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Transmission Line Basics II - Class 6 Prerequisite Reading assignment: CH2 Acknowledgements: Intel Bus Boot Camp:  Michael Leddige
Real Computer Issues Transmission Lines  Class  6 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
Agenda ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6
Two Transmission Line Viewpoints ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6
Transmission Line Concept Transmission Lines  Class  6 Power Plant Consumer Home ,[object Object],[object Object],[object Object],Transmission Line Could be considered as Non-Transmission Line
PC Transmission Lines Transmission Lines  Class  6 ,[object Object],[object Object],[object Object],Micro- Strip Stripline 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) Signal (stripline)  Ground/Power Signal (microstrip)  Copper Trace Copper Plane FR4 Dielectric W
Key point about transmission line operation ,[object Object],[object Object],[object Object],Transmission Lines  Class  6 Voltage and current on a transmission line is a function of both time and  position .
Examples of Transmission Line Structures- I ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6
Segment 2: Transmission line equivalent circuits and relevant equations Transmission Lines  Class  6 ,[object Object],[object Object],[object Object]
E & H Fields – Microstrip Case ,[object Object],Transmission Lines  Class  6 Remember fields are setup given an applied forcing function. (Source) How does the signal move from source to load?
Transmission Line “Definition” ,[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6
Presence of Electric and Magnetic Fields  ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6
[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],T-Line Equivalent Circuit Transmission Lines  Class  6 lL 0 lR 0 lC 0 lG 0
Ideal T Line ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6 lL 0 lC 0
Signal Frequency and Edge Rate    vs.    Lumped or Tline Models Transmission Lines  Class  6 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.
T Line Rules of Thumb Transmission Lines  Class  6 Td < .1 Tx Td < .4 Tx May treat as lumped Capacitance  Use this 10:1 ratio for accurate modeling of transmission lines May treat as RC on-chip, and treat as LC for PC board interconnect So, what are the rules of thumb to use?
Other “Rules of Thumb” ,[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6
When does a T-line become a T-Line? Transmission Lines  Class  6 ,[object Object],[object Object],When do we need to use transmission line analysis techniques vs. lumped circuit analysis?  Tline Wavelength/edge rate
Equations & Formulas How to model & explain transmission line behavior
Relevant Transmission Line Equations ,[object Object],Transmission Lines  Class  6 Characteristic Impedance equation In class problem: Derive the high frequency, lossless approximation for Z0    is the attenuation (loss) factor    is the phase (velocity) factor
Ideal Transmission Line Parameters ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6 Don’t forget these relationships and what they mean! . ; ; ; 1 ; ; ; ; 0 0 0 0 0 0 0 0 0 0 0 0 0 d 0 0 0         r r L C v T Z L Z T C C L T C L Z        
Parallel Plate  Approximation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6 To a first order, t-line capacitance and inductance can be approximated using the parallel plate approximation. Base equation
Improved Microstrip Formula ,[object Object],[object Object],[object Object],Transmission Lines  Class  6 From Hall, Hall & McCall: Valid when: 0.1 < W C /T D  < 2.0 and 1 <   r  < 15 You can’t beat a field solver
Improved Stripline Formulas ,[object Object],Transmission Lines  Class  6 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 can’t beat a field solver
Refection coefficient ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6
Reflection and  Transmission Transmission Lines  Class  6   Incident Reflected Transmitted
Special Cases to Remember Transmission Lines  Class  6 Phone call Voice Changer   Friday, 18 June 2010 22:53 | Written by EEE-LAB |                 User Rating:    / 6   PoorBest    Voice manipulation device specially intended for props 9V Battery operation Parts  List : P1______________10K Log. Potentiometer R1,R10__________10K 1/4W Resistors R2_______________1K 1/4W Resistor R3______________50K 1/2W Trimmer Cermet or Carbon R4,R6,R7,R14___100K 1/4W Resistors R5______________47K 1/4W Resistor R8______________68K 1/4W Resistor R9_______________2K2 1/2W Trimmer Cermet or Carbon R11_____________33K 1/4W Resistor R12_____________18K 1/4W Resistor R13_____________15K 1/4W Resistor C1,C2,C3,C8,C9_100nF 63V Polyester Capacitors C4______________10µF 25V Electrolytic Capacitor C5_____________220nF 63V Polyester Capacitor (Optional, see Notes) C6_______________4n7 63V Polyester Capacitor C7______________10nF 63V Polyester Capacitor C10____________220µF 25V Electrolytic Capacitor IC1___________LM358 Low Power Dual Op-amp IC2_________TDA7052 Audio power amplifier IC MIC1__________Miniature electret microphone SPKR______________8 Ohm Small Loudspeaker SW1____________DPDT Toggle or Slide Switch SW2,SW3________SPST Toggle or Slide Switches J1____________6.3mm or 3mm Mono Jack socket B1_______________9V PP3 Battery (See Notes) Clip for PP3 Battery Although this kind of voice effect can be obtained by means of some audio computer programs,  a few correspondents required a stand-alone device, featuring microphone input and line or  loudspeaker outputs. Notes: * The pass-band filter can be bypassed by means of SW1A and B: in this case, a  non-manipulated microphone signal will be directly available at the line or  loudspeaker outputs after some amplification through IC1A. * R3 sets the gain of the microphone preamp. Besides setting the microphone gain, this  control can be of some utility in adding some amount of distortion to the signal,  thus allowing a more realistic imitation of a telephone call voice. * R9 is the steep control of the pass-band filter. It should be used with care, in order  to avoid excessive ringing when filter steepness is approaching maximum value. * P1 is the volume control and SW2 will switch off amplifier and loudspeaker if desired. * C5 is optional: it will produce a further band reduction. Some people think the  resulting effect is more realistic if this capacitor is added. * If the use of an external, moving-coil microphone is required, R1 must be omitted,  thus fitting a suitable input jack. * This circuit was intended to be powered by a 9V PP3 battery, but any dc power supply in the  6 - 12V range can be used successfully.   Last Updated (Saturday, 26 February 2011 14:16) 1       Zo Zo  0     Zo Zo Zo Zo  1 0 0      Zo Zo  Vs Zs Zo Zo A: Terminated in  Zo Vs Zs Zo B: Short Circuit Vs Zs Zo C: Open Circuit Audio  -  Amplifier   Next >
Assignment – Building the SI Tool Box Transmission Lines  Class  6 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?
Transmission line equivalent circuits and relevant equations Transmission Lines  Class  6 ,[object Object],[object Object]
Review: Voltage Divider Circuit ,[object Object],[object Object],Transmission Lines  Class  6 Why do we care for?  Next page….  R S R L V S V L R S R L R L V S V L + =
Solving Transmission Line Problems ,[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6 These are the steps for solving all t-line problems.
Determining Launch Voltage ,[object Object],[object Object],Transmission Lines  Class  6 Vs Zo Rs Vs 0 TD Rt A  B  t=0, V=Vi (initial voltage) R S Z 0 Z 0 V S V i + = R S R t R t V S V f + =
Voltage Delivered to the Load Transmission Lines  Class  6 ,[object Object],[object Object],[object Object],[object Object],[object Object],Vs Zo Rs Vs 0 TD   Rt A  B  t=0, V=Vi t=TD, V=Vi +   B (Vi ) t=2TD,  V=Vi +   B (Vi) +   A  B )(Vi ) (signal is reflected) (initial voltage) Zo Rt Zo Rt      V reflected  =    (V incident ) V B  = V incident  + V reflected
Voltage Reflected Back to the Source Transmission Lines  Class  6 Vs Zo Rs Vs 0 TD   Rt A  B  t=0, V=Vi t=TD, V=Vi +   B (Vi ) t=2TD,  V=Vi +   B (Vi) +   A  B )(Vi ) (signal is reflected) (initial voltage)  A  B
Voltage Reflected Back to the Source Transmission Lines  Class  6 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Zo Rs Zo Rs      V reflected  =    (V incident ) V A  = V launch  + V incident  + V reflected
Problems ,[object Object],Transmission Lines  Class  6 Solved Homework
Step-Function into T-Line: Relationships ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6 Solution Phone call Voice Changer   Friday, 18 June 2010 22:53 | Written by EEE-LAB |                 User Rating:    / 6   PoorBest    Voice manipulation device specially intended for props 9V Battery operation Parts List : P1______________10K Log. Potentiometer R1,R10__________10K 1/4W Resistors R2_______________1K 1/4W Resistor R3______________50K 1/2W Trimmer Cermet or Carbon R4,R6,R7,R14___100K 1/4W Resistors R5______________47K 1/4W Resistor R8______________68K 1/4W Resistor R9_______________2K2 1/2W Trimmer Cermet or Carbon R11_____________33K 1/4W Resistor R12_____________18K 1/4W Resistor R13_____________15K 1/4W Resistor C1,C2,C3,C8,C9_100nF 63V Polyester Capacitors C4______________10µF 25V Electrolytic Capacitor C5_____________220nF 63V Polyester Capacitor (Optional, see Notes) C6_______________4n7 63V Polyester Capacitor C7______________10nF 63V Polyester Capacitor C10____________220µF 25V Electrolytic Capacitor IC1___________LM358 Low Power Dual Op-amp IC2_________TDA7052 Audio power amplifier IC MIC1__________Miniature electret microphone SPKR______________8 Ohm Small Loudspeaker SW1____________DPDT Toggle or Slide Switch SW2,SW3________SPST Toggle or Slide Switches J1____________6.3mm or 3mm Mono Jack socket B1_______________9V PP3 Battery (See Notes) Clip for PP3 Battery Although this kind of voice effect can be obtained by means of some audio computer programs,  a few correspondents required a stand-alone device, featuring microphone input and line or  loudspeaker outputs. Notes: * The pass-band filter can be bypassed by means of SW1A and B: in this case, a  non-manipulated microphone signal will be directly available at the line or  loudspeaker outputs after some amplification through IC1A. * R3 sets the gain of the microphone preamp. Besides setting the microphone gain, this  control can be of some utility in adding some amount of distortion to the signal,  thus allowing a more realistic imitation of a telephone call voice. * R9 is the steep control of the pass-band filter. It should be used with care, in order  to avoid excessive ringing when filter steepness is approaching maximum value. * P1 is the volume control and SW2 will switch off amplifier and loudspeaker if desired. * C5 is optional: it will produce a further band reduction. Some people think the  resulting effect is more realistic if this capacitor is added. * If the use of an external, moving-coil microphone is required, R1 must be omitted,  thus fitting a suitable input jack. * This circuit was intended to be powered by a 9V PP3 battery, but any dc power supply in the  6 - 12V range can be used successfully.   Last Updated (Saturday, 26 February 2011 14:16) Audio  -  Amplifier   Next >
Step-Function into T-Line with Open Ckt ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6 Solution
Waveshape: Step-Function into T-Line with Open Ckt  Transmission Lines  Class  6 This is called “reflected wave switching” Solution
Problem 1b: Relationships ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6 Solution
Problem 1b: Solution ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6 Solution
Waveshapes for Problem 1b  Transmission Lines  Class  6 Note that a properly terminated wave settle out at 0.5 V Solution Solution
Transmission line step response Transmission Lines  Class  6 ,[object Object],[object Object],[object Object],Complex signal reflections at different types of transmission line “discontinuities” will be analyzed in this chapter. Lattice diagrams will be introduced as a solution tool.
Lattice Diagram Analysis – Key Concepts ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Transmission Lines  Class  6 The lattice diagram is a tool/technique to simplify the accounting of reflections and waveforms Vs Rs Zo V(source) V(load) TD = N  ps 0 Vs Rt Time V(source) V(load) a source  load  b A c A’ B’ C’ d B e 0 N  ps 2N  ps 3N  ps 4N  ps 5N  ps
Lattice Diagram Analysis – Detail Transmission Lines  Class  6 V(source) V(load) V launch source  load  V launch   load V launch 0 V launch (1+  load ) V launch (1+  load  +  load   source ) Time 0 2N  ps 4N  ps V launch   load  source V launch    load  source V launch    load   source V launch (1+  load +   load  source +    load   source ) Time N  ps 3N  ps 5N  ps Vs Rs Zo V(source) V(load) TD = N  ps 0 Vs Rt
Transient Analysis – Over Damped Transmission Lines  Class  6
Transient Analysis – Under Damped Transmission Lines  Class  6 1 50 50 33333 . 0 50 25 50 25 3333 . 1 50 25 50 ) 2 (                             Zo Zl Zo Zl Zo Zs Zo Zs Zo Zs Zo Vs V load source initial   Assume Zs=25 ohms  Zo =50ohms Vs=0-2 volts Vs Zs Zo V(source) V(load) TD = 250  ps 0 2 v Time V(source) V(load) 1.33v 3333 . 0   source  1  load  1.33v 1.33v -0.443v 0v 2.66v 1.77v -0.443v 2.22v 0.148v 0 500  ps 1000  ps 1500  ps 2000  ps 2500  ps 1.92 0.148v 2.07 Response from lattice diagram 0 0.5 1 1.5 2 2.5 3 0 250 500 750 1000 1250 1500 1750 2000 2250 Time, ps Volts Source Load
Two Segment Transmission Line Structures Transmission Lines  Class  6
Assignment ,[object Object],[object Object],Transmission Lines  Class  6 Previous examples are the preparation

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Class06 transmission line_basics

  • 1. Transmission Line Basics II - Class 6 Prerequisite Reading assignment: CH2 Acknowledgements: Intel Bus Boot Camp: Michael Leddige
  • 2. Real Computer Issues Transmission Lines Class 6 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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  • 15. Signal Frequency and Edge Rate vs. Lumped or Tline Models Transmission Lines Class 6 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.
  • 16. T Line Rules of Thumb Transmission Lines Class 6 Td < .1 Tx Td < .4 Tx May treat as lumped Capacitance Use this 10:1 ratio for accurate modeling of transmission lines May treat as RC on-chip, and treat as LC for PC board interconnect So, what are the rules of thumb to use?
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  • 19. Equations & Formulas How to model & explain transmission line behavior
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  • 26. Reflection and Transmission Transmission Lines Class 6   Incident Reflected Transmitted
  • 27. Special Cases to Remember Transmission Lines Class 6 Phone call Voice Changer Friday, 18 June 2010 22:53 | Written by EEE-LAB |     User Rating:   / 6 PoorBest  Voice manipulation device specially intended for props 9V Battery operation Parts List : P1______________10K Log. Potentiometer R1,R10__________10K 1/4W Resistors R2_______________1K 1/4W Resistor R3______________50K 1/2W Trimmer Cermet or Carbon R4,R6,R7,R14___100K 1/4W Resistors R5______________47K 1/4W Resistor R8______________68K 1/4W Resistor R9_______________2K2 1/2W Trimmer Cermet or Carbon R11_____________33K 1/4W Resistor R12_____________18K 1/4W Resistor R13_____________15K 1/4W Resistor C1,C2,C3,C8,C9_100nF 63V Polyester Capacitors C4______________10µF 25V Electrolytic Capacitor C5_____________220nF 63V Polyester Capacitor (Optional, see Notes) C6_______________4n7 63V Polyester Capacitor C7______________10nF 63V Polyester Capacitor C10____________220µF 25V Electrolytic Capacitor IC1___________LM358 Low Power Dual Op-amp IC2_________TDA7052 Audio power amplifier IC MIC1__________Miniature electret microphone SPKR______________8 Ohm Small Loudspeaker SW1____________DPDT Toggle or Slide Switch SW2,SW3________SPST Toggle or Slide Switches J1____________6.3mm or 3mm Mono Jack socket B1_______________9V PP3 Battery (See Notes) Clip for PP3 Battery Although this kind of voice effect can be obtained by means of some audio computer programs, a few correspondents required a stand-alone device, featuring microphone input and line or loudspeaker outputs. Notes: * The pass-band filter can be bypassed by means of SW1A and B: in this case, a non-manipulated microphone signal will be directly available at the line or loudspeaker outputs after some amplification through IC1A. * R3 sets the gain of the microphone preamp. Besides setting the microphone gain, this control can be of some utility in adding some amount of distortion to the signal, thus allowing a more realistic imitation of a telephone call voice. * R9 is the steep control of the pass-band filter. It should be used with care, in order to avoid excessive ringing when filter steepness is approaching maximum value. * P1 is the volume control and SW2 will switch off amplifier and loudspeaker if desired. * C5 is optional: it will produce a further band reduction. Some people think the resulting effect is more realistic if this capacitor is added. * If the use of an external, moving-coil microphone is required, R1 must be omitted, thus fitting a suitable input jack. * This circuit was intended to be powered by a 9V PP3 battery, but any dc power supply in the 6 - 12V range can be used successfully. Last Updated (Saturday, 26 February 2011 14:16) 1       Zo Zo  0     Zo Zo Zo Zo  1 0 0      Zo Zo  Vs Zs Zo Zo A: Terminated in Zo Vs Zs Zo B: Short Circuit Vs Zs Zo C: Open Circuit Audio - Amplifier Next >
  • 28. Assignment – Building the SI Tool Box Transmission Lines Class 6 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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  • 34. Voltage Reflected Back to the Source Transmission Lines Class 6 Vs Zo Rs Vs 0 TD Rt A B t=0, V=Vi t=TD, V=Vi +  B (Vi ) t=2TD, V=Vi +  B (Vi) +  A  B )(Vi ) (signal is reflected) (initial voltage)  A  B
  • 35.
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  • 39. Waveshape: Step-Function into T-Line with Open Ckt Transmission Lines Class 6 This is called “reflected wave switching” Solution
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  • 42. Waveshapes for Problem 1b Transmission Lines Class 6 Note that a properly terminated wave settle out at 0.5 V Solution Solution
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  • 45. Lattice Diagram Analysis – Detail Transmission Lines Class 6 V(source) V(load) V launch source  load  V launch  load V launch 0 V launch (1+  load ) V launch (1+  load +  load  source ) Time 0 2N ps 4N ps V launch  load  source V launch   load  source V launch   load   source V launch (1+  load +   load  source +   load   source ) Time N ps 3N ps 5N ps Vs Rs Zo V(source) V(load) TD = N ps 0 Vs Rt
  • 46. Transient Analysis – Over Damped Transmission Lines Class 6
  • 47. Transient Analysis – Under Damped Transmission Lines Class 6 1 50 50 33333 . 0 50 25 50 25 3333 . 1 50 25 50 ) 2 (                             Zo Zl Zo Zl Zo Zs Zo Zs Zo Zs Zo Vs V load source initial   Assume Zs=25 ohms Zo =50ohms Vs=0-2 volts Vs Zs Zo V(source) V(load) TD = 250 ps 0 2 v Time V(source) V(load) 1.33v 3333 . 0   source  1  load  1.33v 1.33v -0.443v 0v 2.66v 1.77v -0.443v 2.22v 0.148v 0 500 ps 1000 ps 1500 ps 2000 ps 2500 ps 1.92 0.148v 2.07 Response from lattice diagram 0 0.5 1 1.5 2 2.5 3 0 250 500 750 1000 1250 1500 1750 2000 2250 Time, ps Volts Source Load
  • 48. Two Segment Transmission Line Structures Transmission Lines Class 6
  • 49.