Direct current compensation system and method for scattering parameter rational functions

摘要

A direct current compensation method for S-parameter rational functions reads S-parameters f(sk), which are generated at given frequency sk, from a storage unit. An S-parameter, which is generated at frequency sk=0 is supplemented into the S-parameters f(sk), upon the condition that there is no S-parameter which is generated at the frequency sk=0. An S-parameter ration function is generated according to the S-parameters f(sk). A DC level of the S-parameter rational function is compensated to generate a compensated S-parameter rational function.

主权项

1. A direct current (DC) compensation method for S-parameter rational functions, the method comprising:
reading S-parameters f(sk) which are generated at given frequency sk from a storage unit, the S-parameters indicative of an n-port network; supplementing an S-parameter, which is generated at frequency sk=0, into the S-parameters f(sk) using an interpolation method, upon the condition that there is no S-parameter which is generated at the frequency sk=0; generating an S-parameter rational function according to the S-parameters f(sk) using a vector fitting algorithm; compensating a DC level of the S-parameter rational function to generate a compensated S-parameter rational function, comprising:
(a) computing the pole values pm using first formulas as follows:p2⁢u=u/100+j·usN-s1,p2⁢u-1=u/100-j·usN-s1, where u=1˜M/2, and M is a total number of the pole values;
(b) generating a matrix X:X:[r1…rMdr~1…r~M] using unknown variables rm, d, and of functions (σf)fit(s) and σfit(s), wherein the functions (σf)fit(s) and σfit(s) are shown as follows:(σ⁢⁢f)fit⁢(s)=f⁡(0)+s⁡(∑m=1M⁢rms-pm+d),σfit⁡(s)=∑m=1M⁢r~ms-pm+1; (c) substituting the pole values pm and the S-parameters f(sk) into matrixes A and B, wherein the matrixes A and B are shown as follows:matrix⁢⁢A=[s1s1-p1…s1s1-pMs1-f⁡(s1)s1-p1…-f⁡(s1)s1-pM…………………sksk-p1…sksk-pMsk-f⁡(sk)sk-p1…-f⁡(sk)sk-pM…………………sKsK-p1…sKsK-pMsN-f⁡(sK)sK-pM…-f⁡(sK)sK-pM],⁢matrix⁢⁢B=[f⁡(s1)-f⁡(0)…f⁡(sk)-f⁡(0)…f⁡(sK)-f⁡(0)]; (d) computing the unknown variables rm, d, and using a formula X=(AT A)−1 AT B, to get the functions (σf)fit(s) and σfit(s);(e) recording the got (σf)fit(s) as (σf)fit—old(s) upon the condition that steps (b)˜(d) are only executed one time, and computing the pole values pm again using second formulas as follows:σfit⁡(s)=∑m=1M⁢r~ms-pm+1=∏m=1M⁢(s-zm)∏m=1M⁢(s-pm), where pm=zm, m=1˜M;
(f) repeating steps (b)˜(d), determining if |(σf)fit(s)−(σf)fit—old(s)|