Differential Impedance finally made simple

Transcription

1 Slide - Differential Impedance finally made simple Eric Bogatin President Bogatin Enterprises eric@bogent.com Slide -2 Overview What s impedance Differential Impedance: a simple perspective Coupled Transmission line formalism Measuring differential impedance Emulating effects of a split in return path Calculating differential impedance

2 Slide -3 First Order Model of a Transmission Line (Loss Less Model) x C L L L L L C C C C C (unbalanced transmission line) L C = C L x L = L L x capacitance inductance (loop) The circuit analysis result: Z 0 = L L TD = LtotalCtotal C υ = L L L C L Slide -4 be the signal courtesy ICE

3 Slide -5 0th Order Model of Transmission Line x C L = Capacitance per length [pf/in] V in C C C C C C C C C C = C L x Q = CV, every t = x v I, V definition of Transmission Line: I = Q t = vc L xv x = vc L V What s the impedance? Slide -6 Instantaneous Impedance of a Transmission Line I = vc L V Z = V I = Z 0 = vc L V vc L V = vc L Features of the impedance: looks like a resistor dependant on intrinsic properties only is an intrinsic property independent of length defined as the "characteristic impedance" = Z 0 also called the surge impedance or wave impedance

4 Slide -7 Characteristic Impedance and Capacitance per Length increase h What happens to the capacitance per length? The characteristic impedance? w = 0 mils h = 5 mils 50 Ohm PCB cross section increase w What happens to the capacitance per length? The characteristic impedance? Z 0 ~ C L Slide -8 What Does it Mean to Have a 50 Ohm Line? Verrrry longgggg 50 Ohm coax Ω What will Ohm-meter read? For the first second? After 3 seconds? After 0 sec?

5 Slide -9 An important Distinction THE impedance of the transmission line (may be time dependent) The instantaneous impedance of the transmission line The Characteristic impedance of the transmission line Just referring to the impedance may be a bit ambiguous Slide -0 Return Path in T Lines Current into signal line TD = sec Where is the return path? For DC currents: For RF currents? When does current come out return path?

6 Current Flow in the Transmission Line signal Slide - L L L L L L C C C C C C It s a propagating wave. What happens initially if the end is open?, shorted?, terminated? To control impedance, manage the return path as carefully as the signal path Slide -2 The Growing Importance of Differential Pair Use Early Applications for Differential Pairs MECL I 962 MECL II 966 MECL III 968 MECL 0k 979 MECL 0kH 98 ANSI/TIA/EIA is the generic physical layer standard for LVDS. It was approved in November of 995, and first published in March of 996. Example: high speed serial transmission TI.8 Gbps LVDS TRX IEEE394 IEEE488 Gigabit Ethernet

7 Slide -3 What s a Differential Pair Transmission Line???? Slide -4 What s a Differential Pair Transmission Line? Answer:..any two, coupled transmission lines (with their return paths). 2 A special case: a symmetric pair What s differential impedance?

8 Slide -5 Differentially Driving a Differential Pair V = v 0v V = 0 v Difference signal 2 2 What is the difference signal? Slide -6 The Difference Signal V = v 0v V = 0 v Difference signal Difference voltage = 2v : -v +v What is the impedance the difference signal sees?

9 Slide -7 Differential Impedance Differential Impedance: the impedance the difference signal sees Z ( diff ) V = I ( diff ) one 2V = I one 2( Z 0 small) Differential impedance decreases as coupling increases C 2 +v -v I one x I two C C 22 How will the capacitance matrix elements be affected by spacing? Slide -8 Capacitance Matrix Elements C 2 4 C C 22 +v S +v Capacitance per Length (pf/in) C C Edge to Edge Separation (mils) What happens to the differential impedance as S gets smaller?

10 How to Terminate the Difference Signal? Slide -9 V = v 0v V = 0 v Difference signal Z ( diff ) V = I ( diff ) one 2V = I one 2( Z 0 small) If there is no coupling, and each line is 50W, what resistor terminates the differential pair? Terminate with a resistor to match impedance of the difference signal Slide -20 Formalism: Mode Pattern for Identical Traces Hyperlynx simulation +v -v +v +v I odd x x I even Mode: odd, or, or a Mode: even, or 2, or b Corresponds to differential driven Corresponds to common driven What is I odd compared to I even? How do they vary with spacing?

11 Slide -2 Odd and Even Mode Impedance Z = odd V I odd Z = even V I even Hyperlynx simulation +v -v +v +v I odd x x I even Mode: odd, or, or a Mode: even, or 2, or b Odd mode current increases as traces are brought together Odd mode impedance decreases Even mode current decreases as traces are brought together Even mode impedance increases Slide -22 Differential Impedance and Odd Mode Impedance V = v 0v V = 0 v Difference signal ( ) V diff 2 V Z( diff ) = = = 2 x Z I I one one odd

12 Slide -23 The Characteristic Impedance Matrix I I 2 x x V V 2 Define a Characteristic Impedance Matrix V = + ZI Z2I2 V = + 2 Z22I2 Z2I How is Z 2 influenced by coupling? Is Z 2 large or small? Characteristic Impedance Matrix [ohms]: Hyperlynx simulation Slide -24 (Special case: symmetric) Definition of Odd and Even Mode Impedance I I 2 x x V V 2 Define: V odd = V 2 ( ) V V even = V + V 2 2 ( ) 2 Z Z odd even V = I V = I odd V even =0 even V odd =0 What is the voltage when V even = 0? When V odd = 0?

13 Odd Mode: I Odd and Even Mode Impedance V + = ZI Z2I2 V + = I 2 I = 2 = Z22I2 Z2I V odd Z odd Slide -25 ( V V 2 ) = ( Z Z 2 ) I ( ) = 2 = Z Z 2 Odd mode impedance is reduced with coupling V even = V + V = Z + Z 2 Even Mode: I 2 ( 2 ) ( 2 ) Z even = Z + Z 2 Even mode impedance is increased with coupling I Slide -26 Mode Impedances Odd mode impedance is the impedance of one line when the pair is driven differentially Differential impedance: ( ) ( ) Z odd = ( ) Z Z 2 V diff 2V Z diff = = = 2( Z ) = odd 2 Z Z I I ( ) 2 Even mode impedance is the impedance of one line when the pair is driven commonly Z even = Z + Z 2 Common impedance: Z = Z = common even Z + Z 2

14 Slide -27 Summary So Far A differential pair is any two transmission lines Special case: symmetric lines Differential driving has symmetric, opposite signal on each line Differential impedance is the impedance the difference signal sees With no coupling, current into one line depends on capacitance per length of the line With coupling, current into one line depends on how the other line is driven The impedance of one line will depend on how the other line is driven The differential impedance will be twice the impedance of one line when the pair is driven differentially Slide -28 How can differential impedance be measured?

15 Slide -29 TDR Equipment HP 83480A Digital Communications Analyzer (mainframe) TDR: TDT: DTDR: DTDT: Time Domain Reflection Time Domain Transmission Differential Time Domain Reflection Differential Time Domain Transmission HP 54754A Differential TDR Module Two independent TDR channels - simultaneous TDR/TDT - simultaneous differential TDR HP 83484A 2 Channel 50 GHz Module Two independent voltage channels Slide -30 Conventional Single Channel TDR TDR: 400 mv output, unloaded 50W output impedance V measured (DUT) Device Under Test 3 different line width microstrips, each 9 inches long 50W cable TDR response w = h w = 2h w = 8h 50 mv/div 500 psec/div --400mV --300mV --200mV --00mV --0mv

16 Slide -3 Converting Reflected Voltage into Impedance Voltage scale V ρ = V reflected incident Z DUT ρ = 50Ω + ρ Impedance scale Plotting impedance directly 70W- 60W- 50W- 40W- 30W- 20W- 0W/div 500 psec/div Slide -32 Two Channel Differential TDR: Differential or Common Driven Driving differential signal open open Driving common signal open open 400mV-- 200mV-- 0mV mV mV-- 400mV-- 200mV-- 0mV mV mV-- Channel Channel 2 Channel Channel psec/div 200 psec/div

17 Slide -33 Measuring Odd and Even Impedance of Tightly Coupled Lines Measured Impedance of one trace, as the other is driven: Odd mode impedance: differentially driven pair Even mode impedance: commonly driven pair For identical lines: Z = ½ (Z even + Z odd ) Z 2 = ½ (Z even Z odd ) 60W 55W Extracted Characteristic impedance matrix 50W 45W 40W 500 psec/div Replace this with a good one Z even Common driven Not driven Differentially driven Z odd Slide -34 Direct Measurement of Differential Impedance Z diff = Z odd + Z odd2 05W 50W 45W 40W Differential impedance Line 2 Z odd Line Z odd 00W 95W 90W

18 Slide -35 Measuring Differential Impedance of Low Impedance Traces 50W- 40W- 30W- 20W- Z odd Differential impedance -00W - 80W - 60W - 40W Slide -36 Full Characterization of a Differentially Driven, Differential Pair TDR V V2 TDR2 00mV/div V V 2 V diff 200mV/div 50mV/div 50W cable SMA TDR2 TDR 2V comm

19 Slide -37 Full Characterization of a Single End Driven, Differential Pair TDR V FEXT NEXT 00mV/div V FEXT Odd mode has shorter TD than even mode V diff 200mV/div 50mV/div 50W cable SMA NEXT TDR 2V comm Slide -38 Differential Pair Over Split in the Return Path inch What will be the behavior when: single end driven differentially driven?

20 Slide -39 Full Characterization of a Single End Driven, Differential Pair Over a Split in the Return Path 00mV/div V FEXT 200mV/div SMA V diff 2V comm 50mV/div 50W cable TDR NEXT return current Slide -40 Full Characterization of a Differentially Driven, Differential Pair Over a Split in the Return Path 00mV/div V V 2 V diff 200mV/div SMA 2V comm 50mV/div 50W cable TDR2 TDR

21 Slide -4 Measured Impedances 30W- 40W- 20W- 00W- Differential impedance 70W- 50W- Z odd Ansoft Maxwell 2D Extractor Slide -42 Impedance as the Dielectric Thickness Increases Characteristic Impedance (Ohms) Dielectric Thickness (mils) Ansoft Maxwell 2D Extractor Z Z diff Z 2 Z diff ~ 40 Ohms with the bottom plane as the return path, when far away (when Z 2 is a large fraction of Z, coupling dominates, differential impedance approaches single ended impedance)

22 Slide -43 What Are the Return Currents When Driven Differentially? Return Currents in Differential Pairs Slide -44 Most return current is carried by the plane when trace to plane coupling >> trace to trace coupling Ex: most board level interconnects Most return current is carried by the other trace when trace to plane coupling << trace to trace coupling Ex: most connectors, shielded twisted pair, twisted pair

23 Slide -45 First Order Approximations to Differential Impedance: Microstrip s Z diff = Z 0.48exp h Impedance (Ohms) s 2 0 h National Semiconductor model Apnote Edge to Edge Separation (mils) 2(Z -Z 2 ) Symbols are extracted with field solver Line is National model Z Z 2 Slide -46 First Order Approximations to Differential Impedance: Stripline s Z diff = 2Z exp 2. 9 b National Semiconductor model Apnote 905 b s Impedance (Ohms) Edge to Edge Separation (mils) 2(Z -Z 2 ) Z Z 2 Symbols are extracted with field solver Line is National model Note, accurate only for Z 0 values near 50 Ohms!

24 Slide -47 Impact from Width of the Line b = 5 mils s = 5 mils Sweeping w b s National Semi model Impedance (Ohms) Z diff Z 0 0 Z Line Wdith (mils) filled with air Radius of shield, r 3 Shielded Twin Leads, Changing Shield Size differential impedance approaches single ended impedance when r s > 3 x pitch Slide -48 r = 0 mils Single ended impedance = 20W r 2 = 25 mils ε = 4 Pitch = 50 mils Impedance (Ohms) Z com Radius of Shield (mils) Ansoft Maxwell 2D Extractor Z Z 2 Z dif

25 Slide -49 Summary The impedance of one line in a differential pair depends on how the other is being driven: Measure odd impedance by driving differentially Measure even impedance by driving in common Requires Differential TDR (DTDR) Characteristic impedance matrix elements can be extracted from odd and even impedances A gap in the return path causes huge increase in cross talk in single ended lines due to high mutual inductance If you must cross a split plane, better to use a diff pair Some increase in differential impedance Very little distortion of differential signal Very little common voltage created Full characterization of differential pairs is possible with DTDR and dual channel amplifier module Slide -50 For more information on resources and references, visit our web site: