High Speed Signal Integrity Analysis Tongtong Yu Zhiyuan Shen 1

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

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

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

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

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

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

General Case and Special Case If load is open 8

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

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

Impedance Discontinuity interconnects Vias 11

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

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

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

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

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

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

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

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

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

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