1. High Speed Signal Integrity Analysis
Tongtong Yu
Zhiyuan Shen 1

2. Ringing and Overshoot Large overshoot -- damage device
Crossing logic threshold 2

3. Transmission Line Effect
Interconnection effect
Different from traditional circuit analysis
Assume velocity ~ velocity in free space 3

4. Basic Equation of Transmission Line
Taking limit
as △ z-> 0
“Telegraph
Equation”
Steady-state
Sinusoids
Approach 4

5. Basic Equation of Transmission Line
Solution :
Define
Then, we can write 5

6. Lossless Transmission Line
R = G = 0
Remember α corresponds
to an exponential decay term 6

7. Transmission Line with Arbitrary Load
What about power ?
Г= 0, for matched load
Г= 1, for open load
Г= -1, for short load 7

8. General Case and Special Case
If load is open 8

9. Analogy to Basic Circuit
Also,
Assuming voltages are RMS value 9

10. Bounce Diagrams Refrence: Eric Bogatin, Signal Integrity – Simplified
Second order RLC step response 10

11. Impedance Discontinuity
interconnects
Vias 11

12. Black box vs. Modeling
Course material Chapter 6(b) 12

13. Frequency vs. Time Frequency Domain Approach Time Domain Approach
Based on frequency transformation
AWE, PRIMA
Stability problem in Pade Approximation
Time Domain Approach
Easy to get transient response
Can handle nonlinearity.
Fast calculation without stability problem 13

14. Method of Characteristics
New variables
Telegraph equation
For lossless lines
Propagation speed 
where 14

15. Method of Characteristics
(1)
(2)
What if the propagation
speed is not constant?
According to (1)
Similarly for Eq (2)
where
Rewrite
them as  15

16. Equivalent Circuit Model
(b)
Circuit in (a) represents the left (source) part equivalent circuit. The voltage potential er(l, t -τ) represents the reflected wave from load before time τ, which has already been calculated in sequential time domain analysis. So, the voltage and current can be calculated with given terminal condition.
Similar for circuit (b), we use voltage potential ei(0, t -τ) 16

17. Method of Characteristics
Lossy Transmission Line
Further, assume
(Distortionless transmission line)
Still ,define 17

18. Method of Characteristics
Lossy Transmission Line
If it does not satisfy
Get several discrete points between x-axis and
t-axis, which are the intersection of Char. lines.
Δt is the time step; Δx = vφΔt is the space step 18

19. Sensitivity Analysis Basic Equation Then, we get Let
Assume p is an arbitrary parameter
of transmission line or terminal load
Then, we get
Let   19

20. References
Eric Bogatin, Signal Integrity – Simplified, Pearson Education,
2005
H. Johnson and M. Graham, High-Speed Digital Design: A Handbook of Black Magic, Pearson Education, 2003
J.F. Mao, et al, Transmission Line Synthesis by the Method of Characteristics, IEEE transactions on Circuits and Systems, vol. 43, no. 6, June 1996
J.F. Mao and E.S. Kuh, Fast Simulation and Sensitivity Analysis of Lossy Transmission Lines by the Method of Characteristics, IEEE transactions on Circuits and Systems, vol. 44, no. 5, May 1997 20

21. Summary Key Words Transmission line Characteristic Impedance
Reflection
S parameter
Frequency/ Time Domain Analysis 21