SPECTRAL ANALYSIS OF ELECTRONIC CIRCUITS
A method for electronic circuit spectral analysis includes receiving a list of parts for an electronic circuit, determining a part admittance matrix with algebraic nodes for each part, and determining a circuit admittance matrix for exterior nodes, interior nodes, and algebraic nodes based on the part admittance matrices. The method also includes reducing interior nodes of the circuit admittance matrix for exterior nodes, interior nodes, and algebraic nodes to determine a circuit admittance matrix for exterior nodes and algebraic nodes, reducing algebraic nodes to transform the circuit admittance matrix for exterior nodes and algebraic nodes into a Green's Function, evaluating the Green's Function to determine a circuit exterior node admittance matrix over a frequency spectrum, and transforming the circuit exterior node admittance matrix to a circuit scattering matrix over the frequency spectrum.
1 . A spectral analysis method for determining performance of an electronic circuit, comprising:
receiving a list of parts for the electronic circuit;
determining a part admittance matrix with algebraic nodes for each part;
determining a circuit admittance matrix for exterior nodes, interior nodes, and algebraic nodes based on the part admittance matrices;
reducing interior nodes of the circuit admittance matrix for exterior nodes, interior nodes, and algebraic nodes to determine a circuit admittance matrix for exterior nodes and algebraic nodes;
reducing algebraic nodes to transform the circuit admittance matrix for exterior nodes and algebraic nodes into a Green's Function;
evaluating the Green's Function to determine a circuit exterior node admittance matrix over a frequency spectrum; and
transforming the circuit exterior node admittance matrix to a circuit scattering matrix that characterizes the performance of the electronic circuit over the frequency spectrum.
2 . The method of claim 1 , wherein evaluating the Green's Function to determine the circuit exterior node admittance matrix comprises:
diagonalizing a Hurwitz matrix of the Green's Function to determine a circuit exterior node admittance matrix; and
vectorizing a frequency calculation over the circuit exterior node admittance matrix.
3 . The method of claim 1 , wherein evaluating the Green's Function to determine the circuit exterior node admittance matrix comprises:
evaluating Green's Function by linear algebra one frequency at a time over the frequency spectrum to determine the circuit exterior node admittance matrix.
4 . The method of claim 1 , wherein evaluating the Green's Function to determine the circuit exterior node admittance matrix comprises:
expanding the Green's Function in Chebyshev Polynomial Moments;
creating truncated Chebyshev Polynomial Moments of the Green's Function by Hurwitz Matrix on vector multiplication of the Chebyshev Polynomial Moments; and
evaluating truncated Chebyshev Polynomial Moments expansion of the Green's Function by Fast Fourier Transform to determine the circuit exterior node admittance matrix.
5 . The method of claim 1 , wherein evaluating the Green's Function to determine the circuit exterior node admittance matrix comprises:
time evolution of the exterior node to algebraic node admittance using an exponential of a Hurwitz matrix; and
Fourier transform of the time series to generate the spectrum.
6 . The method of claim 1 , wherein evaluating the Green's Function to determine the circuit exterior node admittance matrix comprises:
time evolution of exterior node to algebraic node admittance using an exponential of a Hurwitz matrix; and
filtering diagonalization of the time evolution to generate the circuit exterior node admittance matrix.
7 . The method of claim 1 further comprising modeling a non-electronic system as an equivalent circuit prior to determining the parts admittance matrix.
8 . The method of claim 1 , wherein the Green's Function has a spectral dependence on a Hurwitz matrix.