Direct Extraction Method of HBT Equivalent-Circuit Elements Relying Exclusively on $S$-Parameters Measured at Normal Bias Conditions

Abstract

A new direct parameter-extraction scheme applied to a heterojunction bipolar transistor (HBT) small-signal equivalent circuit with distributed base-collector junction capacitance is presented. The proposed method relies exclusively on <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameters measured at low and high frequencies in normal bias conditions, and without using approximations based on anticipated values. The extraction results obtained from low-frequency modeling allow the extraction of the parasitic inductances at high frequency. This is performed by formulating expressions based on ac-current-source consideration different from the previously published one, without affecting the physical signification of the HBT model. This method presents a simple way for the extraction of the model parameters directly. An experimental validation on an InP double HBT device was carried out, using the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameters measured in a frequency range of 40 MHz-50 GHz over a wide range of bias points. The modeling results are presented, showing that the proposed method can yield a good fit between measured and calculated <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> -parameters.