Agilent Specifying Calibration Standards for the Agilent 8510 Network Analyzer

Application Note 8510-5B

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IntroductionMeasurement errors Measurement calibration Calibration kit Standard definition Class assignment Modification procedure Select standards Define standards Standard number Standard type

Open circuit capacitance: C0, C1, C2 and C3

Short circuit inductance: L0, L1, L2 and L3

Fixed or sliding Terminal impedance Offset delay Offset Z0

Offset loss Lower/minimum frequency Upper/maximum frequency Coax or waveguide Standard labels

Assign classes Standard classes S

11A,B,C and S

22A,B,C

Forward transmission match/thru Reverse transmission match/thru Isolation Frequency response TRL Thru TRL Reflect TRL Line Adapter Standard class labels TRL options Calibration kit label

Enter standards/classes Verify performance User modified cal kits and Agilent 8510 specifications Modification examples Modeling a thru adapter Modeling an arbitrary impedance Appendix A Calibration kit entry procedure Appendix B Dimensional considerations in coaxial connectors Appendix CCal coefficients model

Table of contents

Known devices called calibration standardsprovide the measurement reference for net-work analyzer error-correction. This notecovers methods for specifying these stan-dards and describes the procedures for theiruse with the Agilent Technologies 8510 net-work analyzer.

The 8510 network analyzer system has thecapability to make real-time error-correctedmeasurements of components and devicesin a variety of transmission media.Fundamentally, all that is required is a setof known devices (standards) that can bedefined physically or electrically and usedto provide a reference for the physical inter-face of the test devices.

Agilent Technologies supplies full calibrationkits in 1.0-mm, 1.85-mm, 2.4-mm, 3.5-mm, 7-mm, and Type-N coaxial interfaces. The8510 system can be calibrated in other inter-faces such as other coaxial types, waveguideand microstrip, given good quality stan-dards that can be defined.

The 8510’s built-in flexibility for calibrationkit definition allows the user to derive aprecise set of definitions for a particular setof calibration standards from precise physi-cal measurements. For example, the charac-teristic impedance of a matched impedanceairline can be defined from its actual physi-cal dimensions (diameter of outer and innerconductors) and electrical characteristics(skin depth). Although the airline isdesigned to provide perfect signal transmis-sion at the connection interface, the dimen-sions of individual airlines will varysomewhat—resulting in some reflection dueto the change in impedance between the testport and the airline. By defining the actualimpedance of the airline, the resultantreflection is characterized and can beremoved through measurement calibration.

The scope of this product note includes ageneral description of the capabilities of the8510 to accept new cal kit descriptions viathe MODIFY CAL KIT function found in the8510 CAL menu. It does not, however,describe how to design a set of physicalstandards. The selection and fabrication ofappropriate calibration standards is as var-ied as the transmission media of the partic-ular application and is beyond the scope ofthis note.

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IntroductionThis product note covers measurement calibrationrequirements for the Agilent 8510B/C networkanalyzer. All of the capabilities described in thisnote also apply to the Agilent 8510A with the following exceptions: response & isolation calibra-tion; short circuit inductance; class assignmentsfor forward/reverse isolation, TRL thru, reflect,line and options; and adapter removal.

Measurement errorsMeasurement errors in network analysis can beseparated into two categories: random and system-atic errors. Both random and systematic errors arevector quantities. Random errors are non-repeat-able measurement variations and are usuallyunpredictable. Systematic errors are repeatablemeasurement variations in the test setup.

Systematic errors include mismatch and leakagesignals in the test setup, isolation characteristicsbetween the reference and test signal paths, andsystem frequency response. In most microwavemeasurements, systematic errors are the most sig-nificant source of measurement uncertainty. Thesource of these errors can be attributed to the sig-nal separation scheme used.

The systematic errors present in an S-parametermeasurement can be modeled with a signal flow-graph. The flowgraph model, which is used for errorcorrection in the 8510 for the errors associated withmeasuring the S-parameters of a two port device, isshown in the figure below.

The six systematic errors in the forward directionare directivity, source match, reflection tracking,load match, transmission tracking, and isolation.The reverse error model is a mirror image, giving atotal of 12 errors for two-port measurements. Theprocess of removing these systematic errors fromthe network analyzer S-parameter measurement iscalled measurement calibration.

EDF, EDR-Directivity ELF, ELR-Load MatchESF, ESR-Source Match ETF, ETR-Trans. TrackingERF, ERR-Refl. Tracking EXF, EXR-Isolation

Measurement calibrationA more complete definition of measurement cali-bration using the 8510, and a description of theerror models is included in the 8510 operating andprogramming manual. The basic ideas are summa-rized here.

A measurement calibration is a process whichmathematically derives the error model for the8510. This error model is an array of vector coeffi-cients used to establish a fixed reference plane ofzero phase shift, zero magnitude and knownimpedance. The array coefficients are computed bymeasuring a set of “known” devices connected at afixed point and solving as the vector differencebetween the modeled and measured response.

Figure 1. Agilent 8510 full 2-port error model

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The array coefficients are computed by measuringa set of “known” devices connected at a fixed pointand solving as the vector difference between themodeled and measured response.

The full 2-port error model shown in Figure 1 is an example of only one of the measurement calibra-tions available with the 8510. The measurementcalibration process for the 8510 must be one ofseven types: RESPONSE, RESPONSE & ISOLATION,Sll 1-PORT, S22 1-PORT, ONE PATH 2-PORT, FULL2-PORT, and TRL 2-PORT. Each of these calibrationtypes solves for a different set of the systematicmeasurement errors. A RESPONSE calibrationsolves for the systematic error term for reflec-tion or transmission tracking depending on the S-parameter which is activated on the 8510 at thetime. RESPONSE & ISOLATION adds correction for crosstalk to a simple RESPONSE calibration.An S11 l-PORT calibration solves for the forwarderror terms, directivity, source match and reflec-tion tracking. Likewise, the S22 1-PORT calibrationsolves for the same error terms in the reversedirection. A ONE PATH 2-PORT calibration solvesfor all the forward error terms. FULL 2-PORT andTRL 2-PORT calibrations include both forward andreverse error terms.

The type of measurement calibration selected bythe user depends on the device to be measured(i.e., 1-port or 2-port device) and the extent ofaccuracy enhancement desired. Further, a combi-nation of calibrations can be used in the measure-ment of a particular device.

The accuracy of subsequent test device measure-ments is dependent on the accuracy of the testequipment, how well the “known” devices are mod-eled and the exactness of the error correctionmodel.

Calibration kitA calibration kit is a set of physical devices calledstandards. Each standard has a precisely known orpredictable magnitude and phase response as afunction of frequency. In order for the 8510 to usethe standards of a calibration kit, the response ofeach standard must be mathematically defined andthen organized into standard classes which corre-spond to the error models used by the 8510.Agilent currently supplies calibration kits with 1.0-mm (85059A), 1.85-mm (85058D), 2.4-mm(85056A/D/K), 3.5-mm (85052A/B/C/D/E), 7-mm(85050B/C/D) and Type-N (85054B) coaxial con-nectors. To be able to use a particular calibrationkit, the known characteristics from each standardin the kit must be entered into the 8510 non-volatile memory. The operating and service manu-als for each of the Agilent calibration kits containthe physical characteristics for each standard inthe kit and mathematical definitions in the formatrequired by the 8510.

Waveguide calibration using the 8510 is possible.Calibration in microstrip and other non-coaxialmedia is described in Agilent Product Note 8510-8A.

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Standard definitionStandard definition is the process of mathematical-ly modeling the electrical characteristics (delay,attenuation and impedance) of each calibrationstandard. These electrical characteristics can bemathematically derived from the physical dimen-sions and material of each calibration standards orfrom its actual measured response. A standard definition table (see Table 1) lists the parametersthat are used by the 8510 to specify the mathemati-cal model.

Class assignmentClass assignment is the process of organizing cali-bration standards into a format which is compati-ble with the error models used in measurementcalibration. A class or group of classes correspondto the seven calibration types used in the 8510.The 17 available classes are identified later in thisnote (see Assign classes).

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Table 1. Standard definitions table

Table 2. Standard class assignments

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Modification procedureCalibration kit modification provides the capabilityto adapt to measurement calibrations in other con-nector types or to generate more precise errormodels from existing kits. Provided the appropri-ate standards are available, cal kit modificationcan be used to establish a reference plane in thesame transmission media as the test devices and ata specified point, generally the point of device con-nection/insertion. After calibration, the resultantmeasurement system, including any adapterswhich would reduce system directivity, is fully cor-rected and the systematic measurement errors aremathematically removed. Additionally, the modifi-cation function allows the user to input more pre-cise physical definitions for the standards in agiven cal kit. The process to modify or create a calkit consists of the following steps:

1. Select standards2. Define standards3. Assign classes4. Enter standards/classes5. Verify performance

To further illustrate, an example waveguide cali-bration kit is developed as the general descriptionsin MODIFY CAL KIT process are presented.

Select standardsDetermine what standards are necessary for cali-bration and are available in the transmissionmedia of the test devices.

Calibration standards are chosen based on the fol-lowing criteria:

• A well defined response which is mechanicallyrepeatable and stable over typical ambient tem-peratures and conditions. The most commoncoaxial standards are zero-electrical-lengthshort, shielded open and matched load termina-tions which ideally have fixed magnitude andbroadband phase response. Since waveguideopen circuits are generally not modelable, thetypes of standards typically used for waveguidecalibration are a pair of offset shorts and a fixedor sliding load.

• A unique and distinct frequency response. Tofully calibrate each test port (that is to providethe standards necessary for S11 or S22 1-PORTcalibration), three standards are required thatexhibit distinct phase and/or magnitude at eachparticular frequency within the calibrationband. For example, in coax, a zero-length shortand a perfect shielded open exhibit 180 degreephase separation while a matched load will pro-vide 40 to 50 dB magnitude separation fromboth the short and the open. In waveguide, apair of offset shorts of correct length providephase separation.

• Broadband frequency coverage. In broadbandapplications, it is often difficult to find stan-dards that exhibit a known, suitable responseover the entire band. A set of frequency-bandedstandards of the same type can be selected inorder to characterize the full measurementband.

• The TRL 2-PORT calibration requires only a sin-gle precision impedance standard—a transmis-sion line. An unknown high reflection deviceand a thru connection are sufficient to completethis technique.

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Define standardsA glossary of standard definition parameters usedwith the Agilent 8510 is included in this section.Each parameter is described and appropriate con-versions are listed for implementation with the8510. To illustrate, a calibration kit for WR-62 rec-tangular waveguide (operating frequency range12.4 to 18 GHz) will be defined as shown in Table1. Subsequent sections will continue to developthis waveguide example.

The mathematical models are developed for eachstandard in accordance with the standard defini-tion parameters provided by the 8510. These stan-dard definition parameters are shown in Figure 2.

Figure 2. Standard definition models

Model for reflection standard(short, open, load or arbitraryimpedance)

Model for transmission standard (Thru)

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Each standard is described using the StandardDefinition Table in accordance with the 1- or 2-port model. The Standard Definition table for awaveguide calibration kit is shown in Table 1. Eachstandard type (short, open, load, thru, and arbi-trary impedance) may be defined by the parame-ters as specified below.

• Standard number and standard type• Fringing capacitance of an open, or inductance

of a short, specified by a third order polynomial• Load/arbitrary impedance, which is specified as

fixed or sliding• Terminal resistance of an arbitrary impedance• Offsets which are specified by delay, Z0, Rloss

• Frequency range• Connector type: coaxial or waveguide• Label (up to 10 alphanumeric characters)

Standard numberA calibration kit may contain up to 21 standards(See Table 1). The required number of standardswill depend on frequency coverage and whetherthru adapters are needed for sexed connectors.

For the WR-62 waveguide example, four standardswill be sufficient to perform the FULL 2-PORT cali-bration. Three reflection standards are required,and one transmission standard (a thru) will be suf-ficient to complete this calibration kit.

Standard typeA standard type must be classified as a “short”“open,” “load”, “thru,” or “arbitrary impedance.”The associated models for reflection standards(short, open, load, and arbitrary impedance) andtransmission standards (thru) are shown in Figure 1.

For the WR-62 waveguide calibration kit, the fourstandards are a 1/8 λλ and 3/8 λ λ offset short, a fixedmatched load, and a thru. Standard types areentered into the Standard Definition table underSTANDARD NUMBERS 1 through 4 as short, short,load, and thru respectively.

Open circuit capacitance: C0 , C1 , C2 and C3

If the standard type selected is an “open,” the C0

through C3 coefficients are specified and then usedto mathematically model the phase shift caused byfringing capacitance as a function of frequency.

As a reflection standard, an “open” offers theadvantage of broadband frequency coverage, whileoffset shorts cannot be used over more than anoctave. The reflection coefficient (Γ = pe-je) of aperfect zero-length-open is 1 at 0° for all frequen-cies. At microwave frequencies however, the magni-tude and phase of an “open” are affected by theradiation loss and capacitive “fringing” fields,respectively. In coaxial transmission media, shield-ing techniques are effective in reducing the radia-tion loss. The magnitude (p) of a zero-length“open” is assigned to be 1 (zero radiation loss) forall frequencies when using the Agilent 8510Standard Type “open.”

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It is not possible to remove fringing capacitance,but the resultant phase shift can be modeled as afunction of frequency using C0 through C3 (C0 +Cl

x f + C2 x f2 + C3 x f3,with units of F(Hz), C0(fF),C1(10-27F/Hz), C2(10-36F/Hz2) and C3(10-45F/Hz3),which are the coefficients for a cubic polynomialthat best fits the actual capacitance of the “open.”

A number of methods can be used to determine thefringing capacitance of an “open.” Three tech-niques, described here, involve a calibrated reflec-tion coefficient measurement of an open standardand subsequent calculation of the effective capaci-tance. The value of fringing capacitance can be cal-culated from the measured phase or reactance as afunction of frequency as follows.

Ceff – effective capacitance∆∅ – measured phase shiftf – measurement frequencyF – faradZ0 – characteristic impedanceX – measured reactance

This equation assumes a zero-length open. Whenusing an offset open the offset delay must bebacked-out of the measured phase shift to obtaingood C0 through C3 coefficients.

This capacitance can then be modeled by choosingcoefficients to best fit the measured responsewhen measured by either method 3 or 4 below.

1. Fully calibrated 1-Port–Establish a calibratedreference plane using three independent standards(that is, 2 sets of banded offset shorts and load).Measure the phase response of the open and solvefor the capacitance function.

2. TRL 2-PORT–When transmission lines standardsare available, this method can be used for a com-plete 2-port calibration. With error-correctionapplied the capacitance of the open can be meas-ured directly.

3. Gating–Use time domain gating to correct themeasured response of the open by isolating thereflection due to the open from the source matchreflection and signal path leakage (directivity). Figure 3 shows the time domain response of theopen at the end of an airline. Measure the gatedphase response of the open at the end of an airlineand again solve for the capacitance function.

tan( )∆∅2

2πfZ0

12πfX

Ceff = =

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NoteIn some cases (when the phase response is linearwith respect to frequency) the response of an opencan be modeled as an equivalent “incremental”length.

This method will serve as a first order approxima-tion only, but can be useful when data or stan-dards for the above modeling techniques are notavailable.

For the waveguide example, this parameter is notaddressed since opens cannot be made valid stan-dards in waveguide, due to the excessive radiationloss and indeterminant phase.

Short circuit inductance L0 , L1, L2 and L3

If the standard type selected is a ‘short,’ the L0

through L3 coefficients are specified to model thephase shift caused by the standard’s residualinductance as a function of frequency. The reflec-tion coefficient of an ideal zero-length short is 1 at180° at all frequencies. At microwave frequencies,however, the residual inductance can produceadditional phase shift. When the inductance isknown and repeatable, this phase shift can beaccounted for during the calibration.

Figure 3. Time domain response of open at the end of an airline

2πf (∆length)c

∆∅(radians) =

The inductance as a function of frequency can bemodeled by specifying the coefficients of a third-order polynomial (L0 + L1 x f + L2 x f2 + L3 x f3),with units of L0(nH), L1(10-24H/Hz), L2(10-33 H/Hz2) and L3(10-42H/Hz3).

For the waveguide example, the inductance of theoffset short circuits is negligible. L0 through L3 areset equal to zero.

Fixed or slidingIf the standard type is specified to be a load or anarbitrary impedance, then it must be specified asfixed or sliding. Selection of “sliding” provides asub-menu in the calibration sequence for multipleslide positions and measurement. This enables cal-culation of the directivity vector by mathematicallyeliminating the response due to a non-ideal termi-nal impedance. A further explanation of this tech-nique is found in the Measurement Calibration section in the Agilent 8510 Operating andProgramming manual.

The load standard #4 in the WR-62 waveguide cali-bration kit is defined as a fixed load. Enter FIXEDin the table.

Terminal impedanceTerminal impedance is only specified for “arbitraryimpedance” standards. This allows definition ofonly the real part of the terminating impedance inohms. Selection as the standard type “short,”“open,” or “load” automatically assigns the termi-nal impedance to be 0, ∞ or 50 ohms respectively.

The WR-62 waveguide calibration kit example doesnot contain an arbitrary impedance standard.

Offset delayIf the standard has electrical length (relative to thecalibration plane), a standard is specified to havean offset delay. Offset delay is entered as the one-way travel time through an offset that can beobtained from the physical length using propaga-tion velocity of light in free space and the appro-priate permittivity constant. The effectivepropagation velocity equals . See Appendix Bfor a further description of physical offset lengthsfor sexed connector types.

Delay (seconds) =

= precise measurement of offset length in metersεr = relative permittivity (= 1.000649 for coaxial

airline or air-filled waveguide in standard labconditions)

c = 2.997925 x 108 m/s

In coaxial transmission line, group delay is con-stant over frequency. In waveguide however, groupvelocity does vary with frequency due to disper-sion as a function of the cut-off frequency.

√εr

c

12

c√εr

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The convention for definition of offset delay inwaveguide requires entry of the delay assuming nodispersion. For waveguide transmission line, theAgilent 8510 calculates the effects of dispersion asa function of frequency as follows:

fco = lower cutoff frequencyf = measurement frequency

NoteTo assure accurate definition of offset delay, aphysical measurement of offset length is recom-mended.

The actual length of offset shorts will vary by man-ufacturer. For example, the physical length of a 1/8 λ offset depends on the center frequency chosen.In waveguide this may correspond to the arith-metic or geometric mean frequency. The arithmeticmean frequency is simply (F1 + F2)/2, where F1 andF2 are minimum and maximum operating frequen-cies of the waveguide type. The geometric meanfrequency is calculated as the square root of F1 xF2. The corresponding (λg) is then calculated fromthe mean frequency and the cutoff frequency of thewaveguide type. Fractional wavelength offsets arethen specified with respect to this wavelength.

For the WR-62 calibration kit, offset delay is zerofor the “thru” (std #4) and the “load” (std #3). Tofind the offset delay of the 1/8 λ and 3/8 λ offsetshorts, precise offset length measurements are nec-essary. For the 1/8 λ offset short, l = 3.24605 mm, εr = 1.000649, c = 2.997925 x 108m/s.

Delay =(3.24605 x 10 -3 m) (√1.000649)

= 10.8309 pS2.997925 x 108 m/s

For the 3/8 λ offset short, I = 9.7377 mm, εr = 1.000649, c = 2.997925 x 108 m/s.

Delay = (9.7377 x 10-3 m) (√1.000649)

= 32.4925 pS2.997925 x 108 m/s

Offset Z0

Offset Z0 is the characteristic impedance within theoffset length. For coaxial type offset standards,specify the real (resistive) part of the characteris-tic impedance in the transmission media. The char-acteristic impedance in lossless coaxialtransmission media can be calculated from itsphysical geometry as follows.

Actual delay = Linear delay

1 - (fco/f)2

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µr = relative permeability constant of the medium(equal to 1.0 in air)εr = relative permittivity constant of the medium(equal to 1.000649 in air)D = inside diameter of outer conductord = outside diameter of inner conductor

The 8510 requires that the characteristic imped-ance of waveguide transmission line is assigned tobe equal to the SET Z0.

The characteristic impedance of other transmis-sion media is not as easily determined throughmechanical dimensions. Waveguide impedance, forexample, varies as a function of frequency. In suchcases, normalized impedance measurements aretypically made. When calibrating in waveguide, theimpedance of a “matched” load is used as theimpedance reference. The impedance of this load ismatched that of the waveguide across frequency.Normalized impedance is achieved by entering SETZ0 and OFFSET Z0 to 1 ohm for each standard.

Offset Z0 equal to system Z0 (SET Z0) is theassigned convention in the 8510 for matched wave-guide impedance.

Offset lossOffset loss is used to model the magnitude loss dueto skin effect of offset coaxial type standards only.The value of loss is entered into the standard defi-nition table as gigohms/second or ohms/nanosec-ond at 1 GHz.

The offset loss in gigohms/second can be calculat-ed from the measured loss at 1 GHz and the physi-cal length of the particular standard by thefollowing equation.

where:dBlOSS |1 GHz =measured insertion loss at 1 GHzZ0 = offset Z0

= physical length of the offset

The 8510 calculates the skin loss as a function offrequency as follows:

Note: For additional information refer to Appendix C.

For all offset standards, including shorts or opens,enter the one way skin loss. The offset loss inwaveguide should always be assigned zero ohms bythe 8510.

Z0 = = 59.9585 µε In

1

2πD

d

µr

εr( ) InD

d( )

Offset loss = GΩs 10 log

e(10) e

r1 GHz

dBloss 1 GHz C Z0( )

Offset loss X GΩ

s 1GHzf(GHz) Offset loss

GΩs

=( ) ( )

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Therefore, for the WR-62 waveguide standard defi-nition table, offset loss of zero ohm/sec is enteredfor all four standards.

Lower/minimum frequencyLower frequency defines the minimum frequency atwhich the standard is to be used for the purposesof calibration.

NoteWhen defining coaxial offset standards, it may benecessary to use banded offset shorts to specify asingle standard class. The lower and upper fre-quency parameters should be used to indicate thefrequency range of desired response. It should benoted that lower and upper frequency serve a dualpurpose of separating banded standards whichcomprise a single class as well as defining the over-all applicable frequency range over which a cali-bration kit may be used.

In waveguide, this must be its lower cut-off fre-quency of the principal mode of propagation.Waveguide cutoff frequencies can be found in mostwaveguide textbooks. The cutoff frequency of thefundamental mode of propagation (TE10) in rectan-gular waveguide is defined as follows.

f = c 2a

c = 2.997925 x 1010 cm/sec.a = inside width of waveguide, larger dimension in cm

As referenced in offset delay, the minimum fre-quency is used to compute the dispersion effects inwaveguide.

For the WR-62 waveguide example, the lower cutofffrequency is calculated as follows.

f = c = 2.997925 x 1010 cm/s = 9.487 GHz2a 2 x 1.58 cm

c = 2.997925 x 1010 cm/sa = 1.58 cm

The lower cut-off frequency of 9.487 GHz is enteredinto the table for all four WR-62 waveguide standards.

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Upper/maximum frequencyThis specifies the maximum frequency at whichthe standard is valid. In broadband applications, aset of banded standards may be necessary to pro-vide constant response. For example, coaxial offsetstandards (i.e., 1/4 λ offset short) are generally spec-ified over bandwidths of an octave or less.Bandwidth specification of standards, using mini-mum frequency and maximum frequency, enablesthe 8510 to characterize only the specified bandduring calibration. Further, a submenu for bandedstandards is enabled which requires the user tocompletely characterize the current measurementfrequency range. In waveguide, this is the uppercutoff frequency for the waveguide class and modeof propagation. For the fundamental mode of prop-agation in rectangular waveguide the maximumupper cutoff frequency is twice the lower cutofffrequency and can be calculated as follows.

F(upper) = 2 x F(lower)

The upper frequency of a waveguide standard mayalso be specified as the maximum operating fre-quency as listed in a textbook.

The MAXIMUM FREQUENCY of the WR-62 wave-guide cal kit is 18.974 GHz and is entered into thestandard definition table for all four standards.

Coax or waveguideIt is necessary to specify whether the standardselected is coaxial or waveguide. Coaxial transmis-sion line has a linear phase response as

Waveguide transmission line exhibits dispersivephase response as follows:

where

Selection of WAVEGUIDE computes offset delayusing the dispersive response, of rectangular wave-guide only, as a function of frequency as

This emphasizes the importance of entering “fco” asthe LOWER FREQUENCY.

Selection of COAXIAL assumes linear response ofoffset delay.

1-(fco/f)2 Delay (seconds) Linear delay

=

1-(λ/λco)2 λg λ

=

2π∅(radians)λg

=

2π2πf(delay)∅(radians)

λ ==

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NoteMathematical operations on measurements (anddisplayed data) after calibration are not correctedfor dispersion.

Enter WAVEGUIDE into the standard definitiontable for all four standards.

Standard labelsLabels are entered through the title menu and maycontain up to 10 characters. Standard Labels areentered to facilitate menu driven calibration.Labels that describe and differentiate each stan-dard should be used. This is especially true formultiple standards of the same type.

When sexed connector standards are labeled, male(M) or female (F), the designation refers to the testport connector sex—not the connector sex of thestandard. Further, it is recommended that the labelinclude information carried on the standard suchas the serial number of the particular standard toavoid confusing multiple standards which are simi-lar in appearance.

The labels for the four standards in the waveguideexample are; #1-PSHORT1, #2-PSHORT2, #3-PLOAD,and #4-THRU.

Assign classesIn the previous section, define standards, the characteristics of calibration standards werederived. Class assignment organizes these stan-

dards for computation of the various error modelsused in calibration. The Agilent 8510 requires afixed number of standard classes to solve for the nterms used in the error models (n = 1, 3, or 12).That is, the number of calibration error termsrequired by the 8510 to characterize the measure-ment system (1-Port, 2-Port, etc.) equals the num-ber of classes utilized.

Standard ClassesA single Standard Class is a standard or group of(up to 7) standards that comprise a single calibra-tion step. The standards within a single class areassigned to locations A through G as listed on theClass Assignments table. It is important to notethat a class must be defined over the entire fre-quency range that a calibration is made, eventhough several separate standards may be requiredto cover the full measurement frequency range. Inthe measurement calibration process, the order ofstandard measurement within a given class is notimportant unless significant frequency overlapexists among the standards used. When two stan-dards have overlapping frequency bands, the laststandard to be measured will be used by the 8510.The order of standard measurement between dif-ferent classes is not restricted, although the 8510requires that all standards that will be used withina given class are measured before proceeding tothe next class. Standards are organized into speci-fied classes which are defined by a StandardsClass Assignment table. See Table 2 for the classassignments table for the waveguide calibration kit.

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S11 A,B,C and S22 A,B,CS11 A, B,C and S22 A,B,C correspond to the S11 andS22 reflection calibrations for port 1 and port 2respectively. These three classes are used by theAgilent 8510 to solve for the systematic errors;directivity, source match, and reflection tracking.The three classes used by the 7-mm cal kit arelabeled “short,” “open,” and “loads.” “Loads” refersto a group of standards which is required to com-plete this standard class. A class may include a setof standards of which there is more than oneacceptable selection or more than one standardrequired to calibrate the desired frequency range.

Table 2 contains the class assignment for the WR-62 waveguide cal kit. The 1/8 λ offset short (stan-dard #1) is assigned to S11A. The 3/8 λ offset short(standard #2) is assigned to S11B. The matchedload (standard #3) is assigned to S11C.

Forward transmission match and thruForward Transmission (Match and Thru) classescorrespond to the forward (port 1 to port 2) trans-mission and reflection measurement of the“delay/thru” standard in a FULL 2-PORT or ONE-PATH 2-PORT calibration. During measurementcalibration the response of the “match” standard isused to find the systematic Load Match error term.Similarly the response of the thru standard is usedto characterize transmission tracking.

The class assignments for the WR-62 waveguide calkit are as follows. The thru (standard #4) isassigned to both FORWARD TRANSMISSION andFORWARD MATCH.

Reverse transmission match and thruReverse Transmission (Match and Thru) classescorrespond to the reverse transmission and reflec-tion measurement of the “delay/thru” standard.For S-parameter test sets, this is the port 2 to port 1transmission path. For the reflection/transmissiontest sets, the device is reversed and is measured inthe same manner using the forward transmissioncalibration.

The class assignments for the WR-62 waveguide calkit are as follows. The thru (Standard #4) isassigned to both REVERSE TRANSMISSION andREVERSE MATCH.

IsolationIsolation is simply the leakage from port 1 to port 2internal to the test set.

To determine the leakage signals (crosstalk), eachport should be terminated with matched loadswhile measuring S21 and S12.

The class assignments for forward and reverse iso-lation are both loads (standard #3).

Frequency responseFrequency Response is a single class which corre-sponds to a one-term error correction that charac-terizes only the vector frequency response of thetest configuration. Transmission calibration typi-cally uses a “thru” and reflection calibration typi-cally uses either an “open” or a “short.”

NoteThe Frequency Response calibration is not a sim-ple frequency normalization. A normalizedresponse is a mathematical comparison betweenmeasured data and stored data. The important dif-ference is, that when a standard with non-zerophase, such as an offset short, is remeasured aftercalibration using Frequency Response, the actualphase offset will be displayed, but its normalizedresponse would display zero phase offset (meas-ured response minus stored response).

Therefore, the WR-62 waveguide calibration kit classassignment includes standard #1, standard #2, andstandard #4.

19

TRL ThruTRL Thru corresponds to the measurement of theS-parameters of a zero-length or short thru connec-tion between port 1 and port 2. The Thru, Reflectand Line classes are used exclusively for the threesteps of the TRL 2-PORT calibration. Typically, a“delay/thru” with zero (or the smallest) OffsetDelay is specified as the TRL Thru standard.

TRL ReflectTRL Reflect corresponds to the S11 and S22 meas-urement of a highly reflective 1-port device. TheReflect (typically an open or short circuit) must bethe same for port 1 and 2. The reflection coeffi-cient magnitude of the Reflect should be close to 1but is not specified. The phase of the reflectioncoefficient need only be approximately specified(within ± 90 degrees).

TRL LineTRL Line corresponds to the measurement of theS-parameters of a short transmission line. Theimpedance of this Line determines the referenceimpedance for the subsequent error-correctedmeasurements. The insertion phase of the Lineneed not be precisely defined but may not be thesame as (nor a multiple of pi) the phase of theThru.

TRM ThruRefer to “TRL Thru” section.

TRM ReflecRefer to “TRL Reflec” section.

TRM MatchTRM Match corresponds to the measurement of theS-parameters of a matched load. The input reflec-tion of this Match determines the reference imped-ance for the subsequent error-correctedmeasurements. The phase of the Match does notneed to be precisely defined.

AdapterThis class is used to specify the adapters used forthe adapter removal process. The standard num-ber of the adapter or adapters to be characterizedis entered into the class assignment. Only an esti-mate of the adapter’s Offset Delay is required

(within ± 90 degrees). A simple way to estimatethe Offset Delay of any adapter would be as fol-lows. Perform a 1-port calibration (Response or S11 1-PORT) and then connect the adapter to thetest port. Terminate the adapter with a short cir-cuit and then measure the Group Delay. If theshort circuit is not an offset short, the adapter’sOffset Delay is simply l/2 of the measured delay. If the short circuit is offset, its delay must be sub-tracted from the measured delay.

Modifying a cal set with connector compensationConnector compensation is a feature that providesfor compensation of the discontinuity found at theinterface between the test port and a connector.The connector here, although mechanically com-patible, is not the same as the connector used forthe calibration. There are several connector fami-lies that have the same characteristic impedance,but use a different geometry. Examples of suchpairs include:

3.5 mm / 2.92 mm3.5 mm / SMASMA / 2.92 mm2.4 mm / 1.85 mm

The interface discontinuity is modeled as alumped, shunt-susceptance at the test port refer-ence plane. The susceptance is generated from acapacitance model of the form:

C=C0 + C1 x f + C2 x f2 + C3 x f3

where f is the frequency. The coefficients are pro-vided in the default Cal Kits for a number of typi-cally used connector-pair combinations. To addmodels for other connector types, or to change thecoefficients for the pairs already defined in a CalKit, use the “Modifying a Calibration Kit” proce-dure in the “Calibrating for System Measurements”chapter of the 8510 network analyzer systemsOperating and Programming Manual (part number08510-90281). Note that the definitions in thedefault Cal Kits are additions to the StandardClass Adapter, and are Standards of type “OPEN.”

20

Each adapter is specified as a single delay/thrustandard and up to seven standards numbers canbe specified into the adapter class.

Standard Class labelsStandard Class labels are entered to facilitatemenu-driven calibration. A label can be any user-selected term which best describes the device orclass of devices that the operator should connect.Predefined labels exist for each class. These labelsare

S11A, S11B, S11C, S22A, S22B, S22C, FWD TRANS,FWD MATCH, REV TRANS, REV MATCH,RESPONSE, FWD ISOLATION, REV ISOLATION,THRU, REFLECT, LINE, and ADAPTER.

The class labels for the WR-62 waveguide calibra-tion kit are as follows; S11A and S22A–PSHORT1;S11B and S22B–PSHORT2; S11C and S22C–PLOAD;FWD TRANS, FWD MATCH, REV TRANS and REVMATCH–PTHRU; and RESPONSE–RESPONSE.

TRL optionsWhen performing a TRL 2-PORT calibration, cer-tain options may be selected. CAL Z is used tospecify whether skin-effect-related impedance vari-ation is to be used or not. Skin effect in lossytransmission line standards will cause a frequency-dependent variation in impedance. This variationcan be compensated when the skin loss (offsetloss) and the mechanically derived impedance(Offset Z0) are specified and CAL Z0: SYSTEM Z0

selected. CAL Z0: LINE Z0 specifies that the imped-ance of the line is equal to the Offset Z0 at all frequencies.

The phase reference can be specified by the Thruor Reflect during the TRL 2-PORT calibration. SETREF: THRU corresponds to a reference plane set byThru standard (or the ratio of the physical lengthsof the Thru and Line) and SET REF: REFLECT cor-responds to the Reflect standard.

LOWBAND FREQUENCY is used to select the mini-mum frequency for coaxial TRL calibrations. Belowthis frequency (typically 2 to 3 GHz) full 2-port calibrations are used.

NoteThe resultant calibration is a single cal set combining the TRL and conventional full 2-portcalibrations. For best results, use TRM calibrationto cover frequencies below TRL cut-off frequency.

Calibration kit labelA calibration kit label is selected to describe theconnector type of the devices to be measured. If anew label is not generated, the calibration kit labelfor the kit previously contained in that calibrationkit register (CAL 1 or CAL 2) will remain. The pre-defined labels for the two calibration kit registersare:

Calibration kit 1 Cal 1 Agilent 85050B7-mm B.1

Calibration kit 2 Cal 2 Agilent 85052B3.5-mm B.1

21

Again, cal kit labels should be chosen to bestdescribe the calibration devices. The “B.1” defaultsuffix corresponds to the kit’s mechanical revision(B) and mathematical revision (1).

NoteTo prevent confusion, if any standard definitionsin a calibration kit are modified but a new kit labelis not entered, the default label will appear withthe last character replaced by a “*”. This is not thecase if only a class is redefined without changing astandard definition.

The WR-62 waveguide calibration kit can belabeled simply – P BAND.

Enter standards/classesThe specifications for the Standard Definitiontable and Standard Class Assignments table can beentered into the 8510 through front panel menu-driven entry or under program control by an exter-nal controller. The procedure for entry of standarddefinitions, standard labels, class assignments,class labels, and calibration kit label is describedin Appendix A.

NoteDO NOT exit the calibration kit modificationprocess without saving the calibration kit defini-tions in the appropriate register in the 8510.Failure to save the redefined calibration kit willresult in not saving the new definitions and theoriginal definitions for that register will remain.Once this process is completed, it is recommendedthat the new calibration kit should be saved ontape.

Verify performanceOnce a measurement calibration using a particularcalibration kit has been generated, its performanceshould be checked before making device measure-ments. To check the accuracy that can be obtainedusing the new calibration kit, a device with a welldefined frequency response (preferably unlike anyof the standards used) should be measured. It isimportant to note that the verification device mustnot be one of the calibration standards. Calibratedmeasurement of one of the calibration standards ismerely a measure of repeatability.

A performance check of waveguide calibration kitsis often accomplished by measuring a zero lengthshort or a short at the end of a straight section ofwaveguide. The measured response of this deviceon a polar display should be a dot at 1 ∠ 180°. Thedeviation from the known is an indication of theaccuracy. To achieve a more complete verificationof a particular measurement calibration, (includingdynamic accuracy) accurately known verificationstandards with a diverse magnitude and phaseresponse should be used. NBS traceable or Agilentstandards are recommended to achieve verifiablemeasurement accuracy. Further, it is recommend-ed that verification standards with known but dif-ferent phase and magnitude response than any ofthe calibration standards be used to verify per-formance of the 8510.

22

User modified cal kits and Agilent 8510 specificationsAs noted previously, the resultant accuracy of the8510 when used with any calibration kit is depend-ent on how well its standards are defined and isverified through measurement of a device withtraceable frequency response.

The published Measurement Specifications for the8510 Network Analyzer system include calibrationwith Agilent calibration kits such as the 85050B.Measurement calibrations made with user definedor modified calibration kits are not subject to the8510 performance specifications although a proce-dure similar to the standard verification proceduremay be used.

Modification examplesModeling a “thru” adapterThe MODIFY CAL KIT function allows more precisedefinition of existing standards, such as the “thru.”For example, when measuring devices with thesame sex coaxial connectors, a set of “thru” stan-dards to adapt non-insertable devices on each endis needed. Various techniques are used to cancelthe effects of the “thru” adapters. However, usingthe modify cal kit function to make a precise defi-nition of the “thru” enables the 8510 to mathemati-cally “remove” the attenuation and phase shift dueto the “thru” adapter. To model correctly a “thru”of fixed length, accurate gauging (see OFFSETDELAY) and a precise measurement of skin-lossattenuation (see OFFSET LOSS) are required. Thecharacteristic impedance of the “thru” can befound from the inner and outer conductor diame-ters and the permittivity of the dielectric (see OFF-SET Z0).

Modeling an arbitrary impedance standardThe arbitrary impedance standard allows the userto model the actual response of any one port pas-sive device for use as a calibration standard. Aspreviously stated, the calibration is mathematicallyderived by comparing the measured response tothe known response which is modeled through thestandard definition table. However, when theknown response of a one-port standard is notpurely reflective (short/open) or perfectly matched(load) but the response has a fixed real impedance,then it can be modeled as an arbitrary impedance.A “load” type standard has an assigned terminalimpedance equal to the system Z0. If a given loadhas an impedance which is other than the systemZ0, the load itself will produce a systematic error insolving for the directivity of the measurement sys-tem during calibration. A portion of the incidentsignal will be reflected from the mismatched loadand sum together with the actual leakage betweenthe reference and test channels within the meas-urement system. However, since this reflection issystematic and predictable (provided the terminat-ing impedance is known) it may be mathematicallyremoved. The calibration can be improved if thestandard’s terminal impedance is entered into thedefinition table as an arbitrary impedance ratherthan as a “load.”

A procedure similar to that used for measurementof open circuit capacitance (see method #3) couldbe used to make a calibrated measurement of theterminal impedance.

23

Appendix ACalibration kit entry procedureCalibration kit specifications can be entered intothe Agilent 8510 using the 8510 disk drive, a diskdrive connected to the system bus, by front panelentry, or through program control by an externalcontroller.

Disk procedureThis is an important feature since the 8510 caninternally store only two calibration kits at onetime while multiple calibration kits can be storedon a single disk.

Below is the generic procedure to load or store cal-ibration kits from and to the disk drive or diskinterface.

To load calibration kits from disk into the Agilent 85101. Insert the calibration data disk into the 8510network analyzer (or connect compatible disk driveto system bus).

2. Press the DISC key; select STORAGE IS: INTERNAL or EXTERNAL; then press the followingdisplay softkeys:LOADCAL KIT 1-2CAL KIT 1 or CAL KIT 2 (This selection determineswhich of the 8510 non-volatile registers that thecalibration kit will be loaded into.)FILE #_ or FILE NAME (Select the calibration kitdata to load.) LOAD FILE.

3. To verify that the correct calibration kit wasloaded into the instrument, press the CAL key. Ifproperly loaded, the calibration kit label will beshown under “CAL 1” or “CAL 2” on the CRT dis-play.

To store calibration kits from the Agilent 8510 onto a disk1. Insert an initialized calibration data disk intothe 8510 network analyzer or connect compatibledisk drive to the system bus.

2. Press the DISC key; select STORAGE IS: INTERNAL or EXTERNAL; then press the followingCRT displayed softkeys:STORECAL KIT 1-2CAL KIT 1 or CAL KIT 2 (This selection determineswhich of the 8510 non-volatile calibration kit regis-ters is to be stored.)FILE #_ or FILE NAME (Enter the calibration kitdata file name.) STORE FILE.

3. Examine directory to verify that file has beenstored. This completes the sequence to store a cali-bration kit onto the disk.

To generate a new cal kit or modify an existingone, either front panel or program controlled entrycan be used.

In this guide, procedures have been given to definestandards and assign classes. This section will listthe steps required for front panel entry of the stan-dards and appropriate labels.

24

Front panel procedure: (P-band waveguide example)1. Prior to modifying or generating a cal kit, storeone or both of the cal kits in the 8510’s non-volatile memory to a disk.

2. Select CAL menu, MORE.

3. Prepare to modify cal kit 2: press MODIFY 2.

4. To define a standard: press DEFINE STANDARD.

5. Enable standard no. 1 to be modified: press 1,X1.

6. Select standard type: SHORT.

7. Specify an offset: SPECIFY OFFSETS.

8. Enter the delay from Table 1: OFFSET DELAY,0.0108309, ns.

9. Enter the loss from Table 1: OFFSET LOSS, 0,X1.

10. Enter the Z0 from Table 1: OFFSET Z0, 50, X1.

11. Enter the lower cutoff frequency: MINIMUMFREQUENCY, 9.487 GHz.

12. Enter the upper frequency: MAXIMUM FRE-QUENCY, 18.97 GHz.

13. Select WAVEGUIDE.

14. Prepare to label the new standard: PRIORMENU, LABEL STANDARD, ERASE TITLE.

15. Enter PSHORT 1 by using the knob, SELECTLETTER soft key and SPACE soft key.

16. Complete the title entry by pressing TITLEDONE.

17. Complete the standard modification by press-ing STANDARD DONE (DEFINED).

Standard #1 has now been defined for a 1/8 λ P-bandwaveguide offset short. To define the remainingstandards, refer to Table 1 and repeat steps 4 -17.To define standard #3, a matched load, specify“fixed.”

The front panel procedure to implement the classassignments of Table 2 for the P-band waveguidecal kit are as follows:

1. Prepare to specify a class: SPECIFY CLASS.

2. Select standard class S11A.

3. Inform the 8510 to use standard no. 1 for theS11A class of calibration: l, X1, CLASS DONE(SPECIFIED).

25

4. Change the class label for S11A: LABEL CLASS,S11A, ERASE TITLE.

5. Enter the label of PSHORT 1 by using the knob,the SELECT soft key and the SPACE soft key.

6. Complete the label entry procedure: TITLEDONE, LABEL DONE.

Follow a similar procedure to enter the remainingstandard classes and labels as shown in the tablebelow:

Finally, change the cal kit label as follows:

1. Press LABEL KIT, ERASE TITLE.

2. Enter the title “P BAND.”

3. Press TITLE DONE, KIT DONE (MODIFIED). Themessage “CAL KIT SAVED” should appear.

This completes the entire cal kit modification forfront panel entry. An example of programmedmodification over the GPIB bus through an exter-nal controller is shown in the Introduction ToProgramming section of the Operating and Servicemanual (Section III).

Standard Standard Classclass numbers label

S11B 2 PSHORT 2S11C 3 PLOADS22A 1 PSHORT 1S22B 2 PSHORT 2S22C 3 PLOADFWD TRANS 4 THRUFWD MATCH 4 THRUREV TRANS 4 THRUREV MATCH 4 THRURESPONSE 1,2,4 RESPONSE

26

Appendix BDimensional considerations in coaxial connectorsThis appendix describes dimensional considera-tions and required conventions used in determin-ing the physical offset length of calibrationstandards in sexed coaxial connector families.

Precise measurement of the physical offset lengthis required to determine the OFFSET DELAY of agiven calibration standard. The physical offsetlength of one and two port standards is as follows.

One port standard–Distance between “calibrationplane” and terminating impedance.

Two port standard–Distance between the Port 1and Port 2 “calibration planes.”

The definition (location) of the “calibration plane”in a calibration standard is dependent on thegeometry and sex of the connector type. The “cali-bration plane” is defined as a plane which is per-pendicular to the axis of the conductor coincidentwith the outer conductor mating surface. This mat-ing surface is located at the contact points of theouter conductors of the test port and the calibra-tion standard.

To illustrate this, consider the following connectortype interfaces:

7-mm coaxial connector interfaceThe “calibration plane” is located coincident toboth the inner and outer conductor mating sur-faces as shown. Unique to this connector type isthe fact that the inner and outer conductor matingsurfaces are located coincident as well as havinghermaphroditic (sexless) connectors. In all othercoaxial connector families this is not the case.

3.5-mm coaxial connector interfaceThe location of the “calibration plane” in 3.5-mmstandards, both sexes, is located at the outer con-ductor mating surface as shown.

Type-N coaxial connector interfaceThe location of the “calibration plane” in Type-Nstandards is the outer conductor mating surfacesas shown below.

NoteDuring measurement calibration using the Agilent85054 Type-N Calibration Kit, standard labels forthe “opens” and “shorts” indicate both the stan-dard type and the sex of the calibration test port.The sex (M or F) indicates the sex of the test port,NOT the sex of the standard. The calibration planein other coaxial types should be defined at one ofthe conductor interfaces to provide an easily veri-fied reference for physical length measurements.

27Female type-N Male type-N

7 mm Coaxial connector

Type-N coaxial connector interfaceThe location of the “calibration plane” in Type-N standards is the outer conductor mating surfaces as shown below.

Note: 1.0mm, 1.85mm and 2.4mm connectors not shown, but similar to 3.5mm calibration planes.

28

29

Appendix CCal coefficients modelOffset devices like offset shorts and offset opens canbe modeled by the following signal flow graph :

Figure 1 Signal flow graph model of offset devices

The offset portion of the open or short, is modeledas a perfectly uniform lossy air dielectric transmis-sion line. The expected coefficient of reflection, Γ,of the open or short then can be solved by signalflow graph technique.

Equation 1

The terms Zo, and are related to the calcoefficients - Offset Zo, Offset Loss, and OffsetDelay - as follows:

Recall that

Equation 2

L ≈ L + 0Rω

30

Their first order approximations, R is small and G=0, are:Equation 3

Since Equation 4

For coaxial devices

31

then:Equation 5

Equation 6

If the Offset delay=0, then the coefficient of reflection, Γ = ΓL.

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