Error Correction in Vector Network Analyzers - SDR-Kits

Bringing this to a common denominatorΓ in = (S 11S 22 − S 12 S 21 )S − S 11S 22 S − 1(62)and using an abbreviation for the determinant of the S-matrix∆ S = S 11 S 22 − S 12 S 21 (63)we obtain the final resultΓ in = b 1= ∆ SS − S 11a 1 S 22 S − 1(64)A.2 Identifications of Agilent’s error termsThe error terms in [1] can be identified with ours.A.2.1Forward error termse 11 = S S = − b c(65)e 22 = S L (66)e 00 = a c(67)e 10 e 01 = 1 c − abc 2 (68)Note that e 10 e 32 is related to the thru calibration. It is effectively removed in our equations byworking with the renormalized M ij ’s , see section A.2.3.A.2.2Backward error termse ′ 11 = S L (69)e ′ 22 = S S = − b c(70)e ′ 33 = a c(71)e ′ 23e ′ 32 = 1 c − abc 2 (72)Note that e ′ 23e ′ 01 is related to the thru calibration. It is effectively removed in our equations byworking with the renormalized M ij ’s , see section A.2.3.10