Patent Document ID: 20040261042
Application ID: 10839953
Patent Flag: 0

Claim One:
1. A method of model-order reduction of RLC circuits. constructs the congruence transformation matrix U&equals;&lsqb;V q SV q &rsqb;. Therefore, moments of Y(s) can be matched by moments of &Ycirc;(s) up to (2k −1)st-order by applying the congruence transformation matrix, that is, &Ycirc; (i) ( s 0)&equals; Y (i) ( s 0 ), for 0 &lE;i &lE;2 k −1, where T (N&plus;sM)B represents the transfer function of the original system, and matrices M, N, and B are corresponding MNA matrices; q is generated by the Krylov subspace methods; let A&equals;−(N&plus;s 0 M) −1 M and R&equals;(N&plus;s 0 M) −1 B; s 0 is an given expansion frequency such that (N&plus;s 0 M) is nonsingular; the k th-order block Krylov subspace generated by A and R is defined as K(A,R,k)&equals;colsp&lcub;R,AR,...,A k−1 R&rcub;&equals;colsp(V q ), where q&lE;km; colsp(V q ) represents span the vector space by columns of matrix V q ; nv,−I ni ), where I represents an identity matrix; nv and ni are the dimension of the node voltages and the branch currents; T ({circumflex over (N)}&plus;s{circumflex over (M)}){circumflex over (B)} represents the transfer function of the reduced-order system, and matrices {circumflex over (M)}, {circumflex over (N)}, and {circumflex over (B)} are corresponding reduced-order MNA matrices that is generated by the congruence transformation: {circumflex over (M)}&equals;U T MU,{circumflex over (N)}&equals;U T NU,{circumflex over (B)}&equals;U T B; (i) (s 0 ) is the i th-order moment of Y(s) at so and &Ycirc; (i) (s 0 ) is the i th-order moment of &Ycirc;(s) at s 0.