TABLE OF CONTENTS In this section, we present the method for efficient computation of moments using classic circuit analysis techniques. We start with the modified nodal analysis (MNA) formulation of the general RLC linear circuits and derive the recursive moment computation formula, which is the most critical step for all the moment-matching methods and Krylov subspace projection-based model order reduction methods.
For a general linear network, we can apply modified nodal analysis to formulate it in the state space equation form
where G and C are the conductive and storage element matrices; B and L are the input and output positions matrices; and state variables x can be nodal voltage or branch currents of the linear circuit.
Upon applying the Laplace transformation of the state equation, we have the state equations in the s domain
Assuming the initial condition is zero, X(0)=0, and the impulse response ( U(s)= 1) is applied, the state equation will become
Expanding X(s) using Taylor s series at s=0, we obtain
We then obtain the state moment computation formula in a recursive form
Notice that G ?1 here means we solve G x= b and G ?1 is used for solving for all the moments. Numerically, we only need to perform one LU decomposition of G= LU and then use the L and U matrices to solve for all moments...
