Method for determining the steady state behavior of a circuit using an iterative technique

• US 6,151,698 A
• Filed: 04/28/1997
• Issued: 11/21/2000
• Est. Priority Date: 04/30/1996
• Status: Expired due to Term

• Current Assignee: Cadence Design Systems Incorporated (Cadence Group)
• Original Assignee: Cadence Design Systems Incorporated (Cadence Group)
• Inventors: Kundert, Kenneth S., Telichevesky, Ricardo, White, Jacob K.
• Primary Examiner(s): Lintz, Paul R.
• Assistant Examiner(s): Siek, Vuthe
• Application Number:
  US08/847,884
• Time in Patent Office: 1,303 Days
• Field of Search: 364/488, 364/489, 364/490, 364/578, 395/500, 716/1, 703/13, 703/14, 703/22
• US Class Current: 703/14
• CPC Class Codes: G06F 30/367 Design verification, e.g. using simulation, simulation program with integrated circuit emphasis [SPICE], direct methods or relaxation methods

Abstract

An efficient method for determining the periodic steady state response of a circuit driven by a periodic signal, the method including the steps of 1) using a shooting method to form a non-linear system of equations for initial conditions of the circuit that directly result in the periodic steady state response; 2) solving the non-linear system via a Newton iterative method, where each iteration of the Newton method involves solution of a respective linear system of equations; and 3) for each iteration of the Newton method, solving the respective linear system of equations associated with the iteration of the Newton method via an iterative technique. The iterative technique may be a matrix-implicit application of a Krylov subspace technique, resulting in a computational cost that grows approximately in a linear fashion with the number of nodes in the circuit.

Claims

1. In a circuit simulation tool, a method for determining a periodic steady state response of a circuit driven by a periodic signal, the periodic signal being an input to the circuit, the method comprising the steps of:

producing a first linear system of equations characterizing nodal voltages of said circuit;

producing a second non-linear system of equations based on the first system of equations using a shooting method, the second non-linear system of equations representing initial conditions of the circuit that directly result in the periodic steady state response;

solving the second non-linear system of equations using a Newton iterative method to produce the periodic steady state response of the circuit, including producing for each iteration of the Newton method a corresponding third linear system of equations based on the second non-linear system of equations;

for each iteration of the Newton method, solving its corresponding third linear system of equations using a matrix-implicit iterative technique, including providing a plurality of matrices stored in a memory to contain coefficients relating to the third linear system of equations, each of the matrices having an identical structure, the structure indicating locations of non-zero elements in each of the matrices;

wherein data representing the structure is stored in the memory only once, and for each of the matrices, data representing non-zero elements of the matrix are stored in the memory apart from the data representing the structure; and

providing the periodic steady state response to the circuit simulation tool.

2. The method of claim 1, wherein the matrix-implicit technique is a Krylov-subspace technique.

3. The method of claim 3, wherein the matrix-implicit technique uses a generalized minimal residual algorithm.

4. The method of claim 3, wherein the matrix-implicit technique uses a generalized conjugate residual algorithm.

5. In a circuit simulation tool, a method for determining a first small-signal quasiperiodic steady state response of a circuit driven by a large periodic signal to a small sinusoid of a first frequency, the first small-signal steady state response covering a plurality of timepoints that span a period of the large periodic signal, the plurality of timepoints including a last timepoint, the method comprising the steps of:

forming a first linear system of equations for the first small-signal steady state response of the circuit at a particular one of the timepoints;

solving the first linear system of equations using a matrix-implicit iterative technique based on a class of Krylov subspace techniques, including producing a first matrix-vector product and storing the first matrix-vector product in a memory;

determining a second small-signal quasiperiodic steady state response of the circuit to a small sinusoid of a second frequency, the second small-signal steady state response covering the plurality of timepoints, the step of determining the second small-signal steady state response comprising the substeps of;

(i) forming a second linear system of equations for the second small-signal steady state response at the particular timepoint;

(ii) solving the second linear system of equations using a Krylov-subspace technique, including producing a second matrix-vector product required by recycling the first matrix-vector product; and

providing the first and second small-signal steady state responses to a circuit simulation tool.

6. The method of claim 5, wherein the particular timepoint is the last timepoint.

7. The method of claim 6, wherein the matrix-implicit technique uses a generalized minimal residual algorithm.

8. The method of claim 6, wherein the matrix-implicit technique uses a generalized conjugate residual algorithm.