# Transmission Line Basics II - Class 6 Prerequisite Reading assignment: CH2 Acknowledgements: Intel Bus Boot Camp: Michael Leddige

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• Slide 1
• Transmission Line Basics II - Class 6 Prerequisite Reading assignment: CH2 Acknowledgements: Intel Bus Boot Camp: Michael Leddige
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• 2 Transmission Lines Class 6 Real Computer Issues Dev a Dev b Clk Switch Threshold Signal Measured here An engineer tells you the measured clock is non-monotonic and because of this the flip flop internally may double clock the data. The goal for this class is to by inspection determine the cause and suggest whether this is a problem or not. data
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• 3 Transmission Lines Class 6 Agenda The Transmission Line Concept Transmission line equivalent circuits and relevant equations Reflection diagram & equation Loading Termination methods and comparison Propagation delay Simple return path ( circuit theory, network theory come later)
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• 4 Transmission Lines Class 6 Two Transmission Line Viewpoints Steady state ( most historical view) Frequency domain Transient Time domain Not circuit element Why? We mix metaphors all the time Why convenience and history
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• 5 Transmission Lines Class 6 Transmission Line Concept Power Plant Consumer Home Power Frequency (f) is @ 60 Hz Wavelength ( ) is 5 10 6 m ( Over 3,100 Miles)
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• 6 Transmission Lines Class 6 PC Transmission Lines Integrated Circuit Microstrip Stripline Via Cross section view taken here PCB substrate T W Cross Section of Above PCB T Signal (microstrip) Ground/Power Signal (stripline) Ground/Power Signal (microstrip) Copper Trace Copper Plane FR4 Dielectric W Signal Frequency (f) is approaching 10 GHz Wavelength ( ) is 1.5 cm ( 0.6 inches) Micro- Strip Stripline
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• 7 Transmission Lines Class 6 Key point about transmission line operation The major deviation from circuit theory with transmission line, distributed networks is this positional dependence of voltage and current! Must think in terms of position and time to understand transmission line behavior This positional dependence is added when the assumption of the size of the circuit being small compared to the signaling wavelength Voltage and current on a transmission line is a function of both time and position.
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• 8 Transmission Lines Class 6 Examples of Transmission Line Structures- I Cables and wires (a)Coax cable (b)Wire over ground (c)Tri-lead wire (d)Twisted pair (two-wire line) Long distance interconnects
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• 9 Transmission Lines Class 6 Segment 2: Transmission line equivalent circuits and relevant equations Physics of transmission line structures Basic transmission line equivalent circuit ?Equations for transmission line propagation Physics of transmission line structures Basic transmission line equivalent circuit ?Equations for transmission line propagation
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• 10 Transmission Lines Class 6 Remember fields are setup given an applied forcing function. (Source) How does the signal move from source to load? E & H Fields Microstrip Case The signal is really the wave propagating between the conductors
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• 11 Transmission Lines Class 6 Transmission Line Definition General transmission line: a closed system in which power is transmitted from a source to a destination Our class: only TEM mode transmission lines A two conductor wire system with the wires in close proximity, providing relative impedance, velocity and closed current return path to the source. Characteristic impedance is the ratio of the voltage and current waves at any one position on the transmission line Propagation velocity is the speed with which signals are transmitted through the transmission line in its surrounding medium.
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• 12 Transmission Lines Class 6 Presence of Electric and Magnetic Fields Both Electric and Magnetic fields are present in the transmission lines These fields are perpendicular to each other and to the direction of wave propagation for TEM mode waves, which is the simplest mode, and assumed for most simulators(except for microstrip lines which assume quasi-TEM, which is an approximated equivalent for transient response calculations). Electric field is established by a potential difference between two conductors. Implies equivalent circuit model must contain capacitor. Magnetic field induced by current flowing on the line Implies equivalent circuit model must contain inductor.
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• 13 Transmission Lines Class 6 General Characteristics of Transmission Line Propagation delay per unit length (T 0 ) { time/distance} [ps/in] Or Velocity (v 0 ) {distance/ time} [in/ps] Characteristic Impedance (Z 0 ) Per-unit-length Capacitance (C 0 ) [pf/in] Per-unit-length Inductance (L 0 ) [nf/in] Per-unit-length (Series) Resistance (R 0 ) [ /in] Per-unit-length (Parallel) Conductance (G 0 ) [S/in] T-Line Equivalent Circuit lL 0 lR 0 lC 0 lG 0
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• 14 Transmission Lines Class 6 Ideal T Line Ideal (lossless) Characteristics of Transmission Line Ideal TL assumes: Uniform line Perfect (lossless) conductor (R 0 0) Perfect (lossless) dielectric (G 0 0) We only consider T 0, Z 0, C 0, and L 0. A transmission line can be represented by a cascaded network (subsections) of these equivalent models. The smaller the subsection the more accurate the model The delay for each subsection should be no larger than 1/10 th the signal rise time. lL 0 lC 0
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• 15 Transmission Lines Class 6 Signal Frequency and Edge Rate vs. Lumped or Tline Models In theory, all circuits that deliver transient power from one point to another are transmission lines, but if the signal frequency(s) is low compared to the size of the circuit (small), a reasonable approximation can be used to simplify the circuit for calculation of the circuit transient (time vs. voltage or time vs. current) response.
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• 16 Transmission Lines Class 6 T Line Rules of Thumb Td
• 22 Transmission Lines Class 6 Parallel Plate Approximation Assumptions TEM conditions Uniform dielectric ( ) between conductors T C > T D T-line characteristics are function of: Material electric and magnetic properties Dielectric Thickness (T D ) Width of conductor (W C ) Trade-off T D ; C 0 , L 0 , Z 0 W C ; C 0 , L 0 , Z 0 To a first order, t-line capacitance and inductance can be approximated using the parallel plate approximation. Base equation
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• 23 Transmission Lines Class 6 Improved Microstrip Formula Parallel Plate Assumptions + Large ground plane with zero thickness effective To accurately predict microstrip impedance, you must calculate the effective dielectric constant. From Hall, Hall & McCall: Valid when: 0.1 < W C /T D < 2.0 and 1 < e r < 15 You cant beat a field solver
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• 24 Transmission Lines Class 6 Improved Stripline Formulas Same assumptions as used for microstrip apply here From Hall, Hall & McCall: Symmetric (balanced) Stripline Case T D1 = T D2 Offset (unbalanced) Stripline Case T D1 > T D2 Valid when W C /(T D1 +T D2 ) < 0.35 and T C /(T D1 +T D2 ) < 0.25 You cant beat a field solver
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• 25 Transmission Lines Class 6 Refection coefficient Signal on a transmission line can be analyzed by keeping track of and adding reflections and transmissions from the bumps (discontinuities) Refection coefficient Amount of signal reflected from the bump Frequency domain =sign(S11)*|S11| If at load or source the reflection may be called gamma ( L or s ) Time domain is only defined a location The bump Time domain analysis is causal. Frequency domain is for all time. We use similar terms be careful Reflection diagrams more later
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• 26 Transmission Lines Class 6 Reflection and Transmission Incident Reflected Transmitted
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• 27 Transmission Lines Class 6 Special Cases to Remember 1 Zo 0 1 0 0 Vs Zs Zo A: Terminated inZo Vs Zs Zo B: Short Circuit Vs Zs Zo C: Open Circuit
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• 28 Transmission Lines Class 6 Assignment Building the SI Tool Box Compare the parallel plate approximation to the improved microstrip and stripline formulas for the following cases: Microstrip: W C = 6 mils, T D = 4 mils, T C = 1 mil, r = 4 Symmetric Stripline: W C = 6 mils, T D1 = T D2 = 4 mils, T C = 1 mil, r = 4 Write Math Cad Program to calculate Z0, Td, L & C for each case. What factors cause the errors with the parallel plate approximation?
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• 29 Transmission Lines Class 6 Transmission line equivalent circuits and relevant equations Basic pulse launching onto transmission lines Calculation of near and far end waveforms for classic load conditions Basic pulse launching onto transmission lines Calculation of near and far end waveforms for classic load conditions
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• 30 Transmission Lines Class 6 Review: Voltage Divider Circuit Consider the simple circuit that contains source voltage V S, source resistance R S, and resistive load R L. The output voltage, VL is easily calculated from the source amplitude and the values of the two series resistors. RSRS RLRL VSVS VLVL RSRS RLRL RLRL VSVS VLVL + = Why do we care for? Next page.
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• 31 Transmission Lines Class 6 Solving Transmission Line Problems The next slides will establish a procedure that will allow you to solve transmission line problems without the aid of a

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