Patent Document ID: 20100023288
Application ID: 12572696
Patent Flag: 0

Claim One:
1. A method for characterizing linear properties of an electrical component having n>1 ports, which linear properties are described in a matrix Y relating a voltage applied to the ports to a current through the ports, wherein a frequency dependence of Y is approximated by Y ( s ) ≅ Y rat ( s ) = ∑ m R m s - a m + D + sE wherein m runs through 1 to a number N of poles, R m with m=1 to N are frequency independent matrices, D and E are frequency independent matrices or zero, s denotes a complex angular frequency iω and a m with m=1 to N are complex angular frequencies of the poles, said method comprising: a) obtaining a set of values Y(s) of Y at discrete frequencies s, and, for each value Y(s), obtaining eigenvalues λ i and eigenvectors t i with i=1 to n; b) fitting a set of n vector equations λ i  λ i  ( ∑ m = 1 N r ~ m s - a m + 1 )  σ ( s ) t i ≅ 1  λ i  ( ( ∑ m = 1 N R m s - a m + D + sE ) · t i ) to the eigenvalues λ i and eigenvectors t i , wherein {tilde over (r)} m is a frequency-independent scalar with m=1 to N, by using a first set of pole frequencies a m and by varying {tilde over (r)} m , R m and, if assumed to be non-zero, D and E; c) calculating a second set of pole frequencies from: 
 { a m }=eig ( A−b·c T ) wherein A is a diagonal matrix holding the first set of pole frequencies a m as diagonal elements, b is a vector of ones, c is a vector holding {tilde over (r)} m for m=1 to N as obtained by step b), and eig is an operator returning a vector holding eigenvalues of a matrix; and d) repeating steps b) and c) by using the second set of pole frequencies a m of step c) as the first set of pole frequencies in a subsequent step b) until a stop condition is met.