A New Analytical Method for Robust Extraction of the Small-Signal Equivalent Circuit for SiGe HBTs Operating at Cryogenic Temperatures

We present a new analytical direct parameter-extraction methodology for obtaining the small-signal equivalent circuit of HBTs. It is applied to cryogenically operated SiGe HBTs as a means to allow circuit design of SiGe HBT low-noise amplifiers for cooled radio astronomy applications. We split the transistor into an intrinsic transistor (IT) piece modeled as a Pi-topology, and the quasi-intrinsic transistor (QIT), obtained from the IT after that the base resistance (R_b) has been removed. The relations between Z-Y-parameters of the IT and QIT are then established, allowing us to propose a new methodology for determining R_b. The present extraction method differs from previous studies in that each of the model elements are obtained from exact equations that do not require any approximations, numerical optimization, or post-processing. The validity of this new extraction methodology is demonstrated by applying it to third-generation SiGe HBTs operating at liquid-nitrogen temperature (77 K) across the frequency range of 2-22 GHz.