Broadband compact models for transformers integrated on conductive silicon substrates

A broadband scalable lumped-element model for multiport transformers integrated on a silicon substrate is presented. The model is based on a pi-T network for the primary and secondary coils and utilizes only frequency-independent elements to model the frequency-dependent resistive losses. Four-port S-parameters are measured for multiport transformers up to 15 GHz and accurate compact models extracted up to 4 GHz, which covers the fundamental frequency bands and their second harmonics of interest for European and US GSM/EGSM and DCS/PCS cellular bands. Good agreement is obtained between modeled and measured transformer performance attributes.