1. Interconnect and Packaging Chapter 1: Spectrum and Resonance (digital vs. analog)
Chung-Kuan Cheng
UC San Diego

2. Digital Input Spectrum
Power spectral density of digital inputs

3. Digital Input Spectrum
Power spectral density of digital inputs
Clock Rate = 1/T
Transition Time t10-90%≤T
Nulls appear at multiples of the clock rate
-20db/decade slope up to kneed frequency which is fknee ≡ 0.5/t10-90%

4. Resonance

5. Resonance

6. Resonance

7. Resonance + Digital Input

8. Resonance + Digital Input

9. Resonance + Digital Input

10. Resonance + Digital Input
Suppose that step responses of the rise transition and the fall transition are different.
How do we modify the algorithm?
Suppose that step responses are different due to history of transition up to m units of time.

11. References
B. K. Casper, M. Haycock, and R. Mooney, “An accurate and efficient analysis method for multi-Gb/s chip-to-chip signaling schemes,” in IEEE Symp. VLSI Circuits, Jun. 2002, pp
R. Shi, W. Yu, Y. Zhu, E. S. Kuh, and C. K. Cheng, “Efficient and accurate eye diagram prediction for high speed signaling,” in Proc. IEEE Int. Conf. Computer Aided Design, San Jose, CA, Nov 2008, pp
J. Ren and D. Oh, “Multiple edge responses for fast and accurate system simulations,” IEEE Trans. Adv. Packag., vol.31, no. 4, pp , Nov
C.C. Chou, T.L. Wu, and C.K. Cheng, "Eye Prediction of Digital Driver with Power Distribution Network Noise“ to appear in IEEE Electrical Performance of Electronic Packaing and Systems, 2012.