Non-Sinusoidal Waves on (Mostly Lossless)Transmission Lines

Transcription

1 Non-Sinusoidal Waves on (Mostly Lossless)Transmission Lines Don Estreich Salazar 21C Adjunct Professor Engineering Science October

2 Outline of Presentation 1. Motivation: Signal Integrity 2. Discontinuities in PCB microstrip and stripline in PCB 3. Some examples of PCB microwave circuits 4. Dispersion in Transmission Lines 5. Time Domain Reflectometry (unit step echoes) 6. Probing PCB and electronic assemblies 7. Brief review of transmission lines (with Smith Chart) 8. Surge impedance terminology 9. Step response for resistive loads 1.Step response for opens and shorts 11.Step response for and capacitive and inductive loads 12.Discontinuities along transmission lines 13.Using lattice diagrams for transmission lines 14.Wrap-up 2

3 Signal Integrity in Packages and PCBs (PWBs) Carrier or Package PCB Interconnect Edge connectors Model with Parasitics 3

4 Signal Integrity in a backplane Fast IC > 2 GHz signals 4

5 Sources of discontinuities in Printed Circuit Boards Most high speed signals are differential Some particular origins of discontinuities in PCB/PWB Agilent Signal Integrity Analysis Series Part 1: Single-Port TDR, TDR/TDT, and 2-Port TDR 5

6 Microstrip and Stripline Transmission Lines Microstrip Stripline Air Dielectric (Alumina) Ground plane 6

7 Printed Circuit Board (PCB) layouts When is a PCB trace a transmission line? What about crosstalk (i.e., coupled lines)? 7

8 Stripline PCB Module (~ DC to 26.5 GHz) with Shielding IC IC IC Microstrip RF Connectors SMA type 8

9 Dispersion on Transmission Lines (1) Remember: pulse-like waveforms are made up of many frequencies. Dispersion is the result of frequency-dependent group velocity the separate frequency components spread out and arrive at differing times. 9

10 Dispersion on Transmission Lines (2) Example of 1111 on an optical fiber shown as the start ( km) & at distances of 5 km and 1 km. 1

11 Dispersion on Transmission Lines (3) Lossy Line Model of Transmission Line R+jωL Z= G+jωC Early telegraph operators experienced the merging of dots and dashes from dispersion over long transmission lines between stations. Heaviside s Condition: No dispersion resulted when G C = R L Group velocity Im (R jl)(g jc) 11

12 Lossy Transmission Lines Ohmic loss in the metallization Skin Effect (frequency-dependent R and L) Radiation losses (unshielded TL) Insulating substrate loss Dielectric losses and leakage (frequency-dependent G Semiconductor substrates Si has lossy substrate from residual resistance GaAs and InP have semi-insulating substrates 12

13 Time Domain Reflectometry (1) Voltage decay transient generated by a fault in a cable. Example Fast step excitation Pulse Generator Reference (t = ) Oscilloscope Transmission Line under test 13

14 Voltage Time Domain Reflectometry Example (2) Multi-section transmission line TDR can locate where discontinuities are present and characteristic impedance of different sections of transmission line. 5 nh 5 nh 6W/.5ns 1 pf 45W/.5ns 5W term Time (ns) 14

15 Time Domain Reflectometry (3) Practical waveforms Ideal waveforms 15

16 Reflection at discontinuity along transmission line I i V i V r V t Z z 1 Z 2 C Pulse echo -I r I t reflection coefficient Z Z transmission coefficient T Z Z Z2 Z Z

17 Probing an RF Printed Circuit Board 17

18 Optimize Probe Performance by Minimizing Tip Length 5 cm Courtesy of Mike McTigue and Dave Dascher, Agilent (Colorado Springs, CO) 1 cm There is still some LC ringing from the tip! 18

19 State-of-the-art in high frequency probing today (to 3 GHz) Infiniium 9 X-series Oscilloscope InfiniiMax III probing system 19

20 Review: Model of transmission lines Single incremental section of line (R jl)(g jc) per meter When R and G are small (our favorite conditions of course) R C G L nepers / meter 2 L 2 C LC radians / meter for R L & G C c group velocity where c 3, km / sec r 2

21 Reflection coefficients on transmission lines V S (t) + _ Z z = z = z L Z + + V1 _ Z L V 2 _ r L ZL Zo Z i L L Zo v (at z z ) v (at z z ) L L Smith Chart Z L L 21

22 Reflection gives standing waves with sinusoidal excitation 22

23 Remember the Smith chart A way to visualize Z = 5 W Z normalized to 5 ohms 23

24 Special cases to remember Terminated in Zo Vs Zs Zo Zo Zo Zo Zo Zo Short Circuit Vs Zs Zo Zo Zo - 1 Open Circuit Vs Zs Zo Zo 1 Zo 24

25 Concept of Surge Impedance (or Surge Admittance) Transmission line model with loss R+jωL L Z = = G+jωC C (if R = and G = ) Characteristic Impedance Z o is defined by equation above. A surge of energy on a transmission line will see an impedance of Z prior to any reflections arriving; hence, Surge Impedance is an alternative name for characteristic impedance. Input Impedance is looking into loaded transmission in steady state. 25

26 Transmission Line Bandwidth Questions: What is the bandwidth of an ideal lossless transmission line? What are practical limitations for bandwidth? 26

27 voltage [V] Step response for Z loaded TL (i.e., matched case) Z z = z = l V S (t) + _ + V1 _ t = V S Z ; T V S (t) = V S u(t) Z + V 2 _ No Reflection V S Z = 5 W V 1 V 2. T 2T 3T 4T time 27

28 voltage [V] Step response for resistively-loaded transmission line Z z = z = l V S + Z ; T + + V S (t) V S R V t _ 1 V S (t) = V S u(t) t = V V S Z = 5 W open R t = ( = 1) ½V S V 2.25 short. T 2T 3T 4T time R t > Z R t = Z ( = ) R t < Z R t = ( = -1) This is just a simple resistive voltage divider but with time delay. 28

29 Voltage (V) Current (A).75I S I 1 Step response for open circuited transmission line I 1 I 2 Z z = z = l V S (t) + V 1 _ t = V S Z ; T V S (t) = V S u(t) + V 2 _ I S.5I S.25I S I 2 T 2 T 3 T 4 T Time V S.75V S V 1 V 2.5V S.25V S T 2 T 3 T 4 T Time 29

30 Voltage and current components for open circuit load Voltage Current V s ½V s 2I I < t 1 l z l z T c V s ½V s 2I I t 1 < t 2 < T l z l z V s ½V s 2I I T < t 3 l z l - I z 3

31 Current (A) Voltage (V).75I S V 1 Step response for short circuited TL I 1 I 2 Z z = z = l V S (t) + V 1 _ t = V S Z ; T V S (t) = V S u(t) + V 2 = _ I S.75I S I 1 I 2.5I S.25I S T 2 T 3 T 4 T Time I S.5I S.25I S V 2 T 2 T 3 T 4 T Time 31

32 BTW This gives us a way to generate fast pulses 32

33 Summary for reflections (up to this point) Reflected voltage and current waves are generated when incident waves encounter a discontinuity in a transmission line The magnitude of the reflection is determined by the impedances of the lines and by the amplitude of the incident signal Special cases: o Open circuits fully reflect the voltage signal o Short circuits reflect the incident signal with equal magnitude but opposite sign o Matched circuits do not generate reflections o Resistive loads generate reflections determined by voltage division of resistances R L and Re[Z ] 33

34 voltage [V] Step response for capacitively-loaded TL V S (t) Z z = z = l Z ; T + V 1 _ t = V S V S (t) = V S u(t) C L + V 2 _ V S Z = 5 W V 2 V 1. T 2T 3T 4T time 34

35 voltage [V] Step response for inductively-loaded TL Z z = z = l V S (t) + V 1 _ t = V S Z ; T V S (t) = V S u(t) L L + V 2 _ V S Z = 5 W V 2 V T 2T 3T 4T time 35

36 Step response for series RL and parallel RC loading a R - Z R - Z V(t)= Vs e R+Z R+Z -t / t V s L where τ = R+Z R - Z Vs 1+ R+ Z Z L R L V s t = b V s -V s RZ where τ = R+Z C R - Z Vs 1+ R+ Z Z L R C t = R - Z V(t)=Vs e R+Z -t / t 36

37 Step response for parallel RL and series RC loading c R - Z V s R+ Z R - Z V(t)= Vs 1+ e R+Z where τ -t / t R - Z RZ = L Z L L R V s t = d V s R - Z V s R+ Z t = V(t)= V s R - Z 2 R+Z e -t / t where τ = ( R+ Z) L 2 V s Z L R C 37

38 Discontinuity at point z along transmission line V i Z Z 1 2 V r Z V t Z 1 Z 2 Z 2 I i I t -I r ρ = Vr ; V V i ρ I = Ir -I i V V r i Z Z Z 2 1 Z 2 1 V 38

39 Inductive discontinuity between Z transmission lines + V S _ Z V Z Z Z V V V x 39

40 Voltage echoes from several embedded components TDR Signatures 4

41 TDR signatures in transmission lines 41

42 Basics of a lattice diagram for transmission line (1) Vs Vs V 1 Z V 2 R S T D R L source load Time = V 1 V 2 a 1 b T D 2 2T D c d 3 T D 4T D e 5T D 42

43 Time Terms for lattice diagram for transmission line (2) source load V 1 V 2 V launch Vs Vs V 1 Z V 2 R S T D R L V launch T D V launch load 2T D V launch (1+ load ) V launch load source V launch (1+ load + load source ) 3T D V launch 2 load source 4T D V launch (1+ load + 2 load source + 2 load 2 source ) V launch 2 load 2 source 5T D 43

44 Example using the lattice diagram V S Z s V 1 Z V source Time = V 1 V 2 2 V 5 ps.8v T D = 25 ps.8v.8v load open v Assume: Z s = 75 ohms Z = 5 ohms & R L is infinite (open circuit) V s = to 2 volts V initial source load Zo 5 Vs ( 2 ) Zs Zo 75 5 Zs Zo 75 5 Zs Zo 75 5 Zl Zo Zl Zo ps.16v 1.6v 15 ps 1.76v.16v 2 ps.32v 1.92v 25 ps.32v 44

45 The lattice diagram is very useful for multiple lines + Z V S _ Z S Easy to analyze multiple sections 45

46 Ringing behavior from reflections Can you explain this? 46