic coupling at the open ends are equal in magnitude but opposite in phase, resulting in no coupling (an all-stop structure)! With capacitive loading at the open ends, the electrostatic coupling sections are shortened and coupling is predominantly magnetic.
In the case of a tunable bandpass, the length of the combline is selected such that the coupling between resonators is reduced at the proper rate as the frequency is increased. A similar technique is used for external coupling. The outside line sections are not resonators but provide external coupling which decreases with frequency.
The responses on the left are circuit theory simulations by GENESYS and on the right are EMPOWER results. The traces are with the varactors at 0.55pF. You can tune the varactors to shift the frequency.
Notice the transmission ripple and return loss predicted by EMPOWER are somewhat higher. The circuit theory simulation does not include the capacitance of the varactor landing pad footprints. This stray capacitance is a higher percentage of the total
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capacitance at higher frequencies and the resulting frequency differences are more significant at higher frequencies. An inherent advantage of electromagnetic simulation is that more of these strays, not only capacitance but path length and others, are incorporated in the simulation thus resulting in improved accuracy.
This example illustrates an important concept which can save significant execution time. The above responses were generated from EMPOWER data for only only 4 frequencies! Furthermore, EMPOWER data does not need to be retaken to tune this filter using the varactors! The length of the coupled lines are less than 90o long and they are not resonant. Resonance is achieved with capacitive loading. The EMPOWER data is taken without the varactors present and the line impedances and couplings change very slowly with frequency. EM data is only required for a few frequencies. This technique can be directly applied to all combline filters, thus saving significant execution time. It can even be applied to interdigital filters by performing the EM analysis with the via holes replaced with ports. After the EM run, the ports are replaced with circuit theory via hole models to achieve resonance. This technique is should not be overlooked!
Filters\Two Level.WSP
EMPOWER Example: Two level microstrip bandpass filter. Features simulation of a filter with coupled microstrip resonators in two metalization levels and comparison with published results of simulation and measurement [1].
Three side-coupled microstrip resonators are on a substrate. An additional resonator is placed on an inverted substrate and over the three resonators to achieve coupling with the input resonators (through one). Both substrates have the same height 0.51 mm and dielectric constant 2.33. They are separated by a foam dielectric with height 3.3 mm and dielectric constant 1.07. Microstrips are 1.49 mm wide (rounded off to 1.5mm). Whole structure is in a box 40 mm by 20 mm.
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Reference:
1) A.A. Melcon, J.R. Mosig, M.Guglielmi, Efficient CAD of boxed microwave circuits based on arbitrary rectangular elements, IEEE Trans., v MTT-47,1999, N 7, p.1045-1058
Filters\Xtal Filter.WSP
Note: This crystal filter requires very high precision components. We strongly recommend changing the "Digits right of decimal" in Options from the Tools menu to 6. You may want to change it back after you are done with this example.
A 4th order Chebyshev filter with a center frequency of 9.001 MHz, a bandwidth of 3 KHz and 300 ohms terminating impedance is designed using a crystal with the following parameters:
Rs = 31 ohms Lm = 24.54 millihenries (24.54E6 nH) Co = 4.18 pF Cm = 0.0127429 pF, which resonates with Lm at the crystal series frequency
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FILTER was used to design the shunt-C coupled bandpass, specifying 24.54E6 nH for the inductor, and then writing the GENESYS file. The shunt-C coupled bandpass filter topology is similar to ladder crystal bandpass filters. Since the shunt-C filter allows specifying the series inductance, designing ladder crystal filters is straightforward. Each series inductor-capacitor pair is converted to a crystal XTL model as shown in the circuit above. The response is shown in the figure below.
The 2.4 pF crystal parallel capacitance causes the high side selectivity to be greater. This places an upper limit on the bandwidth of this type of ladder crystal filter. Placing an inductor in parallel with the crystal to resonate out Co may allow a wider bandwidth.
S/FILTER How To Design This section utilizes examples to illustrate "How To Design" filters that meet important and practical design goals. For example, how to design filters with equal input and output terminations or how to design filters with all series resonators. These requirements often arise in the development of filters for specific applications. For example, when quartz crystals or transmission lines realize the final filter, all series or all shunt resonators are typically required. Direct synthesis creates filters with maximum economy for specific responses but achieving certain desirable topologies must be directed.
One strength of S/FILTER over other synthesis programs is that it provides the user with a rich set of tools for directing the synthesis process. This section uses examples to illustrate how to use these tools. Once mastered, these tools are easily applied to solving your particular requirements.
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Note: Each example in this section lists two filenames. The .WSP file contains the schematic and any associated layouts or optimizations. The .SF$ file contains the S/FILTER settings used to design any filters used in the example.
Equal Termination Example Files:
1. Filters\SFILTER\Equal Termination.WSP
2. Filters\SFILTER\Equal Termination.SF$
This example illustrates how to design filters for equal input and output termination resistance. These techniques may be used to also design filters with specific, unequal, termination resistance such as 50 Ω input and 75 Ω output. Given here is the Design tab of S/FILTER for a 50 Ω, 10.7 MHz IF filter with 300 KHz bandwidth.
The Table in the Extractions tab is Customized to show the TRF Ratio, the number of Inductors and the Permutation (extraction sequence). A transformer ratio of 1:1 would result in a 50 Ω output. The Table was sorted by the transformer ratio by clicking on the TRF Ratio column header. Next the table is scrolled to find a transformer ratio of 1. Although this often occurs, in this case the closest ratios are 0.59 and 1.69 and a transform is required to remove the transformer. The Permutation sequence ∞ 10.4 ∞ DC 11 ∞ is selected as shown here.
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The resulting schematic is
Next, the transformer is removed while keeping a 50 Ω output by selecting L2 and applying a Norton Series transform with the Calculate N option. The following schematic results
Maximum Realizability Example Files:
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1. Filters\SFILTER\Maximum Realizability.WSP
2. Filters\SFILTER\Maximum Realizability.SF$
The final filter schematic in the Equal Termination example has six inductors, a maximum to minimum inductor ratio of 318 and a minimum inductor value of 4.72 nH which is very low for a 10.7 MHz filter. Narrow bandpass filters often have significant realization issues but could we do better in this case? This example illustrates methods for improving the realizability of filters.
To maximize realizability and resonator Q for a 10.7 MHz bandpass, we desire the minimum number of inductors, inductance between 1000 and 100,000 nH, equal 50 W input and output terminations, and no transformer.
The Extraction table can be configured to display Permutations sorted by an error based on departure from user goals. Given here is an Extration Goals setup dialog box.
Next the extractions were sorted first by Error by clicking on the Error column header and then by number of Inductors. The resulting Extraction tab is given here.
The red entries in the table indicate inexact permutations.
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Entry #4 with the Permutation ∞ 10.4 11 ∞ ∞ DC is selected. The minimum inductor is lower than desired but other 4-inductor extractions are less desirable. If 112.75 nH is deemed too small then the 5-inductor extraction 11 ∞ 10.4 ∞ DC ∞ is an alternative.
The 4 inductor permutation has a transformer. It is removed by clicking the Remove Transformer button. Fortunately this reduces the maximum inductor value. The resulting schematic is
All Series Resonators Example Files:
1. Filters\SFILTER\Series Resonators.WSP
2. Filters\SFILTER\Series Resonators.SF$
This example illustrates how to design bandpass filters with all series resonators. A three-section 800 Hz bandwidth communications receiver IF filter centered at 9 MHz is realized using quartz-crystal resonators. The quartz-crystal parameters are Lm = 24E6 nH (24 mH), Cm = 0.01303 pF (13.03 fF, Co = 3.6 pF and Rm = 31 Ω. The motional inductance and capacitance given here series resonate at 9.0 MHz. In the final filter, each crystal may series resonate at slightly different frequencies as determined by the final Cm in the schematic. The filter will be designed with all inductors equal to precisely 24 mH.
The Specifications tab is given here. The extraction sequence ∞ DC ∞ ∞ ∞ ∞ with a series element first is chosen because it results in a series L-C at the input. The source resistance is tuned until the first series inductor is 24 mH. The required resistance is 101.5 Ω. The load resistance is set equal to 101.5 Ω.
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The initial schematic is given here. The number of digits to the right of the decimal in element values has been set to 8 to view the precise values associated with high-Q quartz-crystal resonators.
Next two Norton Shunt transforms are applied to the shunt coupling capacitors to convert the remaining two series inductors into series L-C resonators to conform to the motional element branch of the equivalent circuit model for quartz-crystals. C2 is selected, Apply Norton Shunt is selected and "Choose the transformer ratio (N)" is selected. We desire L2=L1 so a transformer ratio equal to the square root of L2/L1 = 7.587542e-5 is entered.
The schematic after applying the same transform to the second shunt capacitor is given here. The filter is symmetric, after the transforms the input and output resistances are equal, and S/FILTER automatically removed the transformer. If a transformer remains with a ratio near but not exactly 1:1 the transformer may be manually deleted.
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Next, the design is standardized by changing the terminating resistance at ports 1 and 2 from 101.5 to 100 Ω, setting the shunt coupling capacitors to 180 pF, adding 31 Ω series resistors and adding the crystal 3.6 pF static capacitors. The inductors are set one at a time to precisely 24 mH and tuning its series capacitor to correct the response. Finally, the series capacitors are optimized to clean up the tuning. The final response and schematic are given here.
All Parallel Resonators Example Files:
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1. Filters\SFILTER\Parallel Resonators.WSP
2. Filters\SFILTER\Parallel Resonators.SF$
This example illustrates how to design bandpass filters with all parallel resonators. The Specifications tab of S/FILTER shows the filter specifications.
The Extraction tab indicates there are 4 unique extraction sequences. Notice that Series Element First option is not selected so that the first element will be shunt. The table has been customized to show only the extraction sequence and the transformer ratio. Sequence 3 is selected since the transformer ratio is essentially 1 providing equal input and output termination resistance without requiring a transformer.
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The initial schematic for extraction sequence 3 is given here. To create a topology with all parallel resonators the circuit is transformed to place capacitors in parallel with the shunt input and output inductors.
First, C1 is selected and a Norton Series transform is applied. We require a positive capacitor on the left and the resulting negative capacitor on the right will be absorbed by C2. The option is selected "Choose the transformer ratio (N)". To maximize realizability N=SQR(L2/L1) or 0.2003249 is entered. This shifts the impedance of the filter to the right of C1 up an amount which causes L2=L1. The Simplify Circuit transform next combines the two transformers into one transformer at the output.
Next we will apply a Norton Series to the remaining series capacitor to place a capacitor in parallel with the shunt output inductor. This time we want the positive capacitor on the right. Since L3>L1 we choose N=SQR(L3/L1) or 4.991998. Finally, because the transformer ratio is near unity it is absorbed into the load. The History tab with a list of the transforms and the resulting schematic are given here.
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Response Symmetry Example Files:
1. Filters\SFILTER\Response Symmetry.WSP
2. Filters\SFILTER\Response Symmetry.SF$
A symmetrical transmission amplitude response is often desired, particularly for IF filters. Conventional exact transform bandpass filters have a symmetrical response when plotted on a logarithmic frequency scale (geometric symmetry). It is arithmetic symmetry (plots on a linear frequency scale) that is desired in IF filters. Arithmetic symmetry also results in symmetry in the group delay (equal peak group-delay values near the lower and upper cutoffs). None of the popular lowpass to bandpass transforms possess arithmetic symmetry. In 1989 Eagleware developed a lowpass to bandpass transform that results in arithmetic symmetry. You may refer to pages 165 to 167 of HF Filter Design and Computer Simulation for more information on this transform. However, this transform is approximate and is available for all-pole (no finite transmission zeros) filters only.
The direct synthesis routines in S/FILTER offer a more elegant solution to this problem. This example illustrates how to exactly design bandpass filters with arithmetic symmetry. Carassa [Band-Pass Filters Having Quasi-Symmetrical Attenuation and Group-Delay Characteristics, Alta Frequenza, July 1961, p. 488] proved that if the number of transmission zeros at infinity is 3 times the number at DC, the response possesses arithmetic symmetry. This can be maintained even with the addition of transmission zeros at finite frequencies.
The Specifications tab for a 70 MHz IF filter with 30 MHz bandwidth is given here. Notice that the quantity of zeros at infinity are 3 times the quantity at DC. The finite zeros were tuned to 38.7 and 103.2 to achieve a minimum attenuation in the stop band of 42 dB.
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The extraction sequence ∞ 103.2 38.7 ∞ ∞ DC without any transforms results in the schematic here. This sequence resulted in the lowest inductor count (4) and a low ratio of inductors (6.48888) but a transformer ratio of 0.39288.
To remove the transformer the following transforms were applied.
1. C4 was swapped with L3/C5
2. L4 was swapped with C6
3. A Norton Series was applied to C6 using the option "Calculate N to remove existing transformer"
4. Simplify Circuit was clicked
The final schematic is given here.
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Notice that the transformer is removed and the inductor ratio was reduced to 2.56 (L2/L1). The response for this remarkable filter is given here. Notice the excellent transmission and amplitude and group-delay symmetry.
Equal Inductor Example Files:
1. Filters\SFILTER\Equal Inductors.WSP
2. Filters\SFILTER\Equal Inductors.SF$
Modern chip capacitors are small, inexpensive and have high Q. Inductors are more expensive, larger, more susceptible to parasitics and have lower Q. Because filter realizability is largely a function of the ratio of component values, many consider the
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ultimate realizability is filters with all equal inductors. This example illustrates how to design these filters. All transforms are selected to add capacitors and keep the number of inductors at a minimum.
We will start with the IF filter created in the previous example and add Norton transforms until all inductors equal the first inductor.
The following transforms are required:
1. A Norton Shunt is applied to C1 with N = SQR(L2/L1) = 1.60109 followed by Simplify
2. A Norton Series is applied to C4 with N = SQR(L3/L1) = 0.85837 followed by Simplify
3. A Norton Shunt is applied to C9 with N = SQR(L4/L1) = 0.728207 followed by Simplify
At this point the output transformer turns ratio is near unity and the transformer is removed by applying the Absorb TRF Into Load transform.
The final schematic is shown below.
Physical Symmetry Example Files:
1. Filters\SFILTER\Physical Symmetry.WSP
2. Filters\SFILTER\Physical Symmetry.SF$
Symmetry is an element of beauty. It is both appealing and practical. In a previous example we illustrated how to create filters with response symmetry. In this example we illustrate how to create filters with element value symmetry (physical symmetry). Physical symmetry reduces the number of unique element values which must be modeled, designed, purchased, stocked and picked for assembly, thus saving both design and manufacturing effort. The GENESYS electromagnetic simulator EMPOWER automatically detects physical symmetry. When symmetric filters are realized as distributed structures they execute as much as 16X faster and require 16X less memory in EMPOWER. EM simulation of large filters might not be feasible without symmetry.
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Symmetry results naturally, without additional user effort, in filter types that are:
1. All Butterworth
2. Odd-order Chebyshev
3. All Chebyshev coupled-resonator bandpass in FILTER
4. Lowpass filters with finite transmission zero pairings and an odd quantity of zeros at infinity
5. Bandpass filters with finite transmission zero pairings above or below (not both) the passband and odd plus equal quantities of zeros at DC and infinity
Symmetry may be forced:
6. By optimizing the response while forcing symmetry
The design of types 1 through 3 is straightforward using FILTER. These are restricted to all-pole filters. Types 4 and 5 with finite transmission zeros require the direct synthesis techniques of S/FILTER. Types 4 through 6 benefit from additional explanation and are the subject of this section.
Consider the Specification tab of a type 4 2300 MHz lowpass filter shown below. The placement of zeros conforms to the rules of type 4: the number of zeros at infinity is odd (1) and finite zeros are paired at 3800 MHz.
The schematic for the lowpass and the transmission and reflection responses are given here. Notice symmetry of the component values mirrored about the center 4.89 nH inductor.
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Next consider case 6 where symmetry are other objectives are forced during optimization. Consider a 10.7 MHz IF bandpass filter with 400 kHz bandwidth. The following Specification tab defines the design.
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The extraction sequence ∞ DC DC DC ∞ ∞ ∞ ∞ ∞ ∞ DC DC results in the schematic given here.
Using techniques described in the All Series example, 5 Norton transforms are next applied to the shunt-coupling elements to create the series resonator filter given here. A transformer ratio equal to the square root of adjacent capacitors is used is applied to shunt inductors and a ratio equal to the square root of adjacent inductors is applied to shunt capacitors. It is tempting to select the transform option that allows choosing the new inductor right of L2 to equal the original L1, but the transform also modifies L1.
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This filter is approximately symmetrical but forcing values to be physically symmetric disturbs the response. The transformer is deleted and a set of optimization goals equal to the original response is added. Next physical symmetry is forced in the Equations folder by setting element values on the right and left side of the filter equal to each other and by setting all inductors values equal. Optimization is launched to adjust the values marked with "?" to correct the disturbance introduced when the values where changed. The schematic and equation variables are given below.
Also the unloaded Q of all inductors are set at 160. The response after optimization illustrates the insertion loss introduced by finite inductor Q.
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Termination Coupling Example Files:
1. Filters\SFILTER\Termination Coupling.WSP
2. Filters\SFILTER\Termination Coupling.SF$
Consider the final schematic in the earlier All Parallel Resonators example 800 to 1000 MHz bandpass filter. The shunt inductors are 1.93 nH. These are practical values if the parallel resonators are to be converted to transmission line resonators but for an L-C filter 1.93 nH is small. This example illustrates how to use the flexibility of the GENESYS environment to make any desired change to a schematic. We will use series capacitors as approximate impedance transformers at the input and output of the filter to increase the design impedance thus increasing the shunt inductors.
First the filter is designed with termination resistance higher so that the shunt inductors are 10 nH. This requires a termination resistance of 50*(10/1.93)=259.067 Ω. Next the same procedures illustrated in the All Parallel example are used to create a filter with all parallel resonators and series coupling capacitors.
Next, series capacitors are manually added to the schematic at the input and output. These series capacitors step the final termination resistance, Rs=50 Ω, up to the design impedance of the filter, Rp=259.067 Ω. The capacitor value required is given by
where fo is the geometric center frequency equal to SQR(Lower Cutoff * Upper Cutoff). In this case Cs=1.736 pF resulting in a residual capacitance, Cp, that is effectively in parallel with the adjacent resonator.
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This capacitance in this case is 1.403 pF. This capacitance is subtracted from the initial parallel capacitance of the first and last resonators. The schematic after these manual modifications is given here.
This impedance transformation is exact only at fo but for narrow bandwidth filters this process works well. The bandwidth of this filter is 200/SQR(Fl*Fu)=0.224=22.4% which begins to stress the accuracy of the transform. The response of the filter is given as the dashed responses in the plot given here.
Optimization is then applied to correct the response as given by the solid traces.
Parametric Bandpass Example Files:
1. Filters\SFILTER\Parametric Bandpass.WSP
2. Filters\SFILTER\Parametric Bandpass.SF$
In the All Parallel Resonators example we illustrated how to create all-pole filters with all parallel resonators. This is useful when L-C filters will be converted to structures using
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transmission line or ceramic resonators. In this example a similar process is illustrated for filters with transmission zeros at finite frequencies.
A 850 to 950 MHz bandpass with singular zeros at DC, infinity, 751 MHz and 1068 MHz is specified. A passband ripple of 0.177 dB is chosen. Again we start with extractions with a shunt element first. The extraction sequence 751 MHz, DC, 1068 MHz and ∞ was chosen. Next a Norton Series transform was applied to C1 and L2 with a turns ratio of 0.36 followed by a Simply circuit transform. Next a Norton Series was applied to C4 and L4 with the ratio automatically selected to remove the transformer. After simplification the schematic is:
The first transform ratio of 0.36 was found empirically to give somewhat equal inductors. The inductor values are somewhat small for an L-C filter, particularly if high Q is desired in the inductors. If this filter is to be constructed with L-C elements the approximate impedance transformation illustrated in the Termination Coupling example could be employed. In this case we plan to realize the parallel resonators using ceramic resonators. Therefore we desire equal shunt inductors in these resonators. This filter is found using optimization. The shunt inductors are set at 1.0 nH and the remaining element values are optimized to achieve the original response. The final element values are given in the following schematic.
The ratio of maximum to minimum inductor value is 2.49. The ratio for a conventional cookbook realization of this filter is over 7. The parametric bandpass has all parallel resonators as well as an improved inductor ratio. These advantages come at the expense of an additional inductor and capacitor. The response after optimization is given here.
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Next, the conversion of the L-C resonators in this parametric bandpass to ceramic resonators is illustrated. Using the parallel L-C to quarter-wave transmission line equivalent formula given earlier, the three quarter-wave line resonators from left to right have the following parameters
Zo=4.624 Ω Fo=937.033 MHz
Zo=4.432 Ω Fo=898.149 MHz
Zo=4.266 Ω Fo=864.424 MHz
The low line impedance is consistent with the high dielectric constant of ceramic resonators. For other characteristic impedance the original L-C filter is designed with the appropriate shunt inductance. After replacing the L-C resonators with quarter-wave line resonators the responses are given below as dashed traces.
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Recall the L-C/transmission line equivalences are accurate at the resonant frequency only. Notice the passband return loss and transmission are close to the original L-C filter. However, further from the passband the rejection is less than the original filter in lower stopband and greater than the original filter in the upper stopband.
The solid traces are optimization of element values in an attempt to achieve the original stopband rejection. The stopband frequencies were shifted lower to accommodate the effect of the line resonators. Also, for practical reasons, before optimization the characteristic impedance of all three resonators were set equal at 4.6 Ω. The final schematic after optimization is given here.
LP All Pole Files:
1. Filters\SFILTER\LP All Pole.wsp
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2. Filters\SFILTER\LP All Pole.SF$
This is a very straightforward design in S/FILTER using 3 zeroes at infinity and two unit elements. The element values are quite practical, and the response is shown below.
LP All Pole Files:
1. Filters\SFILTER\LP Elliptic.wsp
2. Filters\SFILTER\LP Elliptic.SF$
This example illustrates using S/FILTER to create an exact distributed elliptic lowpass filter.
The transmission zero specifications are:
• # Infinity = 1
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• # Finite = 1,2,3...N
• # UE= 2 x # Finite
The extraction sequence is then UE,FZ,UE,UE,FZ,UE,UE,FZ.......UE,UE,FZ,Infinity,UE. This example uses # Finite = 2 and # UE = 4 and the sequence UE,FZ,UE,UE,FZ,Inf,UE.
Next "Kuroda Wire Line Transfers:Full:Series Shorted (Right or Left)" are applied to each series transmission line and wire line to create transmission lines and stubs. Finally, "TLines:Stepped Resonators:Convert to Two Step Resonator" are applied to the shorted and open wire lines to ground.
Transmission line impedances are typically practical for this structure.
To make this structure more physically realizable, the 24 ohm transmission line was split into two 48 ohm lines. S/FILTER was then closed, and one of the 48 ohm lines was moved up above the other 48 ohm line. Advanced T/LINE was then used to convert the structure to microstrip, yielding this schematic:
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Coaxial Resonator Example Files:
1. Filters\SFILTER\top-c resonator.wsp
2. Filters\SFILTER\top-c resonator.SF$
This example extends the concepts presented in the "All Parallel Resonators Example". Using different specifications, it extends the design process to the use of square coaxial resonators. The example shows the power of the transforms from lumped to distributed elements and the use of "Advanced TLINE" to change electrical line models into physical models.
A fourth order bandpass filter with a bandwidth of 40 MHz centered about 1.0 Ghz was designed with the S/FILTER synthesis program. The initial design in terms of lumped elements (L,C) resulted is shown below (see the SF$ file).
The next step was to split the shunt capacitor into a 15 pf element to combine with the 1.24 nH inductor. Use the "Lumped to distributed equivalent" transform with the "parallel LC to ground to grounded stub". This generates an approximately equivalent transmission line. This electrical transmission line will be converted to a physical model using Advanced TLINE.
For this example, ceramic coaxial resonators will be used. A common configuration is a square shape with circular inner conductor. Specific parameters used were: dielectric constant = 90.5, inner diameter = 1 - 2 mm, and outer side = 4.0 mm. The length will be set by the resonant frequency of the LC network. To convert to a physical line type, select "Convert Using Advanced TLINE" from "Schematic" on the toolbar. Then under "Process" select "Square Coax (Round Conductor)" and "outside" equal to 4 mm. The inner conductor diameter and length are computed automatically. The inner diameter can be set to one of the commercially available sizes. The overall response will be relatively insensitive to this value.
Since the transforms from lumped to distributed elements and from electrical to physical lines involves some approximations, a final optimization is desirable. The capacitors were gang-tuned to preserve symmetry. The optimization goals were:
S21 < -48 db for f < 920 MHz, S21 < -45 db for f > 1080 MHz, S11 < -18 db for ( 980 MHz < f < 1020 MHz )
The resulting responses and component values after optimization are shown in the figures below (see the wsp file). Clearly the requirements were met with reasonable component values. As a final step, the capacitor values were "tuned" to standard values. From the
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tuning window, "standard" was selected and the "value" set at 1%. The values of each of the ganged sets were adjusted manually while observing the frequency response with respect to the optimization goals.
BP Edge Coupled Files:
1. Filters\SFILTER\BP Edge Coupled.wsp
2. Filters\SFILTER\BP Edge Coupled.SF$
This example illustrates using S/FILTER to create an exact distributed edge-coupled bandpass filter.
Note: Although this is a bandpass, the Highpass type option is selected in the Specification tab because this design procedure utilizes the reentrant mode of transmission lines.
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The transmission zero specifications are:
• # Infinity = 0
• # Finite = 0
• # DC = 1
• # UE= 2,4,6...2xN
The extraction sequence is then UE,UE...DC...UE,UE with a series element first.
This example uses # DC = 1 and # UE = 4 and the sequence UE,UE,DC,UE,UE.
Next the following transforms are applied:
1. Basic Operations:Split Series Element is applied to the open wire line at the center
2. Kuroda Wire Line Transfer:Equal:Series Open Right is applied to the UE left of center and each UE to the left.
3. Kuroda Wire Line Transfer:Equal:Series Open Left is applied to the UE right of center and each UE to the right.
4. Simplify Schematic
5. Basic Operations:Split Series Element is applied to each internal open wireline. Do not apply this transform to the end two open wire lines.
6. Coupled Lines:Interdigital Lines:Open,Open is applied to all UE.
7. Simplify Schematic
Transmission line impedances are practical only for Maximally Flat responses or low ripple Chebyshev filters of bandwidth from 20 to 40 %. For a technique to improve realizability of this filter for other parameters please refer to BP Edge Redundant.SF$.
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BP Edge Redundant Files:
1. Filters\SFILTER\BP Edge Redundant.wsp
2. Filters\SFILTER\BP Edge Redundant.SF$
This example illustrates using S/FILTER to create an exact distributed edge-coupled bandpass filter for narrower bandwidth. Realizability is improved by adding redundant transmission lines at the input and output. These lines have a characteristic impedance of 50 ohms so they have no effect on the response. Because transforms are later applied to these redundant elements they must be equal in length to the other lines in the filter. The design process is similar to the BP Edge Coupled topology without redundant lines.
Note: Although this is a bandpass, the Highpass type option is selected in the Specification tab because this design procedure utilizes the reentrant mode of transmission lines.
The transmission zero specifications are:
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• # Infinity = 0
• # Finite = 0
• # DC = 1
• # UE= 2,4,6...2xN
The extraction sequence is then UE,UE...DC...UE,UE with a series element first.
This example has a Cutoff of 950 MHz, an equiripple of 0.07 dB and a 1/4 Wave Freq of the transmission lines of 1000 MHz. It uses uses # DC = 1 and # UE = 4 and the sequence UE,UE,DC,UE,UE.
Next the following transforms are applied:
1. Basic Operations:Insert Element with transmission lines = 50 ohms and length 75mm are applied to the input and output.
2. Basic Operations:Split Series Element is applied to the open wire line at the center
3. Kuroda Wire Line Transfer:Equal:Series Open Right is applied to the UE left of center and each UE to the left including the redundant input line.
4. Kuroda Wire Line Transfer:Equal:Series Open Left is applied to the UE right of center and each UE to the right including the redundant output line.
5. Simplify Schematic
6. Basic Operations:Split Series Element is applied to each internal open wireline. Do not apply this transform to the end two open wire lines.
7. Coupled Lines:Interdigital Lines:Open,Open is applied to all UE.
8. Simplify Schematic
Transmission line impedances are practical for bandwidths narrower than the edge coupled filter without redundant lines. Bandwidths from 20% to a few percent are practical. The practical limit is due to insertion loss in the final filter due to PWB losses. Below 10% bandwidth evanescent modes may propagate, circuit theory models become inaccurate and electromagnetic simulation using EMPOWER is suggested.
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BP Stub with Inverters Files:
1. Filters\SFILTER\BP Stub with Inverters.wsp
2. Filters\SFILTER\BP Stub with Inverters.SF$
This example illustrates using S/FILTER to create distributed bandpass filter with resonating shorted stubs connected by approximate inverters.
Note: Although this is a bandpass, the Highpass type option is selected in the Specification tab because this design procedure utilizes the reentrant mode of transmission lines.
The transmission zero specifications are:
• # Infinity = 0
• # Finite = 0
• # DC = N
• # UE= 0
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This example has a Cutoff of 750 MHz (the mirror upper cutoff is then 1250 MHz), an equiripple of 0.07 dB and a 1/4 Wave Freq of the transmission lines of 1000 MHz. It uses uses # DC = 5.
Next the following transforms are applied:
1. Inverters:Replace Element with Inverter is applied to each open wire line
2. Replace Inverter with: Stub to Ground + Series TLine + Stub to Ground is applied to all ideal inverters
3. Simplify Schematic
Realizability is acceptible for 30 to 70% bandwidth with the stubs becoming too low in impedance for narrower bandwidth.
A/FILTER AFILTER\Lowpass Minimum Inductor.wsp A third order lowpass minimum inductor Chebyshev filter with 0.1 dB ripple and a 10 kHz cutoff is designed and simulated with mA741 op-amps. Measured results are included. The A/FILTER design schematic is shown in figure below.
This filter is designed using LC/GIC transforms. For more information on LC/GIC transforms, see Appendix E. In this particular filter, the transform yields a circuit that
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does not have a DC path to ground. This results in possible railing of bias voltages. To compensate, A/FILTER automatically includes a 100k resistor to ground at the output. This will work fine, as long as 100k is large compared to the impedance of the output capacitor within the filter passband. If it is not, the parallel combination of the shunt resistor and capacitor may cause a mismatch at the load. Therefore, if small valued capacitors must be used, the output resistor may need to be increased to restore the filter response.
There is an inherent loss of 6dB in this filter type. If your application requires no loss or requires gain, this can be achieved by the use of an output buffer. Output buffering is setup from the Setup menu, Preferences Window. Once enabled, the main A/FILTER window will have an input cell for gain to control the gain of the output buffer.
Tuning the grounded resistor in each “D element” (R3 and R7 in the schematic above) directly affects the cutoff frequency. The “D elements” are independent enough that usually only one resistor needs to be adjusted unless a wide tuning range is needed.
This type is very sensitive to op-amp bandwidth. With a 1 MHz bandwidth amplifier, a 10 kHz filter may start to experience rolloff prematurely. This can usually be fixed by optimization within SuperStar.
A/FILTER automatically writes an optimization block into the circuit or schematic file. Several components within each filter type are marked for tuning and/or optimization. These parts can be used to tune the filter response back if other components are set to standard values, or vary slightly due to tolerances. (This will be illustrated in "Lowpass Multiple Feedback" example)
The following figure shows the predicted and measured responses. The circles show the response when using 347 op-amps (3 MHz bandwidth), while the triangles show the response when using mA741 op-amps (1 MHz bandwidth).
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A final note on this filter type is that, even though it is a lowpass type, it will not actually pass DC due to the series capacitor at the input. If your application needs to pass DC, then a large resistor can be added in parallel to the input capacitor. The proper resistor value must be determined experimentally in SuperStar, but is generally in the neighborhood of a 100k. If the value is too large, it will have no effect; if it is too small, the filter will have gain at DC.
AFILTER\Lowpass Minimum Capacitor.wsp A fifth order lowpass minimum capacitor Chebyshev filter with 0.1dB ripple, 0.1dB Aa, and a 5 kHz cutoff frequency is designed and tested with mA741 op-amps. The A/FILTER design screen is shown in the figure below.
Resistors R4 and R8 can be used to completely tune the response to a different cutoff frequency. This filter is very insensitive to component tolerances, but fairly sensitive to op-amp bandwidth.
This type of filter has an inherent loss of 6dB within the passband. The circuit shown was initially constructed with 5% parts, and the response was 6.5dB down in the passband. All resistors and capacitors were replaced with 1% parts, and the new attenuation was 5.9dB.
The following figure shows the predicted and measured responses.
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AFILTER\Lowpass Single Feedback.wsp An eighth order single feedback lowpass Chebyshev filter with 0.1dB ripple, 0.1dB Aa and 10 kHz cutoff with 0dB gain is designed, simulated, and measured. The A/FILTER schematic is shown below.
This filter was designed with non-ideal op-amp parameters. In SCHEMAX, all non-tuned parts were placed on available values, and SuperStar then optimized the response to compensate. The figure below shows a plot of the predicted response of this filter. The solid trace shows the optimized response using LF347 op-amp parameters. The dotted trace shows the same circuit response, except that near-ideal op-amp parameters were added. The “ideal” response starts to roll-off prematurely, while the “non-ideal” response behaves as expected. This illustrates the necessity to correct for non-ideal elements.
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All non-tuned components were set to standard values and the filter was optimized in SuperStar to correct for the non-ideal components and for the standard values.
This filter was tuned in stages. After optimizing the overall response, the output node was moved from the output of the filter to points between each stage to allow SuperStar to show the calculated response for that stage. When the filter was constructed, each stage was tuned by referring to these cumulative responses.
The following figure shows the filter schematic modified to give the first stage response. The output of each successive stage was probed in the same way to obtain the individual responses. Note that when the second and third stages were probed that the responses are actually the cumulative response from all previous stages. The output of the fourth stage is, of course, the complete output of the filter.
The input level should be kept low, since the first section provides almost 20dB of gain near the cutoff. If the input level gets too large, the second and third sections can saturate, destroying the response. If the filter must handle larger signal levels, then the “Reverse
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order of poles" option in the Setup Menu, Preferences window should be toggled. In this example, the Reverse order option was set.
AFILTER\Lowpass Multiple Feedback.wsp A fifth order lowpass multiple feedback Chebyshev filter with a 10kHz cutoff, 0.1dB ripple and 0.1 Aa is designed and simulated with mA741 op-amp parameters. The following figure shows the A/FILTER design screen. This filter should be tuned as in the "Lowpass Single Feedback" example by placing the output between sections and tuning them separately.
In this example, all the capacitors were set to standard values, and the response was tuned using the resistors.
Element Tuning Effects:
R1 - adjusts gain with minimal perturbation of the response R4 & R5 - flattens gain, but cannot fix cutoff frequency R3 - adjusts gain of filter but distorts response R6 - redundant adjustment of R4 & R5. Only adjust if cap values are changed drastically.
R2, R4, R5 and R6 were optimized since the capacitors were changed drastically. Once optimized, only R2, R4 and R5 were adjusted on the bench.
The figure below shows the final schematic with standard value caps and optimized resistor values.
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Bandpass Maximum Gain Dual Amplifier A fourth order bandpass dual amplifier Chebyshev filter with 0.1dB ripple and 0.1 Aa is designed, simulated, and measured with mA741op-amps. The following figure shows the A/FILTER schematic.
This filter should be tuned by probing between sections and tuning the sections individually. The filter response can be completely tuned by adjusting the series resistors between sections.
The predicted and actual (measured) responses for this example are shown below.
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FILTER FILTER\Gaussian_12dB.wsp A Gaussian filter shape is designed using the stored G values. To use this option of FILTER, go to the "G Values" tab of the Filter Properties box. Select the 'Load' button, then G12.PRO from the Proto directory. Notice the set of G values for various filter orders which fill the table of the dialog box.
For this example, the following requirements were selected:
Topology Tab: Type: Lowpass, Subtype: Minimum capacitor Settings: Input Resistance = 50 ohm, Cutoff Frequency = 100 MHz, Order = 7
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The resulting schematic is generated, with parameter values which meet the requirements.
A plot of S21 and S11 are automatically produced. Notice that at the 100 MHz, the gain S21 is -3.0104 db.
M/FILTER MFILTER\Chebyshev Bandpass.wsp Purpose: Demonstrate the use of the M/FILTER synthesis tool to generate a filter with distributed implementation.
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Process: M/FILTER can be used to synthesize thirteen topologies and supports variations on several of the structures. The overall design process can be divided into the following three steps:
1. Select 'Synthesis' from workspace tree. Enter 'Settings' listed above. Note plotted response and layout.
2. Select 'optimize' from 'MFilter Properties' box.
3. Perform EMPOWER simulation for optimized layout design.
The synthesis process is controlled from the 'MFilter Properties' dialog box shown below. For this example, a seventh order Chebyshev filter is to be designed and implemented in microstrip as 'hairpin' structures.
The following data was entered in this dialog box.
'MFilter Properties' dialog box Topology: Type = Bandpass, Shape = Chebyshev, Subtype = Hairpin Settings: Input Resistance = 50, Passband Ripple = 0.05 dB, Attenuation at Cutoff = 3 dB, Order = 7 Low Freq Cutoff = 2000 MHz, High Freq Cutoff = 2500 MHz, Desired resonator Z = 60 Slide factor = 0, Tapped (checked), Length of i/o lines = 20 deg. Options: Create a layout (checked), Manufacturing process (microstrip)
The resulting frequency response plots were generated automatically.
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The M/FILTER tool also produces a schematic of linear models and a corresponding layout, as shown below.
The layout can be used to generate DXF or Gerber type files and can also be used for electromagnetic (EMPOWER) analysis.
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The second step is to optimize the design. M/FILTER automatically sets up optimization criteria based on the frequency response requirements. These criteria can be adjusted as desired. The physical parameters for the hairpin parameters can be found in the Equation block. Optimization is initiated clicking on the 'Optimize' button on the 'MFilter Properties' box. The resulting response which follows demonstrates that the design meets the requirements.
Finally, the optimized design can be analyzed using EMPOWER to confirm the response and detect box modes. This EM simulation can be performed within the same workspace.
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Chapter 6 Oscillators
Oscillators\Bipolar Cavity Oscillator.WSP Illustrates: How to complete nonlinear oscillator analysis in GENESYS using HARBEC. The oscillator simulated is a cavity oscillator taken from "Oscillator Design and Computer Simulation" by Randy Rhea, Noble Publishing, pages 225-231. A different device is used which results in slightly different component values.
The first step in the analysis is to examine the open loop Bode response. The schematic "NL Open Loop" is constructed. Port 1 is the input port and port 2 the output port. In final configuration, port 1 will connect with port 2. The device was built with a nonlinear device model, allowing the DC bias points to be verified and displayed on the schematic.
The frequency is swept over a narrow range as this is a particularly high Q oscillator. L1 was adjusted so that the gain peaked at the same frequency that the phase crosses zero degrees. This frequency, approximately 1100 MHz, should be near the frequency of
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oscillation.
Next, the loop was closed, as shown in the schematic "NL Closed Loop." In addition, a source was attached to the loop, passing through a high-Q LC tank. The purpose of this source is to stimulate the circuit to incite oscillation; the purpose of the tank is to allow the
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signal to be fed at the fundamental but to otherwise isolate the source from loading the circuit.
Then the frequency and amplitude of the source are adjusted until no current is being supplied through the LC tank. At that frequency and amplitude. In that state, the source will not be affecting the circuit, indicating that the state of oscillation has been found.
To get the best starting point, a guess is made for the amplitude and the frequency of the source. The frequency is taken from the open loop analysis; the amplitude is set to 1 Volt as the voltage tap is base of the transistor. Then the a harmonic balance sweep is completed for both frequency and amplitude. The current supplied by the source is plotted for both sweeps ("Freq Sweep" and "Level Sweep"), showing a minimum current at about 1102 MHz and 1.02 Volts.
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With this starting point, the optimizer can be used to find the exact amplitude and frequency. Right click on "Opt1" and select "Optimize" to start the process. Open "Error Current" to watch the error current reduce as the frequency and voltage are adjusted.
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This same process can be used with any oscillator. It provides a very good estimate of the output amplitude frequency that can be combined with the phase noise calculated by using Lesson's Rule with loaded Q calculated from open loop analysis. (See CoaxialOSC.WSP for an example.)
Oscillators\NegR VCO.WSP Illustrates: Post processing, negative resistance
This is a UHF negative resistance oscillator designed by the synthesis program OSCILLATOR. It tunes from 750 to 950 MHz. The graph on the left is the resistance and reactance looking through the transmission line/varactor resonator. If the resistance is negative, when the left side of the resonator is grounded, the circuit will oscillate at the frequency where the net reactance is zero.
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The graph on the upper right plots 1/S11 on a Smith chart. Post processing was used as shown on the lower-right above to calculate 1/S11. The first line, "USING Linear1.NegR" sets the default Simulation/Data for the equation. The next line gets the reciprocal of S11 in complex (rectangular) form. Two important things to notice about this equation:
• The period (.) before RECT is absolutely necessary. All post-processed measurements must have a period, and even though there is a USING statement, there must still be a period in front of the operator. If there was no USING statement, the line "InverseS11 = 1/Linear1.NegR.Rect[S11]" would have been used.
• The operator RECT is required.
The solid traces are for a tuning varactor capacitance of 1.65 pF (oscillation at 950 MHz) and the dashed traces are with a capacitance of 4.5 pF (oscillation at 750 MHz).
Please refer to Oscillator Design and Computer Simulation for additional information on oscillator design.
Oscillators\Coaxial OSC.WSP Illustrates: Post-Processing, Loaded-Q, Phase Noise.
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The circuit above is a coaxial resonator oscillator, designed to be tunable between 800 and 900 MHz. The desired oscillation frequency for this example is 850 MHz. In this example, we will use post-processing to calculate the phase noise of the oscillator. The equations we will use for this are:
Cv=?7.343 Fo=850E6 PdBm=?7 kT=4E-21 NFdB=?6 F=10^(NFdB/10) Flicker=?10000 Ps=1E-3*10^(PdBm/10) 'The function of the next line is not obvious: It gets the frequencies of the baseband simulation. ssbfreq=1e6*freq+0*baseband.loop.db[s11] 'Get the loaded q of the loop at the oscillation frequency. Q=GETVALUEAT(linear1.loop.QL[S21],Fo) 'Calculate Leeson's equation to determine the noise. ssb=10*log(0.5*(Flicker/ssbfreq+1)*((Fo/ssbfreq/2/Q)^2+1)*(kT*F/Ps))
There are a few lines which are of special interest:
• ssbfreq=1e6*freq+0*baseband.loop.db[s11]: This line is a trick used to create a new sweep for post-processing. The linear simulation "Baseband" was created solely to provide a sweep for post-processing. This line gets S11 from the Baseband sweep, then promptly multiplies it by zero. This clears the values, but it will retain the independent frequency data. Next, by adding it to FREQ, this
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creates a "unity" sweep, where each point in the sweep contains the frequency in Hz (orignally in MHz, then multiplied by 1e6).
• Q=GETVALUEAT(linear1.loop.QL[S21],Fo): The GetValueAt function takes a measurement as the first parameter and the frequency as the second parameter. This statement gets the value of linear1.loop.QL[S21] at frequency Fo (850 MHz).
• ssb=10*log(0.5*(Flicker/ssbfreq+1)*((Fo/ssbfreq/2/Q)^2+1)*(kT*F/Ps)): Calculates Leeson's equation. Notice that since ssbfreq contains swept data, the result of this calculation is swept data. The results of this equation are shown in the graph below:
This example shows the power of post-processing in GENESYS. Additional things that could be done include:
• Optimization of SSB and circuit simulation simultaneously.
• A function could be written to determine the actual oscillation frequency when the capacitor is tuned. Fo would be set to this value, and then the phase noise calculations would be at this frequency.
• The entire phase-noise calculation could be put into a function, stored into the model directory, then used for any circuit.
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Chapter 7 Matching
Matching\Synthesis Comparison.wsp This example includes a few circuits to illustrate the use of MATCH and some basic matching concepts. The example deals with matching a 50 ohm source to a 200 ohm load from 100 to 200 MHz using a single network. Bandwidth and network complexity are considered.
In the first attempt, a Tee network is tried. To do this, we right-clicked on Synthesis in the workspace tree and added Match. You can double-click the Tee icon to see this setup. The circuit file and response are given below. The exact component values will depend on how long MATCH has optimized. Because minimum Q was specified in MATCH and the terminations are resistive, the tee network contains two components. (A third element was created but was an insignificantly small inductor which was deleted.) The response is typical of a narrowband matching network. In this example, the 15 dB return loss bandwidth is approximately 127 to 162 MHz, or 24%.
Our second attempt is a second order L-C pseudo lowpass network. Because the pseudo lowpass is synthesized as a bandpass transfer function, the second order network has four components, two inductors and two capacitors. You can double-click the LCPseudoLowpass icon to see this setup.
The results are as given. Notice the return loss is now 15 dB or better across nearly the entire 100 to 200 MHz range. The increased performance results from a four component
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network, as opposed to the previous two components, and from an efficient synthesis algorithm.
Our third attempt is a stepped impedance transmission line is used for the matching network. The 3rd order stepped Zo network has three cascaded transmission lines. The results are given below. Notice the change in the return loss scale to 5 dB per division.
Although there are three elements as opposed to four in the L-C pseudo lowpass, the match is better than 30 dB across the entire band. Each transmission line segment in the stepped Zo matching network is approximately as effective as two lumped elements. However, keep in mind transmission lines are larger than lumped elements.
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Matching\Ill Behaved Load.WSP
In this example, we attempt to match a 50 ohm source to an antenna represented by an R-X data file, ANTENNA.RX. The antenna load is highly frequency dependent. The resistance is approximately 33 ohms and increases slowly with frequency. The antenna resonates between 14 and 14.05 MHz, and the reactance increases rapidly with frequency. This data is typical for narrow band antennas. The frequencies, resistances and reactances in this data file are:
Frequency (MHz) Resistance (ohms) Reactance (ohms)
14.00 31.6 -6.6
14.05 32.0 4.7
14.10 32.4 16.0
14.15 32.7 27.2
14.20 33.1 38.4
14.25 33.5 49.5
14.30 33.9 60.7
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14.35 34.3 71.7 Matching resistive terminations is fundamentally easier than matching between terminations where either or both have a reactive component. Theoretically it is possible to match purely resistive terminations over an arbitrarily wide bandwidth, although it may take a very large number of components and be impractical. When either or both terminations are reactive, there are fundamental relationships between the nature of the terminations, the required bandwidth and the required quality of match.
The matching networks were designed using MATCH. You can view the setups by double-clicking on the Tee and LC Bandpass icons under the synthesis folder.
First we attempted to match the antenna with a Tee network, but the worse case S11 at the band edges was -6dB. We then used a 4th order LC Bandpass network, resulting in the network shown above and the response shown below. The ill-behaved nature of this load is well handled by MATCH even though the element values are certainly difficult.
Matching resistive terminations is fundamentally easier than matching between terminations where either or both have a reactive component. Theoretically it is possible to match purely resistive terminations over an arbitrarily wide bandwidth, although it may take a very large number of components and be impractical.
When either or both terminations are reactive, there are fundamental relationships between the nature of the terminations, the required bandwidth and the required quality of match.
As an exercise try a Monte Carlo analysis of this circuit with the default 5% tolerance on components. Clearly this circuit would need tuning after construction. Tuning all components would be undesirable. As a second exercise, try placing the capacitors on the nearest standard value and optimizing the three inductors for a return loss of -18 dB.
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Matching\Power Amp.wsp
Here we illustrate power amplifier design. Because of the popularity and power of S-parameter based computer programs, much effort has been expended in recent years on measuring high-power S-parameters and using this data for power amplifier design. Unfortunately, if a high-power DUT accidentally oscillates, S-parameter measurement equipment is easily damaged.
A second concern of basing power amplifier design on high-power S-parameters is the following; does matching to the device high-power S-parameters yield the best power output, efficiency and gain?
Historically, power amplifier design has used the following procedures:
• Tuners are placed at the device input and output
• The tuners are adjusted for best power operation
• The device is removed and the tuners are measured
• The manufacturer publishes the device input and output impedances which should be matched
In this example, we’ll design a 800 to 950 MHz 0.75 watt output Motorola MRF559 amplifier with Vcc = 12.5. We’ll design the output matching network. The input network would be designed using the same procedure. The Motorola data sheet for the MRF 559 recommends matching to these device resistances and reactances versus frequency for the output:
800 23.4 -37.7 850 23.7 -36.8 900 23.9 -36.0 950 24.5 -35.6
We drew the "Custom" schematic, consisting of a series line, shunt capacitor, series line and a shorted stub. Our network has fewer parts than the data sheet network, but the resulting match is excellent. Power is delivered to the MRF559 via a shorted stub as in the data sheet. (We specified a 50 ohm source and the load is the file MRF559OU.RX, so the network is oriented backwards.)
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MATCH was then run, which in this example is a shortcut for setting up the simulation, graphs, and optimization blocks. You can see the match setup "PowerAmp" by double-clicking it on the tree. Notice how we specified Custom for the network type and chose the schematic circuit Custom. MATCH then put the terminations on the PowerAmp schematic.
Next, the schematic was copied to a new schematic called "Physical". The terminations were adjusted to be the same as the PowerAmp schematic. "Convert using Advanced TLINE" was then selected from the Schematic menu, and the schematic was converted to microstrip. After tuning, the results are as shown below:
Matching\Unstable Device.wsp Matching an unstable device, particularly if it is potentially unstable in the passband is not good practice. The appropriate technique is to stabilize the device before proceeding with the match. The device is stabilized by adding one or more networks around the device.
In this topic, we will create a multistage 8 to 12 GHz amplifier, matching to an unstable device. We will use two NE71083.330 GaAsFET transistors with a series R-L stabilizing network connected from the drain to the gate.
Finally we write S-parameter for the device and its stabilization network to the file NE71083.STA using the “Write S-data” feature from the SUPERSTAR File menu. This is the device specified in the MATCH setup.
The basic steps that were followed are:
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• Discover that the device you want to match is unstable. You can easily do this in several ways: Read the data sheet, run MATCH and see the warnings. run our Stability template, or run our "Stabilize Device" template.
• Select New from template, choosing the "Stabilize Device" template.
• Change the device as required.
• Optimize to make the device stable
• Choose one of the stabilizing configurations.
• If desired, delete the stability test networks and add the stabilizing network to your device schematic.
• Run MATCH and create the matched amplifier. This example has a 2nd order TRL pseudo lowpass for each of the three matching networks
• Use Advanced TLINE to create a physical representation.
Select Start Level 1 from the Run menu. At this point, MATCH checks the NE71083.330 transistor S-parameter data files and reports that they are potentially unstabile. At this point, Level 1 run would normally be aborted and the device stabilized. Example 7 is a device stabilization example.
We have already stabilized the NE71083.330 by placing a series R-L feedback network from the drain back to the gate consisting of a 330 ohm resistor and a 5 nH inductor. S-parameter data for this stabilized device was stored in the file NE71083.STA.
To continue this example, select the Network menu and change each NE71083.330 S-parameter data file to NE71083.STA. Next, select Start Level 1 from the Run menu, make a few Level 2 passes and finish with Level 3 passes. The return losses will be approximately 7 dB.
Next, run the amplifier in SUPERSTAR. The SUPERSTAR circuit file and our results are given on the following page as the solid curves. The gain ranges from approximately 24 dB at the low end to 20 dB at the high end. Next add the optimization block in the file below to flatten the gain to 20 dB. The result after many rounds is shown as the dotted curves.
Flattening the gain response of an amplifier is a process of finding a good match at frequencies of low gain and a poorer match where the gain is higher than the norm. The processes in MATCH and SUPERSTAR are quite different, but together they form a powerful amplifier design technique. MATCH attempts to find the best match across the band and SUPERSTAR “frequency shapes” this match for a flat response. MATCH finds an excellent starting point for SUPERSTAR optimization.
Because active device gain is typically higher at low frequencies, a flattened amplifier often has a poor match at low frequencies. When flat gain and good match are required, an isolator is added or a balanced amplifier configuration is used. Another technique of achieving both match and flat gain is using resistive or transformer feedback. This
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sacrifices gain and is less common at microwave frequencies where gain is difficult to come by.
In the antenna example, the objective was to obtain a match to a highly reactive, frequency dependent termination. These conditions typically require high order networks. With amplifiers, the match is sacrificed to flatten the gain. High order networks with excellent initial match are overkill. Network selection is based on topologies with amplifier stability and gain flattening capability
Matching\Match and Stability.WSP This example shows that a high frequency GaAsFET (3-18 GHZ) can be stabilized with a feedback network and then matched using the broadband matching program called MATCH.
First, the stability and matching can be observed for the FET by itself. Notice the stability factor K is less than 1 for all frequencies below about 10 GHz. Consequently, the device is potentially unstable and should be stablized before proceeding to match the device.
The FET was stabilized using a "Stabilization Networks.wsp" template. See the "Stability Selection.wsp" workspace to see how the stabilization network was selected for this example.
Amplifier after stabilization from the "Stability Selection.wsp":
The stability factors K and B1, and the matching of the stabilized device can be seen in the respective schematic, table, and graph. Finally, a MATCH is added to the Synthesis folder and a matching circuit can be found for the stabilized device. A second order "TRL Pseudo Lowpass" matching network is used on the input side of the FET and a third order "TRL Pseudo Lowpass" matching network is used on the output side of the FET. The Min TRL Zo is set to 35 ohms and the Max TRL Zo has been set to 60 ohms. The optimize button on the MATCH dialog box can be used to optimize the input and output match. The gain of the circuit can also be added to the optimization so that the resultant gain is greater than the target gain of 6 dB.
After the circuit has been optimized this electrical circuit can be converted to a physical implementation such as microstrip or stripline by using Advanced TLINE and adding a layout. Furthermore, once the physical implementation has been created optimization
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targets can be placed on the physical implementation to optimize the layout for something that can be easily manufactured.
Optimized performance:
Final electrical implementation:
Matching\Stability Selection.WSP This workspace is used to assist in choosing a network and the component values to stabilize the device used in the "Match and Stability.wsp" example.
The "Stabilization Networks.wsp" template (selected "New from Template..." from the "File" menu) is used stabilize an active device. Basically, the workspace contains 4 feedback topologies, Resistive, Shunt RL, Series L, and Shunt C.
Resistive:
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Shunt RL:
Series L:
Shunt C:
The active device was set to the NE71083.330 GaAs FET in the Unstabilized Device schematic.
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The Start and Stop frequencies of the Linear simulation were changed to 3000 and 18000 respectively, to accommodate the frequency range of this device
Graphs and optimization targets exist for each of the feedback topologies. Once optimization is launched the simulator will changed the lumped element values until the best stability and maximum gain is achieved.
The resulting optimization for the Shunt RL Feedback is shown to be:
Notice that both the Series L and Shunt C Feedback topologies produced stability K values less than 1 for some frequencies. Definitely, we should try to avoid these feedback topologies for this active device. The Resistive Feedback topology also had good performance and could also be used.
The results of this stabilization selection was used in the "Match and Stability.wsp" example.
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Chapter 8 Detectors
Detectors\Simple Detector.WSP Illustrates: A simple diode detector circuit.
A blocking capacitor separates the applied DC bias from the input signal; a inductive choke separates the DC supply from the RF supply. The diode is used to peak detect, the capacitor holds the charge, and the resistor sets the bandwidth of the detector.
Shown in the graphs are the spectra and waveforms at the input and at the detector.
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"Vout vs. Pin" shows the DC output voltage as a function of the input power level. Note that the detected voltage shows the typical square-law shape.
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The final graph shows the detected voltage as a function of the detection capacitance. Note that the voltage is largely independent of the capacitance as long as the RC time constant is sufficiently below the input 1GHz signal.
Detectors\Diode Detector with Co-simulation.WSP Illustrates: EM-harmonic balance co-simulation to analyze a simple diode detector including the effects of the metal traces that interconnect the ports and the lumped components. The circuit is shown in the schematic "Detector."
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The layout is in "Layout1." The circuit is driven by two signals that form the complex waveform shown in "Time Input." In addition to detecting the DC level of the signal, the nonlinear character of the diode results in a mixing--a down-conversion--of the two signals.
The "Time Output" shows the detected output, showing a DC level proportional to the level of the input waveform and a ripple that is the product of the two input signals. Higher order feed-through terms are also visible riding on the waveform.
The spectra of the input and output waveforms are shown in "Sch Spectrum" (for the circuit based results) and "EM Spectrum" (for the EM-circuit co-simulation results.
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Note that the time waveforms are nearly identical in the detected signal. Since the inputs to the diode are relatively low in frequency, the parasitic effects are small.
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Chapter 9 Mixer
Mixer\Low Power Mixer.WSP Example: Low Power Mixer
Illustrates: The design of a single transistor mixer designed, built, and measured by Ken Payne of Artetronics. It is a typical design used in low cost, low power applications such as pagers and wireless remotes. The mixer is barely biased on, which operates the transistor in a very nonlinear region. Then, a relatively low power LO is lightly coupled onto the base, together with the RF signal. The transistor then effectively mixes these two signals together.
The Smith charts in this show the port matches of the mixer as calculated using linear and nonlinear device models. Measured results are also shown. Note that the RF and IF ports are well matched at their operating frequencies and mismatched at the other mixing frequencies. The LO port is intentionally mismatched so that the LO will only lightly couple into the mixer.
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Graphs are included that show the spectra and waveforms in the mixer. Two spectral graphs are shown where the Maximum Mixer Order was set at 5 and 10, resulting in 31 and 61 frequencies, respectively. This test was run to make sure that a sufficient number of harmonics were specified to model the circuit. Since the data moved so little, Maximum Mixer Order of 5 is sufficient. Two power sweeps were completed. The first shows the effect of LO drive level on conversion gain. The second shows gain compression resulting from RF drive level.
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Chapter 10 Antennas
Antennas\Patch Antenna Impedance.WSP RAM: 16.0Mbytes Time: 236s/freq Illustrates: Patch antenna impedance and resonance, solid model thinning, benchmark
Shown below is a microstrip fed patch antenna originally investigated by Wolff and Gao [1998]. The substrate is 0.79 mm thick with a relative dielectric constant of 2.2. The original dimensions and dimensions after placement on a 0.18 mm grid are:
Parameter Original (mm) On-Grid (mm)
Substrate Height 20 20.16
Substrate Width 20 20.16
Patch Height 7.2 7.2
Patch Width 3.59 3.6
Microstrip Feedline Width 0.715 0.62
Feed below top 2.9 2.88 (top of microstrip line)
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EMPOWER was run in a 1.0mm tall box with an open cover to simulate free space. Given below are the real and imaginary components of the input impedance of the patch antenna with a reference plane at the junction of the patch and the microstrip feedline. The reported operating frequency of the antenna is 13.12 GHz. The frequency of maximum resistance found by EMPOWER is 13 GHz.
This problem involves metal with a large number of cells in both x and y. The default wire thinning mode of EMPOWER is stressed by this class of problem and EMPOWER reports a maximum radiation resistance at 12.35 GHz. Therefore solid thinning was specified in the EMPOWER properties dialog box. Solid thinning runs faster and requires less memory than no thinning and accuracy is compromised very little if at all. Solid thinning requires significantly more memory and execution time than wire thinning. Wire thinning generally works well with filters and other structures which are a composite of narrow and medium width lines. When wide lines or large patches of metal are involved solid thinning is suggested.
Antennas\Array Driver.WSP Shown below is the schematic for a transmission line match and phasing network to drive a 3-element phased array of loop antennas for receiving. Each loop has a terminal impedance of 560 ohms in series with 4700 nH. Although SUPERSTAR handles complex terminations, in this case we simply placed 4700 nH inductors at the output of the driver.
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In order to produce low sidelobes, it is desired to drive the array with a binomial amplitude distribution; the center element should be driven with twice the amplitude of the end elements. For maximum broadside gain all elements should be driven in phase. Results after optimization are given below. Note that the phases are within 20 degrees and the gain and reflections are good.
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Antennas\Agile Antenna.WSP A microstrip patch antenna loaded with two varactor diodes.
Illustrates: combined EM and circuit theory simulation of a frequency agile antenna, manual connection of lumped element in EMPOWER, comparison with measured data.
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The design contains one common layout with one external and two internal z-directed ports. Schematic "WithParasitics" (shown below) takes data from the EM1 analysis and hooks up two models of the varactor diodes.
Schematic "WithoutParasitics" (not shown) simulates the same structure but the parasitic circuit elements which took the diode case into account have been removed. The result is closer to the experimental (2.35 GHz) [1], which can be explained by the fact that z-directed ports themselves have physical dimensions similar to the diode case, so the corresponding inductance and capacitance which must be taken into account in an equivalent circuit of a lumped element are already inherently included in the EMPOWER simulation.
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Reference: R. Gillard, S. Dauquet, J. Citerne, Correction procedures for the numerical parasitic elements in global electromagnetic simulators. - IEEE Trans., v. MTT-46, 1998, N 9, p. 1298-1306.
Antennas\MAmmannPatch.WSP Illustrates: Simulation of different kind of patch antenna feed and comparison with published measured data [1].
This example is a patch antenna simulation.
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Problems: EM1(Layout1) - patch antenna 36.85 x 36.85 mm x mm on RT Duroid 5870 substrate fed by a coaxial prob. Antenna is made of 1 oz. copper. Substrate height is 3.18 mm, dielectric constant is 2.33. EM2(Layout2) - patch antenna 33.7 x 33.7 mm x mm on two layer substrate composed from 3.18 mm RT Duroid 5870 and a substrate with dielectric constant 4.5 and height 1.54 mm. The antenna is fed by a 2.9 mm microstrip line deposited on the interface of the two dielectrics. The metal parameters are the same as in the probe-fed antenna. Simulation details: The key parameters that must be chosen properly for an antenna simulation are box size and position and boundary conditions at the top cover of the box. A rule of a thumb is to chose the box size as 4-5 of a critical patch size and to remove the top cover by at least one size of the critical size of the patch and put 377 Ohm boundary conditions there. Usually it works as shown here. The solid thinning out is recommended for the patch simulations. The grid cell size was chosen to make the patch smaller on a quarter of the cell size, that increase accuracy of the simulation according to U. Schulz. The problem is the probe-fed patch is simulated as z-directed internal port with size 2.8x2.8 mm. It made thicker to reduce the internal inductance that roughly corresponds to the inductance of a viahole with the same size or to an inductance of the central conductor of the feed coaxial. Simulation results: The probe-fed patch has central frequency 2480 MHz that is about 1% higher
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than in the experiment [1], the bandwidth of lossless patch is 2.8% (3.1% in the experiment). The microstrip-fed patch has central frequency 2400 MHz that is 2% lower than in the experiment [1].
Reference: 1) M. Ammann, Design of rectangular microstrip patch antennas for the 2.4 GHz band, Applied MicrowaveWireless, Nov./Dec., 1997, p. 24-34.
Antennas\Simple Dipole.WSP
EMPOWER Example: Simple Dipole Antenna in Free Space. This example features simulation of free-space boundary conditions, internal port, and description of the electromagnetic analysis results as multi-port for a co-simulation. The layout is a thin dipole 58 mm long and 1 mm wide in free space. Far-field radiation data is also generated and plotted on polar antenna charts.
Simulation details: Cell size 1x1mm, Box size 150x151 mm in the dipole plane and two surfaces with resistance 377 are placed 50 mm off the dipole plane to absorb EM fields. An internal port with current direction along X is placed in the center of the dipole to simulate excitation. The simulation results are shown below:
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Far Field Simulation details:
Data for Theta is generated from 0 to 360, step size 1 Data for Phi is generated from 0 to 360, step size 1 The Far-field radiation plots are shown below:
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Antennas\Thin Loop.WSP
EMPOWER Example: Thin Loop Antenna in Open Space
Features simulation of open space boundary conditions, internal port. The antenna is a thin square loop is 32x32 mm made of 1 mm wide strip line in open space.
Simulation details: Cell size 1x1mm, Box size 150x150 mm in the dipole plane and Two surfaces with resistance 377 are placed 50 mm off the dipole plane to absorb EM fields.
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An internal port with current direction along X is placed in the center of the dipole to simulate excitation. The input impedance and reflection are shown in the graphs below.
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Chapter 11 Resonance Elimination
ResonanceElimination\LowPassWithFictivePorts.WSP EMPOWER Example: Microstrip Low Pass Filter - resonance elimination technique
Illustrates: Comparison of the EM simulation with measured data and data obtained by the method of moments [1]. Demonstrates also effectiveness of the resonance elimination technique. Description of the problem: The filter consists of six microstrip stubs connected symmetrically on both sides along a microstrip line. Box size: 335 x 365 mil. Substrate height: 25 mil Dielectric constant: 9.6 Input and output microstrip line widths: 25 mil. Distance from the microstrip plane to the box top cover: 250 mil. The problem is lossless. Cell size: 5x5 mil. The other dimensions see in the Layout1.
Simulation details: Design Layout1 describes the whole filter that is simulated in EM1 in
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181 frequency points to catch narrow resonances. Design plus8port is the same as Layout1 but with 8 additional internal ports created to break resonances in the structure. The simulation of it needs only 19 frequency points over the frequency range from 2 to 20 GHz to get the resonances back in the design fictiveShort. S-matrices are generalized for all problems. Simulation results: The en-block simulation of the filter is very close to the simulation and experimental data obtained in [1]. The resonance elimination technique gives 10-times acceleration in comparison with the en-block simulation on the equidistant frequency grid.
Reference: 1) J.E. Bracken, D.-K. Sun, Z.J. Cendes S-domain method for simultaneous time and frequency characterisation of electromagnetic devices. - IEEE Trans., v. MTT-46, 1998, N9, p.1277-1290.
ResonanceElimination\MicrostripLineWithFictivePort.WSP EMPOWER Example: One-cell long internal input investigation
Illustrates: That an one-cell long internal port does not affect calculated characteristics of a microstrip line segment when short circuited in a co-simulation. The port width is equal to the line width.
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ResonanceElimination\MicrostripLineWithFictivePort2.WSP EMPOWER Example: One-cell long internal input investigation
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Illustrates: That an one-cell long internal port does not affect calculated characteristics of a microstrip line segment when short circuited in a co-simulation. The port width is equal to the line width.
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ResonanceElimination\ResonantStubFictivePort.WSP EMPOWER Example: A resonant stub in a microstrip line - resonance elimination technique
Illustrates: Comparison of the EM simulation with experimental data [1] and data obtained by the method of moments[2]. Demonstrates also effectiveness of the resonance elimination technique.
Description of the problem: The microstrip line is 0.23 mm wide is on a 0.254 mm thick substrate with dielectric constant 9.9. The microstrip stub is 0.51 mm wide and 1.5 mm long (1.53 in the papers). The structure is in a 2.8028 mm by 3.105 mm box. The top cover is 24.5 mm from the signal layer.
Simulation details: Design Layout1 describes the whole structure that is simulated in EM1. Design plus1port is the same as Layout1 but with an additional internal port created to break resonance in the structure. The simulation of it needs only 7 frequency points to get the resonance back in the design fictiveShort.
The cell size is 0.0637 x 0.0575 mm and S-matrices are generalized for all problems.
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Reference: 1) F. Giannini, G. Bartolucci, M. Ruggieri, Equivalent circuit models for computer-aided design of microstrip rectangular structures. - IEEE Trans., v. MTT-40, 1992, N2, p.378-388.
2) J.E. Bracken, D.-K. Sun, Z.J. Cendes S-domain method for simultaneous time and frequency characterization of electromagnetic devices. - IEEE Trans., v. MTT-46, 1998, N9, p.1277-1290.
ResonanceElimination\TwoLevelBPwithFictivePorts.WSP EMPOWER Example: Two level microstrip bandpass filter - resonance elimination technique
Illustrates: Simulation of a filter with coupled microstrip resonators in two metalization levels and comparison with published results of simulation and measurement [1]. Also demonstrates a resonance elimination technique that uses fictive loaded internal ports to expand S-matrices, to interpolate it and then reduces the expanded descriptor to the initial one. Description of the problem: Two side-coupled microstrip resonators are on a substrate together with an input and output line segments. An additional resonator is placed on an inverted substrate and over the two resonators to achieve coupling with the input and output resonators (through one). Both substrates have the same height 0.51 mm and dielectric constant 2.33. They are separated by a foam dielectric with height 3.3 mm and dielectric constant 1.07. Microstrips are 1.49 mm wide (rounded off to 1.5mm). Whole structure is in a box 40 mm by 20 mm. Simulation details: Design Layout1 describes the whole filter that is simulated in EM1 at 101 frequency points (3 min 40 sec per frequency point). S-parameters are generalized. Design plus3ports is the same filter but with 3 additional internal ports breaking resonators in halves and eliminating resonances when they are 50-Ohms loaded. Corresonding
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simulation EM2 is done only for 5 frequency points in the same frequency range as the initial filter (S-matrix is very smooth). Design fictiveShort takes 5-port data from the simulation EM2 and sets proper boundary conditions in fictive port areas (short circuit conditions). The external ports are normalized to impedances calculated in the EM2 simulation to have generalized parameters of the filter. Thinning out type for both simulations is wire with coefficient 5.
Simulation results: The simulation results obtained by the resonance elimination technique is almost on the top of the en-block simulation results. 20 times acceleration is achieved with simple interpolation technique ( without any loss of accuracy.)
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Reference: 1) A.A. Melcon, J.R. Mosig, M.Guglielmi, Efficient CAD of boxed microwave circuits based on arbitrary rectangular elements, IEEE Trans., v MTT-47, 1999, N 7, p.1045-1058
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Chapter 12 SPECTRASYS
SPECTRASYS\Getting Started\GS1_Setup.WSP Illustrates: This example shows you the basic setup of a system simulation using a power input, two attenuators, an isolator, and an output port.
This example uses a AC Power input port (*INP_PAC) that contains a signal of -50dBm at 100 MHz. Next is an attenuator with a loss of 2dB. The next block is an isolator with an insertion loss of -1dB. The default isolation of the isolator is -30dB. Lastly a 3dB attenuator is made from a T configuration.
Steps:
1. Create the schematic: To place a AC Power input port, you should click on the drop down box named "Place an Input" and select "Input: AC Power". Set the frequency of the input to 100 MHz and power level to -50 dBm. Next, you want to place the attenuator and isolator blocks which are found in the "System" toolbar. Next, you will have to create the T network from resistors which are found in the "Lumped" toolbar.
Note: Currently, Nonlinear elements are not supported. However, you can use any System or Linear elements in GENESYS.
2. Add a simulation: You add a system simulation by right-clicking on "Simulations/Data" folder in the workspace window and selecting "Add System Simulation" from the drop down menu. On the "Path" page set "Path1" to "1,2" and press OK.
3. Add to your analysis:
a. Table1: (Add 'Table1' by right clicking on "Outputs" folder of the workspace window and selecting "Add Table" from the popup menu.)
Add the following measurements:
CF - Channel Frequency
CP - Channel Power in dBm
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GAIN - Individual Stage Gain
CGAIN - Cascaded Gain
b. Input Spectrum: (Add rectangular graph by right clicking on the "Outputs" folder of the workspace window and selecting "Add Rectangular Graph" from the pop-up menu. Set the name "Input Spectrum".)
Set the "Default Simulation/Data or Equations" to "System1.Path1".
Add the measurement: P1 - Power of Node 1
c. Channel Power: (Add a rectangular graph by right clicking on the "Outputs" folder of the workspace window and selecting "Add Rectangular Graph" from the pop-up menu. Set the name to be "Channel Power".)
Add the measurement: CP - Channel Power in dBm
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EXERCISE: Change the loss of the attenuator and watch your spectrums change.
SPECTRASYS\Getting Started\GS2_Spec_Prop.WSP Illustrates: This example shows how SPECTRASYS displays the spectrums at every node and how measurements are defined by paths.
This example is a simple switch matrix that illustrates how every source spectrum is propagated to every node in the system, including all of the undesired sneak paths. In this particular case notice that the switches have a finite amount of port-to-port isolation. 'Input1' can be selected by setting both switch banks to control level '2'. This can be done in the tune window.
Set-up: In this example there are 4 input ports (INP_PAC) and two output ports. Each input port has a unique frequency, power level, and bandwidth. Two banks of switches are used to select any one of the 4 inputs. Each input path has an attenuator at its input. A total of 5 paths have been defined as follows:
Input1toOutput 1,2
Input2toOutput 4,2
Input3toOutput 5,2
Input4toOutput 6,2
Input4toInput1 6,1
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Analysis:
1. Output Spectrum: The output spectrum is the power spectrum located at the output node 2. Notice that the desired signal of 100 MHz (with the switch matrix set to select 'Input2') is actually -0.5 dB below the un-desired signal of 150 MHz on 'Input4'. This is due to the off isolation of the switch 'SPDT_3' which is only 30 dB. (Flip the switch and notice the change in the output spectrum or change the isolation of 'SPDT_3').
2. Input1 Spectrum: This spectrum shows the total spectrum (spectrum seen by a
spectrum analyzer) traveling in each direction at node 4 ('Input2' port node). One spectrum analyzer trace shows the total power leaving 'Input2' port and traveling
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in the direction of the output port. Another total power traces shows the power leaving the attenuator and traveling toward 'Input2'. It's each to see from these two different colored traces that the 100 MHz is traveling toward the output and all other signals are sneak signals and are arriving at the 'Input2' port.
3. Signal Table: The channel frequency, channel power, and node sequence of each
path is displayed in the table.
4. Input1 to Output: This is a level diagram showing the channel power of Input1 along 'Input1toOutput' path which is from node 1 to node 2. Multiple traces can be placed on the same level diagram but if the paths are different the data is not too meaningful since the path node numbers are different.
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EXERCISE: Change the isolation requirements for all three switches to achieve at least a 20 dB signal to noise for each of the 4 outputs.
SPECTRASYS\Getting Started\GS3_Sources.WSP Illustrates: how to use the various SPECTRASYS sources. SPECTRASYS can use both standard schematic sources, plus three different user defined sources.
Basics:
1. SPECTRASYS recognizes three different types of ports which are: a. *INP: Standard Input Port b. INP_PAC: Input: AC Power c. *OUT: Output Port Of these three ports, the INP_PAC is a schematic source since source parameters are defined in the schematic.
2. Three different user defined sources available in SPECTRASYS: a. CW: Continuous Wave (Frequency, Amplitude, and Phase) b. Modulated: (Frequency, Amplitude, Bandwidth, and Phase) c. File: (Frequency Offset, Amplitude, and Phase)
3. No spectrum will be created or processed until a schematic source or a user source has been defined.
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4. User defined sources can be created and placed any of the three acceptable ports (*INP, INP_PAC, or *OUT).
5. Sources can be enable or disabled.
6. User defined sources are created and edited in the System Simulation dialog box.
7. All parameters for any source can be tuned by placing a '?' in front of the parameter to be tuned.
8. Multiple sources can be enabled at the same time on a single input or output port.
Set-up: In this This particular schematic shows a 4 way input combiner that drives an attenuator, isolator, and a coupler. Several sources are defined for the input and output ports.
Adding a Source
1. Open the System Simulation dialog box.
2. Click the 'add' button.
3. Specify: a. Source Name (if desired) b. Input Port Number c. Select the Signal Type (CW, Modulated, File) d. Center Frequency e. BW (Modulated Type only) f. Power (Average)
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g. Phase Shift h. Number of Points (Modulated Type only)
Editing a Source
1. Open the System Simulation dialog box.
2. Click the 'edit' button on the row of the source to be edited.
3. Change the desired parameters.
Deleting a Source
1. Open the System Simulation dialog box.
2. Click the 'Delete' button on the row of the source to be deleted.
Adding Multiple Carriers
Multiple carriers can be added in two ways:
1. Individually add each carrier.
2. Use the 'step and repeat' function.
Step and Repeat
The step and repeat function allows the user to quickly define multiple carriers at set intervals. The user has control over the following parameters between carriers:
a. Frequency Offset
b. Amplitude Offset
c. Phase Offset
d. Number of Signals
The Signal Type, Bandwidth, and Number of Points will be the same for every carrier.
File Sources
The user can define the shape of their source they would like in the frequency domain by using the file option. When a file source is created a file is created with the *.SRC extension that can be saved in the models directory. This file can then be reused or passed to others. This file contains a list of frequency offsets, amplitude offsets, and phase offsets. This allows the user to define a 1.25 MHz CDMA source for example and be able to use this same source over and over again at different frequencies and power levels. All file sources will automatically be loaded in the 'Signal Type' combo box if these files are saved in the 'Models' directory located under the 'GENESYS' directory.
File sources support two modes:
a. Single Sideband (SSB) - Only one half of the source needs to be specified. The other half of the source will be symmetric.
b. Double Sideband - Both the negative and positive offsets of the source need to be specified.
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File example:
----------- 150 MHz File Source ------------- UNITS HZ DBC 'Nominal frequency FREQ 0 'If freq is zero, data is SSB offset. DATA 1e6 -3 2e6 -20 3e6 -25 4e6 -40 5e6 -100 ENDDATA -----------------------------
For more information about 'File Sources' see the simulation manual.
Note: All CW sources are defined to have 1 Hz of bandwidth.
The sources are listed in the SPECTRASYS dialog box shown below.
The resulting spectrum at the output contains continuous wave sources, modulated sources, and multiple frequencies defined in a file.
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Exercises
1. Disable sources and examine the spectrum.
2. Add more carriers to the 'Step and Repeat' source by placing a question mark '?' in the 'Number of Signals' edit box and tune this parameter to add more carriers.
3. Zoom into the carrier at 150 MHz and compare the spectrum with its file source.
SPECTRASYS\Getting Started\GS4_Chan_Meas.WSP Illustrates: the concept of a channel and channelized measurements.
Basics:
CHANNEL DEFINITION: A channel is defined by its frequency and bandwidth. In SPECTRASYS the Channel Frequency and Channel Measurement Bandwidth determine the channel. Each path can have a different channel frequency but all paths for the same simulation all use the same 'Channel Measurement Bandwidth'. The 'Channel Frequency' is specified on the 'Paths' page of the System Simulation dialog box and the 'Channel Measurement Bandwidth' is specified on the 'General' page of the same dialog box. Furthermore, a noise channel can also be specified. However, in this particular case the 'Channel Frequency' and the noise channel frequency will be the same. The bandwidth of the noise channel on the other hand can be independently specified. Additionally, the 'Channel Measurement Bandwidth' is used to scale the broadband signals on a spectrum plot just like the resolution bandwidth does on a spectrum analyzer. For example, the power level of a 1 MHz broadband signal will be 10 dB below the specified power if the 'Channel Measurement Bandwidth' is set to 100 kHz instead of 1 MHz.
MEASUREMENTS: Many of the measurements in SPECTRASYS will use the channel in one form or another. For example the 'Channel Power (CP)' measurement will integrate the node spectrum across this channel.
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Set-up:
This example contains three signal sources on a single input port.
The signals are:
a. Desired Signal at a low power level at 100 MHz
b. Interfering narrowband tone at 95 MHz at a moderately high power level.
c. Interfering broadband signal at 109 MHz at a moderately high power level.
Furthermore, intermod, harmonic, and IP3 calculations have been disabled. In this particular example the channel frequency is set to 100 MHz and the initial channel measurement bandwidth is 1e-6 MHz (1 Hz). Consequently, the channel is defined to be from 99.9999995 to 100.0000005 MHz. The Channel Power (CP) measurement will integrate the power spectrum across this frequency range. The Noise Measurement Bandwidth is set to 30 kHz. Consequently, the noise channel is defined to be from 99.985 to 100.015 MHz. Since there is no frequency translation device in this particular example the channel frequency remains constant at every node along the path.
Observations
1. Channel Table: This table shows the Channel Frequency (CF) at every node along the path. Since the channel bandwidth is 1 Hz (1e-6 MHz) wide only the 100 MHz Desired Signal is present in this bandwidth as shown in the Channel Power (CP) measurement. The Channel Noise Power measurement is showing thermal noise in a 30 kHz bandwidth (since 10 * Log(30,000) = 45dB) then the thermal noise of -173.91 dBm/Hz + 45 dB = -129 dB/Hz). The Carrier to Noise Ratio (CNR) is simply the ratio of the Channel Power to the Channel Noise Power.
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Exercises
1. Tune the Noise Measurement Bandwidth and notice that the Channel Noise Power changes proportionally to the Log of this bandwidth. Notice that the other signals present do not affect this measurement since SPECTRASYS is able to distinguish noise signals from other types of signals.
2. Tune the Channel Measurement Bandwidth and notice that once the bandwidth is 10 MHz then the 95 MHz tone will be included in the Channel Power (CP) measurement and the total power will be higher. Why do we only see -53 dBm of power for the 95 MHz -50 dBm signal when the 'Channel Measurement Bandwidth' is set to 10 MHz instead of -50 dBm? Recall that the 95 MHz signal is a CW signal that has 1 Hz of bandwidth and the signal power will be distributed from 94.9999995 to 95.0000005 MHz. Since the 10 MHz bandwidth is exact, this CW signal is split in half and we only see half power or -53 dBm. If the 'Channel Measurement Bandwidth' is set to 10.000001 MHz bandwidth then we would set the entire -50 dBm signal.
3. Continue tuning the Channel Measurement Bandwidth until the 109 MHz modulated broadband signal falls within the channel. Furthermore, notice that the modulated broadband signal at 109 MHz will have its power scaled proportionally to the Log of the Channel Measurement Bandwidth until the Channel Measurement Bandwidth exceeds the bandwidth of this 2 MHz signal. Once the Channel Measurement Bandwidth (20 MHz) exceeds the upper edge of this signal then, as one would expect, the full power of the signal (-35 dBm) has been reached and will not be scaled past that point.
Additional Observations
1. Notice that as the Channel Measurement Bandwidth is tuned that the modulated broadband signal at 109 MHz scales proportionally to the Log of the bandwidth just as it would on a spectrum analyzer.
SPECTRASYS\Getting Started\GS5_Paths.WSP Illustrates: how to view desired and undesired spectrum paths. It will show how to analyze a system to find where the unwanted sneak paths exist.
Basics:
DEFINITION:
The definition of desired spectrum is spectrum that is traveling in the same direction as the desired path. All other spectrum traveling in the opposite direction will be present at the node of interest but will be specified as undesired (even if the signals have the same frequency) since it doesn't travel along the desired path.
Set-up:
In this example two signals of the same frequency of 100 MHz are combined together. The user can examine the spectrum levels along the various paths to gain an understanding of the differences between desired and undesired spectrum.
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The sources have been defined as follows:
a. Input1: CW 100 MHz, -100 dBm, 0 Deg, 1 Pts
b. Input2: CW 100 MHz, -40 dBm, 0 Deg, 1 Pts
Three paths have been defined on the 'Paths' page as follows:
a. 'Input1toOutput' 1,3
b. 'Input2toOutput' 2,3
c. 'Input2toInput1' 2,1
For this particular example any spectrum originating from Input #1 is desired spectrum along the 'Input1toOutput' path. Any spectrum from 'Input2' will be undesired. Likewise, any spectrum originating from 'Input2' is desired spectrum along the 'Input2toOther' or 'Input2toInput1' paths. And any spectrum from 'Input1' will be undesired. The 'Data Table' has Channel Frequency, Channel Power, Desired Channel Power displayed for 'Input1toOutput' paths. The 'Desired Channel Power' measurement calculates only the desired spectrum along its specified path.
OBSERVATIONS:
1. 'Data Table': Notice how the Channel Power for the 'Input1toOutput' path doesn't begin at the anticipated level of -100 dBm but instead has a level around -90.5 dBm. This is because the high level 100 MHz source on 'Input2' has snuck through the isolation of both the 2 to 1 combiner and the isolator connected to 'Input1'. However, the Desired Channel Power correctly shows the Channel Power for the 'Input1' signals since they are traveling along the 'Input1toOutput' path.
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2. 'Input2 to Input1' graph: This level diagram shows the channel power from 'Input2' to 'Input1'. I can easily be seen that the -90.5 dBm level that appears at 'Input1' is due to the 'Input2' level traveling across the isolation of the 2 to 1 combiner and backwards through the 'Input1' isolator.
3. "Inputs to Output' graph: This graph shows both level diagrams from the inputs
('Input1' and 'Input2') to the output. This graph also shows the difference between the 'Channel Power' and the 'Desired Channel Power' along the 'Input1toOutput' path.
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4. 'Input1 Spec' and 'Output Spec' graphs: Since the graphs display the entire spectrum the user is unable to distinguish between desired and undesired spectrum. Rather, the composite spectrum is shown at each node ... just like a spectrum analyzer.
EXERCISES: Use the table and level diagrams to determine the amount of combiner isolation needed so that the 'Channel Power' and the 'Desired Channel Power' are identical for the first 2 nodes along the 'Input1toOutput' path. (Note: The combiner parameters can be changed directly from the level diagram by double clicking on the combiner.)
SPECTRASYS\Getting Started\GS6_Noise.WSP Illustrates: how SPECTRASYS deals with broadband noise, thermal noise, and element noise generated by components.
Basics: SPECTRASYS can process large blocks of spectrum very quickly and broadband noise is no exception. Noise can come from any of three different sources. These are:
a. Excess noise of passive components
b. Added noise of active components
c. Noise source applied to an input port
Note: 1. Noise will not be calculated unless the 'Calculate Noise' box is checked on the System Simulation dialog box. 2. Any parameter in the System Simulation dialog box can be tuned by placing a '?' in front of the parameter.
LIMITING NOISE FREQUENCY RANGE: There is no upper frequency limit in SPECTRASYS for processing any type of spectrum. Processing frequency components that are not of interest to the user can be a waste of time and resources. SPECTRASYS provides ways to limit noise processing to the frequencies of interest by the user. On the 'Options' page of the System Simulation dialog box the user can specify the frequency range of interest. Any frequency above or below the 'Ignore Spectrum Frequency' 'Above' or 'Below' parameter will be ignored during calculations. The default value for the 'Ignore Spectrum Frequency Below' threshold is: 0 Hz. The default value for the 'Ignore Spectrum Frequency Above' threshold is: 5 times the highest source frequency. Defaults values are used when these parameters are left blank.
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EXCESS NOISE: All passive components will add excess noise at a level equivalent to their loss. For example, a 3 dB pad has a loss of 3 dB (also a noise figure of 3 dB) and would add excess noise to the system corresponding to this loss. Excess noise (in dBm) is calculated as 10 Log (F-1) where F is the noise factor. The conversion of Noise Figure to Noise Factor is:
Noise Factor (F) = 10 ^ (Noise Figure / 10)
ADDED NOISE: All active components will also add excess noise at a level equivalent to their noise figure. This noise is effectively added at the input of the active stage and will be amplified by the gain of the stage. See the Excess Noise section for equations.
THERMAL NOISE: When no broadband noise source is used in the system, thermal noise will be added to the system. The noise temperature and number of points used to represent the noise are specified on the 'Calculate' page of the System Simulation dialog box.
NOISE SOURCE: A broadband noise source can be placed on any port in the system. The user can specify the frequency limits and power level of this source.
HOW IT WORKS: SPECTRASYS uses a complicated noise correlation matrix to determine the powers levels of the noise that appear at every node in the system. The details of this matrix are beyond the scope of this discussion. Suffice it to say that excess noise, added noise, thermal noise, and noise sources are all taken into account.
CHANNEL NOISE POWER: The Channel Noise Power is the total integrated noise power that exists within the channel. This is the base noise measurement that is used for many other noise measurements.
ANALYZER MODE: The 'Analyzer Mode' is basically a virtual spectrum analyzer. The user can enable 'Randomize Noise' to give the appearance of random noise that is present in spectrum analyzers. This parameter does not affect any of the channelized noise measurements and is used for visual effects only. Furthermore, the user can set the noise floor of the analyzer mode to a value representative of his instrument. Typical spectrum analyzers have noise floors in excess of 154 dBm per Hz. This allows the user to see data during the simulation that will be more representative of what will be measured in the lab. The 'Analyzer Mode' parameters are located on the 'Composite' page of the System Simulation dialog box.
OBSERVATIONS:
1. 'Main Path' graph: This level diagram shows the channel power along the main path of the system. The input noise power at the 'Main' input is thermal noise which is -173.91 dBm/Hz for a system that is at 21° C. Since the channel bandwidth is 1 MHz then the total noise power is going to be -173.91 dBm/Hz + 10 Log(1e6) = -113.91 dBm. Since the "gain + noise figure" of the amplifier is 25 dB, then the noise power at the amplifier output is 25 dB higher or -88.91 dBm. The attenuator after the amplifier will attenuate the total noise by the loss of the attenuator since the noise level is way above thermal noise. However, at the output of the coupler the channel noise power is much higher because we have a broadband noise source being fed into the coupled port. The noise source
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placed on the 'Noise' port is at -120 dBm/Hz. Since the channel bandwidth is 1 MHz then the total input noise power is -60 dBm. After passing through the 5 dB attenuator and the 10 dB coupler the resultant noise power level at the output is about -75 dBm. The total power is slightly higher that this because the noise along the main path is also added in.
2. 'Amp Out' graph: Notice that at the amplifier output there are two total noise
power traces that represent noise traveling from two directions (one from the output of the amplifier travelling to the output port and the one from the attenuator traveling to the 'Main' port.) From this spectrum plot the user can quickly identify the broadband noise source from 0 to 200 MHz that is travelling from the 'Noise' port to the 'Main' port.
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EXERCISES FOR THE USER
1. Disable the Noise source in the Systems Simulation dialog box. Notice how the total noise on the last node of the 'Main Path' level diagram is now much lower and only represents the noise along the main path.
2. Tune the 'Ignore Spectrum Frequency Above' parameters on the Systems Simulation dialog box. Observe the noise power levels on the graphs and level diagram to get a better feel for how SPECTRASYS uses this parameter to determine the broadband noise frequency.
3. Tune the 'Channel Measurement Bandwidth' on the System Simulation dialog box by a factor of 10 and notice how the noise power also changes by 10 dB.
4. Disable the 'Randomize Noise' on the 'Analyzer Mode' and observe the effect on the spectrum plots.
SPECTRASYS\Getting Started\GS7_Coherent.WSP Illustrates: how SPECTRASYS deals with coherent and non-coherent addition of signals.
Basics: SPECTRASYS is able to determine which spectrums are coherent and which ones are not. Basically, any signal being derived or created from the same source is coherent. Any other signal sources are considered non-coherent. Furthermore, a noise source is coherent with itself but will not be coherent with other noise signals.
Set-up: A single broadband signal source have been created at 'Input' port at a center frequency of 100 MHz, bandwidth of 20 MHz, and a power level of -50 dBm. This signal is split two ways and is amplified by parallel amplifiers. When these signals are combined back together at the amplifier output their power will be 6 dB higher than each individual signal since these signals are coherent and in phase.
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OBSERVATIONS:
1. 'Output Spec' graph: This spectrum graph shows three components of the spectrum at the parallel amplifier output. One piece of the source signal travels from the input to the output through the top amplifier and the other travels through the bottom amplifier. The last spectral component is the total power. As can be seen from the marker text on this graph the user can identify both of the components traveling through the top and bottom amplifiers with their respective levels and the total power level at the amplifier output. As expected the user can see that these two spectral components have been added coherently since the total is 6 dB higher than the individual component level.
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EXERCISES:
1. Enable the second source which is identical to the first source in the System Simulation dialog box. Notice that the total power level at the at the output only increases by 3 dB. What is the reason? Answer: Both of the two system sources are independent and are considered non-coherent. Consequently, the total power only increases by 3 dB.
2. Tune the phase of the one of the paths. What happens to the output signal when the difference in phase between the paths are 180 degrees? What does the level diagram look like in this case. Notice how it is much easier to the see the signal cancellation that is taking place on the level diagram than a spectrum plot.
SPECTRASYS\Getting Started\GS8_Intermods.WSP Illustrates: how SPECTRASYS deals with intermods and how the non-linear devices handle these intermods. The user will also understand the difference between generated, conducted, and total third order intermod power.
Basics:
There are two intermod modes in SPECTRASYS:
Manual (Advanced) Mode: For this particular mode the user must create a minimum of 3 sources. The first source represents the desired signal and the corresponding channel frequency. The two other sources are the actual 2 tones that are used to create intermods in the channel. The user must make sure that the desired signal and the two interfering tones are spaced properly such that intermods will fall within the bandwidth of the desired channel. Furthermore, for this particular technique there is no restriction on the number of interfering signals used to create the intermods. The total intermod power found within the channel will be used to determine the actual output and input intercept points. For this mode of operation the user needs to only specify the frequency offset from the desired channel to the first interfering tone. If at least 3 sources are not created at the correct frequencies and the tone offset is not set correctly intermods will not appear within the channel and the perception will be that intermods are not working. This mode is enabled when the 'Manual (Advanced)' checkbox has been checked.
Automatic 2 Tone: In this particular mode SPECTRASYS will create the needed 3 sources to calculate intermods and intercept points. However, in this case the user needs to specify some additional information such as the 'Input Port', 'Tone Spacing', 'Gain Test Power Level', and the '2 Tone Power Level' parameters. Three sources are needed to make intermod measurements. The first source is created at the channel frequency and is used to determine the 'in channel' gain of the chain. The user must specify the level of this source through the 'Gain Test Power Level' parameter. This level should be above the noise floor and be well below the level that would cause non-linear behavior. The 'Input Port' specifies the port where the 3 signal sources are created. The 'Tone Spacing' determines the spacing between the desired channel and the first interfering tone. This same spacing is also used
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between the two interfering tones. Because of this spacing we are guaranteed that intermods will be created in the channel. The '2 Tone Power Level' is used to specify the actual level of both interfering tones. For the 'Input Third Order Intercept (IIP3)' and 'Output Third Order Intercept (OIP3)' measurements the '2 Tone Power Level' doesn't really matter since these parameters are based on relative measurements. However, this '2 Tone Power Level' is very important when determining the absolute intermod power level and should be set according to the maximum interference levels seen by the circuit. This mode is enabled as long the 'Manual (Advanced)' checkbox is unchecked.
SPECTRASYS creates intermods for all input sources driving non-linear elements such as amplifiers and mixers. All linear elements will not create intermods. However, these elements will conduct them from prior stages where they were created. The 'Total Third Order Intermod Power (TIM3P)' can be separated into two distinct groups of intermods. The first group is 'Generated' intermods and the second is 'Conducted' intermods from a prior stage. SPECTRASYS is able to separate intermods into these two groups. This allows the user to quickly determine the weak intermod link in a cascade of stages. This total is the non-coherent sum of the Generated and Conducted Third Order Intermod Power. 'Generated Third Order Intermod Power (GIM3P)' is the total third order intermod power that is created in a particular stage. This measurement will only show the intermod levels for the stages that created them. 'Conducted Third Order Intermod Power (CIM3P)' is the total third order intermod power conducted in from the prior stage. This measurement when used in conjunction with the 'Generated Third Order Intermod Power (GIM3P)' will help the user quickly identify the stages in the chain that are the weakest link and are the highest contributor to the intermods. The stage prior to the stage where the conducted intermods are dominant through the rest of the chain is the weak link in the chain.
Set-up:
This example uses two cascaded amplifiers amongst other passive stages such as attenuators and a coupler. The 'Manual (Advance)' intermod test is illustrated in this example. Three input signal sources have been created. Two CW interfering tones at 80 and 100 MHz each having -20 dBm output power. The other signal source is a desired signal at 60 MHz having a power level of -120 dBm. The channel frequency is 60 MHz.
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Analysis:
1. 'Amp #1 In' - This spectrum plot shows the small desired input signal at 60 MHz and the two interfering tones at 80 and 100 MHz at the input of the first amplifier. The power level of each of these interfering tones is -20 dBm.
2. 'Amp #1 Out' - This spectrum shows the resulting third order intermods created
from the two input tones at the output of the first amplifier. The output power of each tone is -10 dBm. Since the output IP3 of the first amplifier is +20 dBm then the difference between the tone the output IP3 is 30 dB. The output power of the third order intermods will be twice this delta value below the tone output power. This results in third order intermod power levels of -70 dBm. (The actual values in the table may be slightly lower due to the reduced amplifier gain with larger power input signals).
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3. 'Amp #2 In' - This spectrum shows the total input spectrum to the 2nd amplifier. This spectrum consists of the three source signals and the third order spectrum created from the first amplifier.
4. 'Amp #2 Out' - This spectrum shows the total output spectrum of the 2nd
amplifier. This spectrum is the combined spectrum from the intermods that were conducted from the output of the 1st amplifier to the output of the 2nd amplifier and the intermods generated from the 2 interfering sources by the 2nd amplifier. The two intermod spectrums (conducted and generated) are combined non-coherently to get the total output spectrum.
5. 'Intermod Table' - This table shows us the numeric values of the Channel
Frequency, Channel Power, Generated Third Order Intermod Power, Conducted Third Order Intermods, Total Third Order Intermod Power, Gain of each stage, the first interfering Tone Channel Frequency, the Tone Channel Power, and Cascaded Gain.
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6. 'Intermod Diagram' - This level diagram is one of the most useful graphs in this
example. This level diagram shows the Generated, Conducted, and Total Third Order Intemod Power along the main path. From this graph the user can quickly identify that the first amplifier stage is the weak link in the chain. In other words, the 'generated' intermods at the output of the first amplifier are dominant and every subsequent stage is dominated by the 'conducted' intermods. Better intermod performance can be achieved by redistributing the gain between the first and second amplifiers.
TONE DISSIMILAR AMPLITUDE: In most cases, analysis on devices assume the tone inputs have equal amplitude. Mathematically, this is the most convenient or easiest way to analyze intermod distortion. However, this method is not always an accurate model of the real problem. When both input amplitudes are equal, the third order IM product level changes 3 dB for every 1 dB change in amplitude. However, when you have dissimilar interfering tone amplitudes the adjacent tone will change by 2 dB for every 1 dB. The alternate tone will change 1 dB for every 1 dB of change.
CHANNEL BANDWIDTH AND INTERMODS: The bandwidth of third order products is greater than the individual bandwidth of the sources that created them. For example, if two 1 Hz tones were used to create intermods the resulting intermod bandwidth would be 3 Hz. The bandwidth follows the intermod equation that determines the frequency except for the fact that bandwidth cannot be subtracted. For example, if
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the third order intermod equation is: Fim3 = F1 - 2*F2 then the equation for the resulting bandwidth would be: BWim3 = BW1 + 2*BW2. If BW1 = 30 kHz and BW = 1 MHz then the resulting bandwidth would be 2.03 MHz. The user needs to make sure that the 'Channel Measurement Bandwidth' is set wide enough to integrate all of this energy.
EXERCISES:
1. Redistribute the gain between the first and second amplifiers to lower the total intermod power at the output of the cascade (node 2). Make sure that the cascaded gain still remains the same (10 dB). One Solution - The total intermod power at the output can be improved by over 5 dB by simply reducing the gain of the first stage from 20 to 16 dB of gain and increasing the gain of the second stage from 10 to 14 dB. The cascaded gain will still be 10 dB.
2. Go into System Simulation dialog box and change the 80 MHz tone source power to -21 dBm. Check each graph, and you will see the difference in tone amplitudes and IM amplitudes. Now go back into System1 properties and change the 100 MHz tone power level to -21 dBm. As you will see, both tones match each others and both IM's are now equal in amplitude as well. (The actual intermod power between the close in intermods (F1 - 2*F2 or F2 - 2*F1) may be slightly different due to other intermods falling on these same frequencies ... other factors such as impedance and frequency roll-off can also contribute to this difference).
SPECTRASYS\Getting Started\GS9_Mixers.WSP Illustrates: how SPECTRASYS simulates mixers as part of RF systems.
Basics: The current mixer model in SPECTRASYS is a non-linear model that uses a 1dB compression point, a third order intercept point, a second order intercept point, and a saturation point. Furthermore, the user is able to specify the isolation parameters of the mixer along with the desired output product: sum or difference. The user can also specify the conversion loss and the LO level of the mixer. One of the uses of the LO Drive Level specification is to provide SPECTRASYS with the absolute power level of the LO so that the user can be notified if the actual LO power is outside the target LO power level range specified on the 'Options' page in the System Simulation dialog box. SPECTRASYS will process all isolation spectrum, LO to RF, RF to IF, and LO to IF. The mixer will also create third order intermods from all of its input sources. Obviously, sum and difference frequencies between all the input signals and all LO signals will be created. During the initial calculation process, SPECTRASYS ignores the desired signal direction through the mixer and signals on either the RF or IF side of the mixer will be converted to the appropriate sum and difference frequencies. Currently, a mixer spur table is not supported.
Set-up: This example contains a mixer with a filter and RF amplifier in the IF chain. Through equations the RF and the LO frequency are tied together so the channel can be changed by simply changing the RF frequency. The initial RF input frequency is 100 MHz and the LO frequency is 90 MHz. Since we have told the mixer that the desired mixer output is a 'difference' and not a 'sum', then the desired IF frequency will be 10 MHz.
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Analysis:
1. 'Mixer Out' graph - This graph shows the isolation (90 and 100 MHz) and sum and difference (190 and 10 MHz) outputs of the mixer. Notice that the level of LO leakage at the mixer output is much larger than the desired sum or difference frequencies. This large LO leakage level can easily drive a subsequent IF amplifier into compression unless that component is filtered.
2. 'IF Out' graph - This graph shows the IF output. The user will be able to see the
10 MHz output as well as the 2nd harmonic of the IF (even though this level is really low). Other components such as the LO leakage and other spurious responses can be seen. Furthermore, this spectrum gives the user a visual indication of the signal to noise ratio at this point in the RF chain.
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3. 'RF In' graph - This shows the spectrum at the input port. The 100 MHz input
signal source can be seen along with the LO radiation signal at 90 MHz. The user should verify that the spurious responses at this point meet the regulatory requirements (i.e. FCC, ETSI, etc.)
4. 'Budget Table' - This table gives a general performance overview of this simple
down-converter. This table shows the Channel Frequency, Channel Power, Channel Noise Power, Carrier-to-Noise Ratio, Cascaded Gain, and Cascaded Noise Figure. Many other parameters could have been presented in the table.
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Exercises:
1. Tune the 'RF' input signal and observe the spectrum at 'RF In', 'IF Out', and 'Mixer Out'.
2. Tune the Noise Figure of the amplifier and observe the cascaded noise figure, channel noise power and 'IF Out' spectrum.
3. Examine the spectrum at other nodes in the system.
4. Plot the Channel Power of the LO from the LO port to the RF input port.
5. Make the Loss in Attenuator ATTN_2 tunable. Adjust the loss until the Mixer is "starved". The Mixer symbol on the schematic will turn orange. What value of loss causes this condition? ( Answer: In the Mixer requirements, the "LO Drive Level" is 7 dBm. On the "Options" page of the System Simulation Parameters dialog box, the Mixer Warning (out-of-range) is set at +/- 2 dB. Therefore, when the 10 dBm level of the LO drive is reduced by 5 dB by the attenuator, then the resulting 5 dBm is at the lower threshold of 7 +/- 2 dBm.)
SPECTRASYS\Amplifiers\Feed Forward Amplifier.WSP Illustrates: the operation of a dual loop feed forward amplifier.
Basics: The power that can be achieved from a power amplifier will be largely determined by the non-linearities in the high power amplifiers stages. A dual loop feed forward amplifier can be used to reduce the level of the intermods at the power amplifier output. The first loop of the feed forward amplifier will combine the non-linear output spectrum from the main amplifier with a phase and amplitude shifted input spectrum. These two spectrums will be combined coherently and the input carriers will be cancelled if the carriers are 180 degrees out of phase and of the same amplitude. We then end up with only intermods in the spectrum. The second loop will amplify and phase shift the intermod only (error) spectrum and it will be added back into the main amplifier path to cancel out the intermods from the output of the power amplifier. These two intermod spectrums must be180 degrees out of the phase and the same amplitude. Since amplifiers and other circuits have delay, a delay line needs to be added to shortest delay path so that the spectrums can arrive at the same time. Phase shifters and gain adjustments are typically added so that the power amplifiers can be adjusted during manufacturing.
Set-up: RFAMP_1 is the main amplifier. Input signals from port 1 will be amplified by this amplifier and intermods will also be created. A sample of this distorted spectrum will be
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taken at COUPLER1_2 this will be passed toSPLIT2_1 where it will be combined with the delayed input spectrum.
A sample of the undistorted input spectrum is taken from COUPLER1_1 and then delayed by about 190 degree by the delay line (RF_DELAY_1). This delay line must be added because there will be delay through RFAMP_1. Enough delay is added to place our phase adjustment (RF_PHASE_1) for this first loop at a good center point in its adjustment range.
Out the output of SPLIT2_1 the input carriers will be canceled if they have the same amplitude and are 180 degrees out of phase. ATTN_VAR_1 is used to adjust the amplitude balance of the carriers. The user can examine the 'Error Amp Spec' graph to see the amplitude error and the 'Error Phase' graph to see the phase error of the carriers at the splitter output.
The intermod only spectrum at the splitter output will be amplified by RFAMP_2 (error amplifier) and will be combined back into the main path through COUPLER1_3. A delay line (RF_DELAY_2) is about 370 degrees long so that the phase shifter (RF_PHASE_2) of the second loop will be set at a good nominal center point. The intermods at the output (port 2) must be the same amplitude and 180 degrees out of phase. ATTN_VAR_2 is used to adjust the amplitude of the intermods.
Observations:
1. The user can examine the output spectrum on the 'Out Spec' graph. With the 'Analyzer Mode' enabled, the user is able to see the output of the power amplifier. Furthermore, having composite spectrum show the individual spectral components, we can quickly see the cancellation level between the individual pieces of the intermods and the actual output.
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2. SPECTRASYS knows the direction of travel of all spectral components at every
node in the system. The total power is represented by a trace for every travel direction at a node. By examining the 'Input Spectrum', the user can see the two input signals traveling from the input port into the power amplifier. Furthermore, the user can also see intermods and other spectrum traveling from inside the power amplifier to the output.
3. With individual components enabled for the composite spectrum, it is very easy
to identify the origin and path the spectrum takes to arrive at the examination point. By placing a marker on the intermod at 1958 MHz the user can identify all of the pieces of spectrum that make up that intermod and the path that it took to get to the input node. We see that the largest offender is -54.1 dBm (marker 'c') and its frequency is 1958 MHz which is the result of the frequency of source 1
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minus the 2nd harmonic of source 2 [S1-2xS2]. This intermod was created at node 6, the output of RFAMP_1. It then propagated to nodes 7,9,13,12,3,12,13,9,14,15,1. We can see that the weak link in the chain is the reverse isolation of RFAMP_2.
4. Adjacent channels can be defined at the intermod frequencies to examine the intermods power along the main path. This can be seen on the 'ACP' (Adjacent Channel Power) level diagram. Through most of the main path in the system, notice how the intermod power of the 1952 and 1958 MHz intermods are at the same power level. From this level diagram the user can quickly see that the intermods are being created in RFAMP_1 and we can also see the cancellation of the intermods at the output. Furthermore, we see the intermod energy reappearing at the amplifier input.
5. Optimization targets have been added to minimize the adjacent channel power.
Examining the optimization targets we can see that the adjacent channel power is trying to be minimized from Min=7 to Max=7. Since adjacent channel power (ACP) is a path (level diagram) measurement we need to tell GENESYS which node to perform the optimization. The user must specify the node index along the path and NOT the node number. Looking at the 'ACP' level diagram and starting with an index of 0 we see that the 7th index is at node 2. 7 in the index that we need to place in the optimizer for all level diagram measurements.
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Exercises:
1. Tune RF_PHASE_1 and examine the phase of the carriers traveling through both paths on the 'Error Phase' graph. Notice the path of amplified spectrum (marker c) and the input sampled path (marker d). The phase difference of these signal is 180 degrees to get the best cancellation.
2. Tune RF_PHASE_2 and examine the phase of the intermods traveling through both paths on the 'Out Phase' graph. Notice path of main spectrum (marker c) and the input sampled path (marker d). Again, the phase difference of these signal is 180 degrees to get the best cancellation.
3. Tune ATTN_VAR_1 and ATTN_VAR_2 and watch the respective amplitude balance for the carriers and intermods with the 'Error Spec' and 'Out Spec' graphs.
4. Tune the reverse isolation of RFAMP_2 and observe the intermod spectrum on the input ('Input Spectrum' graph) and notice that the improvement will change linearly with this isolation until the next dominant component is reached.
5. Run the optimization and notice the improvement in performance.
SPECTRASYS\Amplifiers\Quad Hybrid Matrix Amp.WSP Abstract: The hybrid matrix amplifier is a popular power amplifier configuration that incorporates redundancy. With the traditional design of using a single power amplifier for every transmitter the power amplifier becomes a single point of failure. If the amplifier dies, then so does the carrier and all of the transmitted information. The hybrid matrix amplifier will still provide output power (albeit a lower output power ... due to the loss of one amplifier) for all input signals. Furthermore, the reliability of power amplifiers is typically lower than the transmitter, so the likelihood of losing a carrier can be very high.
Background: 90 Degree hybrid couplers are used at the input to shift each input signal (IN and ISO) by 90 degrees (ISO to 0 is a 90 degree shift and ISO to -90 is a 0 degree shift). These hybrid couplers are also used on the output to combine the amplified signals back
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together. Because of the phasing, carriers will either add or cancel at the output leaving a dedicated output for each carrier.
To illustrate this point let's look at a simple dual hybrid matrix amplifier (HYBRID1_1, RFAMP_1, RFAMP_2, and HYBRID1_2). Signals at the IN port of HYBRID1_1 will have a 90 degree phase shift into RFAMP_2 and a 0 degree phase shift into RFAMP_1. The output of RFAMP_2 will have a 0 degree phase shift at the -90 output port of the HYBRID1_2. This same signal that has a 0 degree output through RFAMP_1 will go through a 90 degree shift through HYBRID1_2 and will add constructively at the -90 output port to produce the desired, amplified output. However, RFAMP_1 will produce a total 0 degree phase shift at 0 port of HYBRID1_2 and RFAMP_2 will produce a total 180 degree phase shift at this same port and the signal will cancel. Consequently, the output port for the dual hybrid matrix amplifier is the -90 port of HYBRID1_2 for and the IN port of HYBRID1_1. The user can use the same logic to examine and verify that signals on the ISO port of HYBRID1_1 will appear at the 0 port of HYBRID1_2.
Set-up: The following table shows the corresponding output ports for the input port and paths for the quad hybrid matrix power amplifier.
Input Port Output Port Path Frequency 1 8 TXA 1800 MHz 2 7 TXB 1810 MHz 5 4 TXC 1820 MHz 6 3 TXD 1830 MHz
Amplifiers specified along the path have been arbitrarily defined for each path since every amplifier will amplify each input carrier.
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Observations:
1. Output spectrums are available for each output. The user can verify by looking at these outputs that the correct carrier is present and all of the other carriers have been cancelled. Consider the TXA output at frequency 1800 MHz. By zooming in on the 1800 MHz region, note that the other carriers are about 37 db lower than the primary output.
2. Level diagrams have also been added for each input. Notice that the loss through
the input hybrid couplers is equal to the 3 dB splitting loss plus the insertion loss. However, the output couplers show a gain of 3 dB (because of the coherent addition taking place at that node) and a loss equal to the insertion loss.
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Exercises:
1. Tune the isolation of the hybrid couplers and observe the levels of the cancelled carriers. Notice that a large change in isolation doesn't affect the cancelled carriers levels much. However, as the isolation is lowered spectrums will propagate for a longer period of time and the simulation will take longer to run.
2. Set the gain of one of the amplifiers and examine the power at each output. Notice every carrier is still present, even though the power for each carrier is lower.
3. Change the 'Phase Balance' of HYBRID1_6 to 5 degrees and notice the A (1800 MHz) and B (1810 MHz) carriers are not cancelled as much as the other carriers.
4. If we want to improve the performance of the carrier cancellation, the user must understand the origin of the spectrum at those carrier frequencies. Since the carriers are evenly spaced, intermods will also appear at those carrier frequencies. To determine the origin of this spectrum, enable the 'Signal', 'Intermods and Harmonics', and 'Show Individual Components ...' and place a marker at 1800, 1810, 1820, or 1830 MHz. Notice that both carrier intermods and other components are present.
SPECTRASYS\TX & RX\TX and RX Chain.WSP Abstract: This example shows a complete path through a transmitter and transmit/receive antennas and finally through a receiver.
Set-up: The schematic, as shown below, has a main path from transmitter IF to receiver IF. The frequencies simulated were:
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Transmitter: IF = 220 MHz, LO = 1740 MHz, RF = 1960 MHz Receiver: IF = 150 MHz, LO = 2110 MHz, RF = 1960 MHz
Observations: The transmit path, shown below, begins at source # 1 and ends at the input to the transmit antenna. Notice the increase in channel power from -10 dBm at the input to over 34 dBm at the antenna.
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The transmitter output spectrum includes harmonics from the mixer and amplifiers. Only the total spectrum was selected for computation and plotting.
The channel power along the entire path clearly shows the attenuation of the radiated path between antennas.
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212
Exercises:
1. Vary the LO frequencies and observe the effect on channel power.
2. Add intermods and re-compute the outputs.
3. Adjust the LO power and "starve" the mixers. Observe the results.
SPECTRASYS\Noise\TX Noise in RX Band.WSP Abstract: This example demonstrates the use of a duplexer for a common antenna used by transmit and receive channels. The issues related to the filter design parameters and performance are examined. In particular, the effects of the transmit signal and noise in the receive band are simulated.
Set-up: The path of the transmit signal is from source # 1, through amplifier (RFAMP_1), and then through channel 'A' of the duplexer. The transmit signal is centered at 1960 MHz with a 1.25 MHz bandwidth. The upper edge of the receive band is at 1910 MHz. The duplexer is formed by two fifth order Elliptic bandpass filters. The passband for channels 'A' (transmit) and channel 'B' (receive band) are 1930 - 1990 MHz and 1850-1910 MHz, respectively. The linear response of the duplexer filters is shown below.
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Observations: Notice that the duplexer filters for both channels are identical. The ripple is 0.5 db. The insertion loss is also 0.5 db. Attenuation in the stopband is 80 db. Of interest is the spectrum of the noise at the input to the receiver LNA (node # 9). The plot
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214
below shows the components from the duplexer and reflected power from the receiver LNA. Also shown is the source signal of 160 MHz through the amplifier and duplexer. Finally, the level diagram gives insight into the source of the noise from the duplexer. The large increase in
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noise power through the transmitter amplifier (+10 db) is only partially offset by filtering (-3 db).
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216
Exercises:
1. Adjust the noise figure of the transmit amplifier. Observe the effect on the receiver noise power.
2. Determine the sensitivity to changes in the filter order, ripple, and stopband attenuation. Why does an increase in the filter order from 5 to 7 have such a dramatic improvement in the noise response?
SPECTRASYS\Transmitters\Diversity TX and Hybrid Amp.WSP Abstract: This example includes two transmit channels combined through a hybrid amplifier. Two mixers are used to up-convert the modulated inputs up to RF frequencies.
Set-up: The sources # 1 and # 3 are 220 MHz modulated signals, which are combined with local oscillator signals of 1735 MHz and 1745 MHz, respectively. The resulting "sum" frequencies are 1955 and 1965 MHz. See example:
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SPECTRASYS\Amplifiers\Quad Hybrid Matrix Amp.WSP for a discussion of hybrid amplifiers. Except for the LO frequencies, the two channels are identical.
Observations: The transmitter output from source # 1 appears at node # 6, as shown below. Notice the significant power at the other (1965 MHz) RF frequency. Insight into this effect is obtained from phase measurements.
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218
GENESYS provides for a phase measurement of the node voltage at any node. Of particular interest is node # 6. The phase of each of the component at 1965 MHz is given. Notice that the paths are identified by node numbers along the path.
Channel power is plotted below in a level diagram for the LO power contribution to Output # 1 (i.e. node 5).
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Exercises:
1. Use power and phase measurements to identify system deficiencies, and make corrections.
221
Index
1 1/S11 ................................................................. 131
2 2-section microstrip combline ......................... 81
3 3-section edge-coupled...................................... 74
4 4-inductor extractions ....................................... 87
8 8 Way.WSP ......................................................... 14
A Agile Antenna.WSP ......................................... 158 All Parallel Resonators Example..............91, 103 All Series Resonators Example ........................ 89 All-pole ................................................................ 97 Alta Frequenza ................................................... 94 Amp Feedback.WSP.......................................... 54 Amp Noise.WSP................................................ 55 Amplier................................................................ 52 Amplifier ....................................2, 57, 58, 60, 139 Amplifier.wsp ..................................................... 57 Amplifiers/Amplifier Tuned.WSP .................. 57 Amplifiers/Amplifier.WSP............................... 58 Amplifiers/SiGe BFP620 Amp.WSP.............. 60 Antenna ........................................2, 158, 160, 162 Antenna load..................................................... 137 ANTENNA.RX............................................... 137 Antennas/MAmmannPatch.WSP ................. 160 Array Driver.WSP............................................ 156 Attenuator ...................................................5, 9, 10
B Balanced Amp.WSP........................................... 52 bandpass dual amplifier Chebyshev filter..... 121 Bandpass Filters, Edge Coupled.................... 110 Bandpass Filters, Edge Redundant................ 112 Benchmarking..................................................... 36
BIP ....................................................................... 29 BipModel............................................................. 29 Box..................................................................... 164 Box Modes....................................................14, 74 Box Modes.WSP ................................................ 41 Box Width........................................................... 31 Branch-line............................................................ 8 BSCouplerDevelopment.wsp........................... 17 BSCouplerFinalRecomp.wsp ........................... 17 BSCouplerFinalWhole.wsp............................... 17 Butterworth......................................................... 97
C Calculate N
remove existing transformer ....................... 94 Calculate N....................................................86, 94 Calculate N To Remove Existing Transformers
......................................................................... 94 Capacitors .................................................102, 103 Carassa................................................................. 94 Cell Size .......................................................31, 164 Chebyshev.....................................................65, 97 Chebyshev coupled-resonator.......................... 97 Circles ............................................................49, 55 Circuit co-simulation ......................................... 58 Coaxial OSC.WSP............................................ 132 Coaxial Resonator Example ........................... 109 Combline............................................................. 81 Combline filter
Design............................................................. 66 Combline filter ................................................... 66 Components/BJT NL Model Fit.WSP .......... 46 Compression....................................................... 60 Computer Simulation ........................................ 94 Connectors.......................................................... 74 Contiguous Diplexer.WSP................................ 65 Convergence properties .................................... 38 Convert Using Advanced TLINE.........109, 139 Cosimulation....................................................... 38 Co-simulation ...........................................149, 162 Coupled lines ...................................................... 74 Coupled Microstrip Lines ................................. 17 Coupled Stepped Z.WSP.................................. 72 Coupled-line ......................................................... 8 Cover Height ...................................................... 31 Crystal ............................................................84, 85 Customized ......................................................... 86
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222
D Data File............................................................ 137 DC bias points ................................................. 127 Decomposition ........................................2, 17, 22 Deembedding .........................................31, 36, 74 Design
combline filter ............................................... 66 Design.................................................................. 66 Designs.............................................................. 103 Detector ....................................................147, 149 Detectors/Simple Detector.WSP.................. 147 Dielectric ........................................................... 103 Dielectric Constant.......................................... 103 DIODE............................................................. 147 Diode detector ................................................. 149 Diode detector circuit ..................................... 147 Diplexers ............................................................. 65 Dipole antenna................................................. 162 Discontinuities ................................................... 55 Dual Mode Coupler.WSP................................. 12
E Eagleware............................................................ 94 Edge Coupled.............................................74, 110 Edge Coupler.WSP...............................................8 Edge Positioning................................................ 36 Edge Redundant .............................................. 112 Edge-Coupled Filter.......................................... 77 EdgeCoupledBenchmark.WSP........................ 74 EdgeCoupledOpened.WSP.............................. 74 Edit Menu........................................................... 52 Electromagnetic ................................................. 97 Electromagnetic simulation.............................. 58 EM ....................................................................... 58 EMPOWER9, 10, 12, 14, 17, 20, 22, 66, 72, 77,
83, 162, 164, 167, 168, 169, 171, 172 Equal Inductor Example .................................. 96 Equal Termination Example............................ 86 Equations ........................................... 7, 29, 43, 97 Etch Factor......................................................... 36 Examples................................................................2 EXAMPLES subdirectory...................................1 Extraction sequence ..................................94, 103 Extractions..................................... 86, 94, 97, 103 Extractions Tab.................................................. 87 Extrapolation...................................................... 31 Extration Goals.................................................. 87
F Feed Forward Amplifier ................................. 202 Fictive port .................................................77, 172
fictive short....................................................... 171 Film.........................................................................9 Film Atten.WSP....................................................5 FILTER ..................................................2, 97, 122 Filters/ComblineDesign/Final Lossy.WSP....66 Finite Zeros .................................................. 94, 97 Force Symmetry..................................................97
G Generalized..........................................................31 Generalized S-Parameters .................................36 Generate Viewer Data .......................................72 GETVALUEAT.............................................. 132 Grid.......................................................................31 Group-delay.........................................................94 Group-Delay Characteristics.............................94
H HARBEC.................................................... 60, 127 Harmonic Balance ........................................... 127 Harmonics ...........................................................60 HF Filter Design.................................................94 High-Q quartz-crystal resonators.....................89 How To Design ..................................................85
I Ill Behaved Load.WSP.................................... 137 Impedances....................................................... 103 Inductor Q...........................................................97 Inductors equal ...................................................96 Infinity......................................................... 94, 103 Instability .............................................................49 Interdigital..................................................... 72, 81 Interdigital.WSP..................................................79 Internal Ports ...........................................162, 164
L LAYOUT...............................................................2 Layout Menu .......................................................52 L-C pseudo lowpass network ........................ 135 Lower Stopband .............................................. 103 Lowpass ...................................................... 94, 135
M M/FILTER ...........................................................2 MATCH....................................... 2, 135, 137, 139 Matching concepts........................................... 135 Matching resistive terminations..................... 137 Matching/Ill Behaved Load.WSP ................. 137
Index
223
Maximum Realizability Example ..................... 87 Measured data................................9, 46, 160, 167 Measured S-parameters ..................................... 46 Measurements...........................................131, 132 MFILTER......................................................... 123 Microstrip......8, 22, 31, 49, 55, 66, 83, 160, 167,
168, 169, 172 Microstrip Line.WSP ......................................... 31 Microwave Circuits ............................................ 55 MIXER.............................................................. 153 Mixer/Low Power Mixer.WSP...................... 153 Model ................................................................... 43 Model Extract..................................................... 29 MOL electromagnetic simulation.................... 38
N Negative Resistance ......................................... 131 NegR VCO.WSP.............................................. 131 NET..................................................................... 52 Noise Circles....................................................... 55 Noise Figure ....................................................... 55 Non-deembedded .............................................. 31 Nonlinear model ................................................ 60 Nonlinear models............................................... 46 Non-resonant simulation ............................79, 81 Nonsymmetrical ................................................. 72 Norton.........................................................94, 103 Norton Series.......................... 86, 91, 94, 96, 103 Norton Shunt ...............................................89, 96 Norton transforms.......................................96, 97
O Odd-order Chebyshev....................................... 97 Operators .......................................................... 131 Optimization.............29, 46, 55, 66, 97, 102, 103 Optimization Targets ........................................ 29 Optimize............................................................ 127 OSCILLATOR.............................................2, 127 Oscillators/Bipolar Cavity Oscillator.WSP.. 127 Output matching................................................ 55
P Parameter extraction.......................................... 29 parameter sweeps ............................................. 147 Parameters......................................................... 103 Parametric Bandpass Example....................... 103 Parasitics.............................................................. 29 Passband......................................................97, 103 Passband ripple ................................................ 103 Patch antenna ................................................... 160 Patch Antenna Impedance.WSP.................... 155
Permutation ..................................................86, 87 Phase Noise ..............................................127, 132 Physical Symmetry ............................................. 97 Physical Symmetry Example ............................ 97 Poor stopband performance ............................ 41 Port Impedance.................................................. 65 Post-processing ................................. 29, 131, 132 Power Amp....................................................... 139 PowerAmp........................................................ 139 Prob-fed antenna ............................................. 160 Pseudo lowpass ................................................ 135
Q Quad Hybrid Matrix Amp.............................. 206 Quarter-wave .................................................... 103 Quartz-crystal resonators.................................. 89
R RAM ...................................................................... 1 Reference Plane..........................................74, 155 Remove existing transformer
Calculate N .................................................... 94 Remove existing transformer ........................... 94 Remove sidewall reactances
de-embedded ................................................. 58 Remove Transformer ........................................ 87 Resonance .................................................167, 171 Resonance Elimination Technique 77, 167, 171 ResonanceElimination/EdgeCoupledWithFicti
vePorts.WSP.................................................. 77 ResonanceElimination/LowPassWithFictivePo
rts.WSP......................................................... 167 ResonanceElimination/MicrostripLineWithFict
ivePort.WSP................................................. 168 ResonanceElimination/MicrostripLineWithFict
ivePort2.WSP .............................................. 169 ResonanceElimination/ResonantStubFictivePo
rt.WSP........................................................... 171 ResonanceElimination/TwoLevelBPwithFictiv
ePorts.WSP .................................................. 172 Resonant stub ................................................... 171 Resonator Q ....................................................... 87 Resonators 72, 79, 83, 85, 87, 97, 102, 103, 109,
172 Response Symmetry Example.......................... 94 Richardson .......................................................... 31 Richardson's Extrapolation .............................. 36 Rubber Bands ................................................. 8, 52
S Series Element First.....................................89, 91
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224
Shunt-coupling ................................................... 97 Sidelobes ........................................................... 156 Signal Control/BSCouplerFinalRecomp.WSP
......................................................................... 20 Signal Control/BSCouplerFinalWhole.WSP. 22 Signal Control/ResistiveBroadband20dB.WSP
......................................................................... 10 Simple Dipole.WSP......................................... 162 Simplify ......................................................... 94, 96 Simplify Circuit ............................................ 91, 94 Single-ended ....................................................... 52 Singly-terminated ............................................... 65 SIR ....................................................................... 72 Smith Chart.................................................55, 131 Smith charts ...................................................... 153 Snap Angle.......................................................... 31 Solid Thinning................................................ 9, 17 S-parameter
difference ....................................................... 29 S-parameter...........................................29, 49, 139 S-parameter measurement .............................. 139 S-Parameters................................................. 46, 77 Specifications...................................................... 91 Specifications Tab........................................ 94, 97 SPECTRASYS .........................................202, 206 SPICE.................................................................. 46 Spiral Inductor2.WSP........................................ 38 Stability ..................................................41, 49, 142 Stability.WSP ...................................................... 49 Stabilization Networks.wsp............................ 143 Stabilize ............................................................. 143 Stopband ........................................................... 103 Stopband performance ..................................... 41 Stripline Standard.WSP..................................... 36 Stub with Inverters .......................................... 114 Subsections ................................................... 31, 41 Symmetrical .................................................. 94, 97
T Termination Coupling Example.................... 102 Termination Coupling.SF$............................. 102 Terminations ........86, 87, 91, 102, 103, 137, 156 Thin Film Attenuator...........................................9 Thin Loop Antenna......................................... 164 Thin Loop.WSP............................................... 164
Top Cover............................................................41 Transformations ......................................102, 103 Transformer...........................87, 94, 97, 102, 103 Transformer Ratio ....................................... 94, 97 Transformers.................................................. 7, 96 Transforms .................................... 94, 96, 97, 102 Transistor.............................................................29 Transmission lines ............................ 85, 102, 103 Transmission lines realize..................................85 Tuned Bandpass..................................................81 Two Level.WSP ..................................................83
U Unstable Device
Matching ...................................................... 140 Unstable Device............................................... 140 Upper Cutoff.................................................... 102 Upper Stopband............................................... 103 User Model.WSP ................................................43
V Varactor.................................................43, 81, 158 Viaholes................................................................55 Viewer ..................................................................12
W Weights.................................................................29 Wilkinson........................................................ 8, 14 WIRE ...................................................................38
X Xfmr Coupler.WSP ..............................................7 Xtal Filter.WSP ...................................................84
Z Zo
Extrapolating..................................................31 Zo................................................................... 31, 36
