T-Matrix De-Embedding of IC Metal Transmission Lines to 18 GHz

Abstract

T-matrix methods are applied to S-parameter data from on-chip metal lines connected to microwave measurement equipment so as to preserve mirror symmetry in the entire system. The propagation constant ¿ and characteristic impedance Zin of a line are derived from measurements on two different lengths of line. It is shown here that Zin can be found with few assumptions about the transition networks. In particular, we present a theorem for determining Zin or its phase for any symmetric or lossless transition network. Multiple lengths of otherwise identical IC line allow redundant, pairwise solutions to be acquired, with high confidence in the final result. Experimental results show that today's IC metal lines at Intel can have flat R, L, G, and C to at least 18 Ghz.