Differential Impedance …finally made simple
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Slide -1 Training for Signal Integrity and Interconnect Design MYTHS Differential Impedance …finally made simple Eric Bogatin President Bogatin Enterprises www.BogatinEnterprises.com 913-393-1305 eric@bogent.com Eric Bogatin 2000 www.BogatinEnterprises.com Slide -2 Training for Signal Integrity and Interconnect Design MYTHS • • • • • • 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 Eric Bogatin 2000 www.BogatinEnterprises.com Slide -3 Training for Signal Integrity and Interconnect Design First Order Model of a Transmission Line (Loss Less Model) MYTHS ∆x L C L C L C L C L C L C C = CL ∆x capacitance L = LL ∆x inductance (loop) (unbalanced transmission line) The circuit analysis result: Z0 = LL CL TD = LtotalC total Eric Bogatin 2000 υ= 1 LLC L www.BogatinEnterprises.com Slide -4 Training for Signal Integrity and Interconnect Design “…be the signal” MYTHS courtesy ICE Eric Bogatin 2000 www.BogatinEnterprises.com Slide -5 Training for Signal Integrity and Interconnect Design MYTHS 0th Order Model of Transmission Line ∆x Vin C C CL= Capacitance per length [pF/in] C C C C C C C C = C L ∆x ∆Q = CV, ∆x every ∆t = v I, V definition of Transmission Line: I = ∆∆Qt = vCL ∆ x V = vCLV ∆x What’s the impedance? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -6 Training for Signal Integrity and Interconnect Design MYTHS Instantaneous Impedance of a Transmission Line I = v C LV V = 1 Z = V = vC vCL I LV 1 Z0= 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" = Z0 • also called the “surge impedance” or “wave impedance” Eric Bogatin 2000 www.BogatinEnterprises.com Slide -7 Training for Signal Integrity and Interconnect Design MYTHS Characteristic Impedance and Capacitance per Length What happens to the capacitance per length? The characteristic impedance? increase h w = 10 mils h = 5 mils 50 Ohm PCB cross section increase w Z0 ~ What happens to the capacitance per length? The characteristic impedance? 1 CL Eric Bogatin 2000 www.BogatinEnterprises.com Slide -8 Training for Signal Integrity and Interconnect Design MYTHS What Does it Mean to Have a 50 Ohm Line? coax 50 Ohm g g g g g lon Verrrry Ω What will Ohm-meter read? For the first second? After 3 seconds? After 10 sec? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -9 Training for Signal Integrity and Interconnect Design MYTHS 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 Eric Bogatin 2000 www.BogatinEnterprises.com Slide -10 Training for Signal Integrity and Interconnect Design MYTHS Return Path in T Lines Current into signal line TD = 1 sec Where is the return path? For DC currents: For RF currents? When does current come out return path? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -11 Training for Signal Integrity and Interconnect Design Current Flow in the Transmission Line MYTHS signal L C L L C C L C L C L 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 Eric Bogatin 2000 www.BogatinEnterprises.com Slide -12 Training for Signal Integrity and Interconnect Design MYTHS The Growing Importance of Differential Pair Use Early Applications for Differential Pairs MECL I MECL II MECL III MECL 10k MECL 10kH 1962 1966 1968 1979 1981 ANSI/TIA/EIA-644-1995 is the generic physical layer standard for LVDS. It was approved in November of 1995, and first published in March of 1996. Example: high speed serial transmission à IEEE1394 à IEEE488 à Gigabit Ethernet TI 1.8 Gbps LVDS TRX Eric Bogatin 2000 www.BogatinEnterprises.com Slide -13 Training for Signal Integrity and Interconnect Design MYTHS What’s a Differential Pair Transmission Line? ??? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -14 Training for Signal Integrity and Interconnect Design MYTHS What’s a Differential Pair Transmission Line? Answer: …..any two, coupled transmission lines (with their return paths). 1 2 A special case: a symmetric pair What’s differential impedance? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -15 Training for Signal Integrity and Interconnect Design Differentially Driving a Differential Pair MYTHS 1 Difference signal V = 0à à1v V = 1và à0v 2 1 2 What is the difference signal? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -16 Training for Signal Integrity and Interconnect Design The Difference Signal MYTHS Difference signal V = 0à à1v V = 1và à0v 1 2 +1 Difference voltage = 2v : -1v à +1v -1 What is the impedance the difference signal sees? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -17 Training for Signal Integrity and Interconnect Design Differential Impedance MYTHS Differential Impedance: the impedance the difference signal sees Z (diff ) = V (diff ) 2V = ≈ 2(Z0 − small ) Ione I one Differential impedance decreases as coupling increases C12 +1v Ione -1v Itwo x C11 C22 How will the capacitance matrix elements be affected by spacing? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -18 Training for Signal Integrity and Interconnect Design MYTHS Capacitance Matrix Elements C12 C11 +1v C22 S +1v Capacitance per Length (pF/in) 4 C11 3 2 1 C21 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Edge to Edge Separation (mils) What happens to the differential impedance as S gets smaller? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -19 Training for Signal Integrity and Interconnect Design How to Terminate the Difference Signal? MYTHS Difference signal V = 0à à1v V = 1và à0v Z (diff ) = V (diff ) 2V = ≈ 2(Z0 − small ) Ione I one If there is no coupling, and each line is 50Ω Ω, what resistor terminates the differential pair? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -20 Training for Signal Integrity and Interconnect Design MYTHS Terminate with a resistor to match impedance of the difference signal Formalism: Mode Pattern for Identical Traces Hyperlynx simulation +1v Iodd +1v -1v +1v Ievenx x Mode: odd, or 1, or a Mode: even, or 2, or b Corresponds to differential driven Corresponds to common driven What is Iodd compared to Ieven? How do they vary with spacing? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -21 Training for Signal Integrity and Interconnect Design Odd and Even Mode Impedance MYTHS Zodd = +1v Iodd V Zeven = Iodd V Ieven +1v -1v Hyperlynx simulation +1v Ievenx x Mode: odd, or 1, or a Mode: even, or 2, or b Odd mode current increases as traces are brought together Even mode current decreases as traces are brought together Odd mode impedance decreases Even mode impedance increases Eric Bogatin 2000 www.BogatinEnterprises.com Slide -22 Training for Signal Integrity and Interconnect Design MYTHS Differential Impedance and Odd Mode Impedance Difference signal V = 1và à0v V = 0à à1v Z (diff ) = V (diff ) 2V = = 2 x Zodd Ione Ione Eric Bogatin 2000 www.BogatinEnterprises.com Slide -23 Training for Signal Integrity and Interconnect Design The Characteristic Impedance Matrix MYTHS I1 x I2 x V1 V2 Define a Characteristic Impedance Matrix V1 = Z11I1 + Z12I 2 How is Z12 influenced by coupling? Is Z12 large or small? V2 = Z 22I 2 + Z 21I1 Characteristic Impedance Matrix [ohms]: 1 2 1 49.6 6.4 2 6.4 49.6 Hyperlynx simulation Eric Bogatin 2000 www.BogatinEnterprises.com Slide -24 Training for Signal Integrity and Interconnect Design MYTHS Definition of Odd and Even Mode Impedance (Special case: symmetric) I1 x I2 x V1 1 (V1 − V2 ) 2 Zodd = 1 Veven = (V1 + V2 ) 2 Zeven = Vodd = Define: V2 Vodd I1 Veven =0 Veven I1 Vodd =0 What is the voltage when Veven = 0? When Vodd = 0? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -25 Training for Signal Integrity and Interconnect Design Odd and Even Mode Impedance MYTHS V1 = Z11I1 + Z12I 2 V2 = Z 22I 2 + Z21I1 Odd Mode: I1 = −I 2 Vodd = Zodd 1 (V − V ) = (Z11 − Z12 )I1 2 1 2 = (Z11 − Z12 ) Odd mode impedance is reduced with coupling Even Mode: 1 (V + V2 ) = (Z11 + Z12 )I1 2 1 Zeven = Z11 + Z12 I1 = I 2 Veven = Even mode impedance is increased with coupling Eric Bogatin 2000 www.BogatinEnterprises.com Slide -26 Training for Signal Integrity and Interconnect Design MYTHS Mode Impedances Odd mode impedance is the impedance of one line when the pair is driven differentially Differential impedance: Z (diff ) = V (diff ) 2V = = 2(Zodd ) = 2(Z11 − Z12 ) I I Even mode impedance is the impedance of one line when the pair is driven commonly Common impedance: Zodd = (Z11 − Z12 ) Zeven = Z11 + Z12 Zcommon = Zeven = Z11 + Z12 Eric Bogatin 2000 www.BogatinEnterprises.com Slide -27 Training for Signal Integrity and Interconnect Design Summary So Far MYTHS • 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 Eric Bogatin 2000 Training for Signal Integrity and Interconnect Design www.BogatinEnterprises.com Slide -28 MYTHS How can differential impedance be measured? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -29 Training for Signal Integrity and Interconnect Design TDR Equipment MYTHS TDR: TDT: DTDR: DTDT: HP 83480A Digital Communications Analyzer (mainframe) Time Domain Reflection Time Domain Transmission Differential Time Domain Reflection Differential Time Domain Transmission HP 83484A 2 Channel 50 GHz Module Two independent voltage channels HP 54754A Differential TDR Module Two independent TDR channels - simultaneous TDR/TDT - simultaneous differential TDR Eric Bogatin 2000 www.BogatinEnterprises.com Slide -30 Training for Signal Integrity and Interconnect Design Conventional Single Channel TDR MYTHS TDR: 400 mV output, unloaded 50Ω Ω output impedance Vmeasured TDR response --400mV (DUT) Device Under Test --300mV w=h 50Ω Ω cable w = 2h w = 8h 3 different line width microstrips, each 9 inches long 50 mV/div 500 psec/div Eric Bogatin 2000 --200mV --100mV --0mv www.BogatinEnterprises.com Slide -31 Training for Signal Integrity and Interconnect Design MYTHS Converting Reflected Voltage into Impedance Voltage scale ρ= Vreflected Vincident ZDUT = 50Ω 1− ρ 1+ ρ Impedance scale 70Ω Ω− 60Ω Ω− 50Ω Ω− Plotting 40Ω Ω− impedance 30Ω Ω− directly 20Ω Ω− 10Ω Ω/div 500 psec/div Eric Bogatin 2000 www.BogatinEnterprises.com Slide -32 Training for Signal Integrity and Interconnect Design MYTHS Two Channel Differential TDR: Differential or Common Driven Driving differential signal 400mV-200mV-- open 0mV--200mV-- open Channel 1 Channel 2 -400mV-200 psec/div Driving common signal 400mV-200mV-- open 0mV-- Channel 1 Channel 2 -200mV-- open -400mV-200 psec/div Eric Bogatin 2000 www.BogatinEnterprises.com Slide -33 Training for Signal Integrity and Interconnect Design MYTHS Measuring Odd and Even Impedance of Tightly Coupled Lines Measured Impedance of one trace, trace as the other is driven: Odd mode impedance: differentially driven pair Even mode impedance: commonly driven pair For identical lines: 500 psec/div Z11 = ½ (Zeven + Zodd) Ω Z12 = ½ (Zeven – Zodd) 60Ω 55Ω Ω 50Ω Ω Extracted 45Ω Ω Characteristic 40Ω Ω impedance matrix Replace this with a good one Zeven Common driven Zodd Not driven Differentially driven 48.5 3.5 3.5 48.5 Eric Bogatin 2000 www.BogatinEnterprises.com Slide -34 Training for Signal Integrity and Interconnect Design MYTHS Direct Measurement of Differential Impedance Zdiff = Zodd1 + Zodd2 105Ω Ω 100Ω Ω Differential impedance 50Ω Ω 45Ω Ω 40Ω Ω 95Ω Ω Line 1 Zodd 90Ω Ω Line 2 Zodd Eric Bogatin 2000 www.BogatinEnterprises.com Slide -35 Training for Signal Integrity and Interconnect Design Measuring Differential Impedance of Low Impedance Traces MYTHS -100Ω Ω - 80Ω Ω Differential impedance - 60Ω Ω - 40Ω Ω 50Ω Ω− 40Ω Ω− 30Ω Ω− Zodd 20Ω Ω− Eric Bogatin 2000 www.BogatinEnterprises.com Slide -36 Training for Signal Integrity and Interconnect Design MYTHS Full Characterization of a Differentially Driven, Differential Pair TDR1 V1 V2 TDR2 V1 100mV/div V2 Vdiff 200mV/div 2Vcomm SMA 50mV/div TDR2 50Ω Ω cable TDR1 Eric Bogatin 2000 www.BogatinEnterprises.com Slide -37 Training for Signal Integrity and Interconnect Design MYTHS Full Characterization of a Single End Driven, Differential Pair TDR1 V1 FEXT NEXT Odd mode has shorter TD than even mode V1 100mV/div FEXT Vdiff 200mV/div 2Vcomm SMA 50mV/div NEXT 50Ω Ω cable TDR1 Eric Bogatin 2000 www.BogatinEnterprises.com Slide -38 Training for Signal Integrity and Interconnect Design MYTHS Differential Pair Over Split in the Return Path 1 inch What will be the behavior when: à single end driven à differentially driven? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -39 Training for Signal Integrity and Interconnect Design Full Characterization of a Single End Driven, Differential Pair Over a Split in the Return Path MYTHS V1 100mV/div FEXT Vdiff 200mV/div 2Vcomm SMA 50mV/div 50Ω Ω cable NEXT TDR1 return current Eric Bogatin 2000 www.BogatinEnterprises.com Slide -40 Training for Signal Integrity and Interconnect Design MYTHS Full Characterization of a Differentially Driven, Differential Pair Over a Split in the Return Path V1 100mV/div V2 Vdiff 200mV/div 2Vcomm SMA 50mV/div TDR2 50Ω Ω cable TDR1 Eric Bogatin 2000 www.BogatinEnterprises.com Slide -41 Training for Signal Integrity and Interconnect Design Measured Impedances MYTHS 140Ω Ω− 120Ω Ω− Differential impedance 100Ω Ω− 70Ω Ω− Zodd 50Ω Ω− 30Ω Ω− Eric Bogatin 2000 www.BogatinEnterprises.com Slide -42 Training for Signal Integrity and Interconnect Design Impedance as the Dielectric Thickness Increases MYTHS Characteristic Impedance (Ohms) Ansoft Maxwell 2D Extractor Z11 200 180 160 Zdiff 140 Z21 Zdiff ~ 140 Ohms with the bottom plane as the return path, when far away 120 100 80 60 40 20 0 0 5 10 15 20 25 30 35 40 Dielectric Thickness (mils) Ansoft Maxwell 2D Extractor 45 50 (when Z21 is a large fraction of Z11, coupling dominates, differential impedance approaches single ended impedance) Eric Bogatin 2000 www.BogatinEnterprises.com Slide -43 Training for Signal Integrity and Interconnect Design MYTHS What Are the Return Currents When Driven Differentially? Eric Bogatin 2000 www.BogatinEnterprises.com Slide -44 Training for Signal Integrity and Interconnect Design Return Currents in Differential Pairs MYTHS 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 Eric Bogatin 2000 www.BogatinEnterprises.com Slide -45 Training for Signal Integrity and Interconnect Design First Order Approximations to Differential Impedance: Microstrip MYTHS s Zdiff = 2Z0 1 − 0.48 exp − 0.96 h s h National Semiconductor model Apnote 905 110 2(Z11-Z21) 100 90 Impedance (Ohms) 80 Symbols are extracted with field solver Line is National model 70 60 Z11 50 40 30 20 10 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Z21 Edge to Edge Separation (mils) Eric Bogatin 2000 www.BogatinEnterprises.com Slide -46 Training for Signal Integrity and Interconnect Design First Order Approximations to Differential Impedance: Stripline MYTHS s Zdiff = 2Z0 1 − 0.347 exp − 2.9 b s b National Semiconductor model Apnote 905 110 2(Z11-Z21) 100 Impedance (Ohms) 90 Symbols are extracted with field solver Line is National model 80 70 60 Z11 50 40 30 20 10 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Edge to Edge Separation (mils) Eric Bogatin 2000 Z21 Note, accurate only for Z0 values near 50 Ohms! www.BogatinEnterprises.com Slide -47 Training for Signal Integrity and Interconnect Design Impact from Width of the Line MYTHS b = 15 mils s = 5 mils Sweeping w s b 110 100 90 80 Impedance (Ohms) National Semi model 70 60 50 Zdiff 40 30 Z11 20 10 Z12 0 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Line Wdith (mils) Eric Bogatin 2000 www.BogatinEnterprises.com Slide -48 Training for Signal Integrity and Interconnect Design Shielded Twin Leads, Changing Shield Size MYTHS Radius of shield, r3 Impedance (Ohms) filled with air r1 = 10 mils Single ended impedance = 120Ω Ω r2 = 25 mils ε=4 Pitch = 50 mils 300 280 260 240 220 200 180 160 140 120 100 80 60 40 20 0 Zcom Z11 Z21 Zdif 0 100 200 300 400 500 600 700 Radius of Shield (mils) differential impedance approaches single ended impedance when rs > 3 x pitch Eric Bogatin 2000 Ansoft Maxwell 2D Extractor www.BogatinEnterprises.com Slide -49 Training for Signal Integrity and Interconnect Design Summary MYTHS • The impedance of one line in a differential pair depends on how the other is being driven: ü Measure odd impedance by driving differentially ü Measure even impedance by driving in common ü 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 ü Some increase in differential impedance ü Very little distortion of differential signal ü Very little common voltage created • Full characterization of differential pairs is possible with DTDR and dual channel amplifier module Eric Bogatin 2000 www.BogatinEnterprises.com Slide -50 Training for Signal Integrity and Interconnect Design MYTHS For more information on resources and references, visit our web site: www.BogatinEnterprises.com Eric Bogatin 2000 www.BogatinEnterprises.com
