1. Fang Gong gongfang@ucla.edu
Homework 3 Solution
Fang Gong

2. Homework 3
Modify the PRIMA code with single frequency expansion to multiple points expansion. You should use a vector fspan to pass the frequency expansion points. Compare the waveforms of the reduced model between the following two cases: 1. Single point expansion at s=1e4. 2. Four-point expansion at s=1e3, 1e5, 1e7, 1e9.
Elfadel, I.M.; Ling, D.D.; , "A block rational Arnoldi algorithm for multipoint passive model-order reduction of multiport RLC networks," Computer-Aided Design, Digest of Technical Papers., 1997 IEEE/ACM International Conference on , vol., no., pp.66-71, 9-13 Nov 1997
Odabasioglu, A.; Celik, M.; Pileggi, L.T.; , "PRIMA: passive reduced-order interconnect macromodeling algorithm ," Computer-Aided Design, Digest of Technical Papers., 1997 IEEE/ACM International Conference on , vol., no., pp.58-65, 9-13 Nov 1997 2

3. (1) Demo file
Assume m frequency points and match n moments at each freq. point. f0 f1 fm
…………
m0 m1 … mn
Single Point Case

4. (2) Prima File f1  s(1) f2 s(2) fm s(m) ………… m1 … mnum σ1=s(1) …
σ(m-1)*num+1=s(m) …
σm*num=s(m)

5. (2) Prima File (cont.) Generate Vectors in Uq
The rest code do not need to be modified in PRIMA.m file.

6. Example: GC9 (G is 11x11) input file
Single Point Expansion: Gr is 6x6
Four Points Expansion: Gr is 10x10
Impulse response for single point expansion

7. Example GC8 (G is 449x449) example
Single Point Expansion: Gr is 6x6
Four Points Expansion: Gr is 24x24