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#### Codes and Benchmarks

Benchmark1. MNA benchmarks of some RLC power/ground networks in digital IC (suitable for model order reduction, power/ground simulation, numerical analysis)

The benchmarks are generated from the Spice netlists of some IBM's RLC power/ground networks (see here for the detailed descriptions and the references by Dr. Sani R. Nassif). The models are formulated by modified nodal analysis (MNA), and are finally in the form of a linear time-invariant descriptor system: Edx(t)/dt=Ax(t)+Bu(t). The sparse E and A are the capacitance and conductance matrices, respectively; B is the multi-port input matrix. You can define an output matrix C by yourself, such that you can map the state variables x(t) to the output y(t) through y(t)=Cx(t). In these models, I have assumed that the input signals u(t) are DC sources, but you can use any waveforms you like to perform time-domain transient simulation.

The benchmarks can be used for numerical analysis, model order reduction, power grid simulation and verification, etc.. For each example, the MNA matrices are contained in the struct "MNA". I have also provided a summary of the circuit netlist in the structure "cktInf": the total number of R, L, C components and their connections in the network; you can also check the names of state variables and input sources in "stateNames" and "sourceNames" [ordered in the same way of x(t) and u(t)], respectively, which can help you control/observe the specific nodes or inputs.

 model dimension (n) # R (n1) # L (n2) # C (n3) # Isources (m1) # Vsources (m2) # port (m=m1+m2) ibmpg1t_MNA.mat 54,265 40,801 277 10,774 10,774 14,308 25,082 ibmpg2t_MNA.mat 164,897 245,163 330 36,838 36,838 330 37,168

These models are generated using my own MATLAB stochastic circuit simulator described in the following paper:

1. Z. Zhang, T. A. El-Moselhy, I. M. Elfadel and L. Daniel, "Stochastic testing method for transistor-level uncertainty quantification based on generalized polynomial chaos," IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems (TCAD), vol. 32, no. 10, pp. 1533-1545, Oct. 2013

Code1. Spectral projector computation, index checking and system decomposition for linear DAEs (or linear time-invariant descriptor systems). updated Dec. 05, 2013

This zipped file contains two folders for analyzing descriptor systems (with its index equal to or below 2). These codes are suitable for systems with sparse E and A matrices (such as those resulting from MNA formulation of interconnect networks) and when E has a small nullity.

The MATLAB functions in the folder "projector_index" (see the README file) can check the index and compute the right spectral projector Pr of a matrix pencil (E,A), which arises from the linear DAE or linear time-invariant descriptor system Edx(t)/dt=Ax(t)+Bu(t).

The Matlab codes in the folder "sysDecomp" (see the README file) are used to decompose a descriptor system into two subsystems: one is impulse-free (with a proper transfer function) and the other has a polynomial transfer function (with is possibly improper).  Based on this projector-based system decomposition, passivity verification/enforcements and model order reduction can be easily performed for each subsystems.

References:

1. Z. Zhang and N. Wong, "An efficient projector-based passivity test for descriptor systems", IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems (TCAD), vol. 29, no. 8, pp. 1203-1214, Aug. 2010

2. Z. Zhang, C.-U. Lei and N. Wong, “GHM: a generalized Hamiltonian method for passivity test of impedance/admittance descriptor systems”, in Proc. Int'l. Conf. on Computer-Aided Design  (ICCAD),  pp. 767-773, San Jose, CA, Nov. 2009.

3. Z. Zhang and N. Wong, “Passivity test of immittance descriptor systems based on generalized Hamiltonian methods”,  IEEE Transactions on Circuits and Systems II: Express Briefs (TCAS-2), vol. 57, no. 1, pp. 61-65, Jan 2010.

4. Z. Zhang, Q. Wang, N. Wong and L. Daniel, “A moment-matching scheme for the passivity-preserving model order reduction of indefinite descriptor systems with possible polynomial parts,” in Proc. Asia and South Pacific Design Automation Conference (ASP-DAC), pp. 49-54, Yokohama, Japan, Jan. 2011.

Code 2. Generalized Hamiltonian method for passivity test of descriptor system.

This zipped file contains two matlab functions. "ghm.m" check the passivity of a Z/Y-parameter descriptor system. "sghm.m" check the passivity of a S-parameter descriptor system. Both functions can handle symmetric descriptor systems with 8x speedup. You may need to first decompose the Z/Y-parameter system if the system contains an improper part, by using our projector-based decomposition codes (see Code 1).

References:

1. Z. Zhang and N. Wong, “Passivity test of immittance descriptor systems based on generalized Hamiltonian methods”,  IEEE Transactions on Circuits and Systems II: Express Briefs (TCAS-2), vol. 57, no. 1, pp. 61-65, Jan 2010.

2. Z. Zhang, C.-U. Lei and N. Wong, “GHM: a generalized Hamiltonian method for passivity test of impedance/admittance descriptor systems”, in Proc. Int'l. Conf. on Computer-Aided Design  (ICCAD),  pp. 767-773, San Jose, CA, Nov. 2009.

3. Z. Zhang and N. Wong, "Passivity check of S-parameter descriptor systems via S-parameter generalized Hamiltonian methods," IEEE Trans. Advanced Packaging (TADVP), vol. 33, no. 4, pp. 1034-1042, Nov. 2010.

4. Z. Zhang and N. Wong, "An extension of the generalized Hamiltonian method to S-parameter descriptor systems," IEEE/ACM Asia and South Pacific Design Automation Conference (ASP-DAC), pp. 43-47, Taipei, Jan 2010.