Wideband closed-form expressions for direct extraction of HBT small-signal parameters for all amplifier bias classes

An accurate, robust and broadband method for the direct extraction of heterojunction bipolar transistor (HBT) small-signal model parameters is proposed. This new approach, modified from previous work by the authors, including additional equivalent-circuit elements, g_o and C_ce, can be applied accurately to all transistor bias points covering the entire forward bias region. First, hot and cold bias conditions are used to determine the parasitic elements (L_b, L_c, L_e, C_bep, C_cep and C_bcp), then the access resistances (R_b, R_c, R_E) are determined using DC flyback measurement. Finally, the intrinsic elements are extracted analytically through a judicious and rigorous derivation of closed-form expressions of the Z-parameters deduced from the measured S-parameters. The analytical expressions allow us to obtain a unique physical solution without having to use a nonlinear system. The method is applied at multiple bias points and over a wide range of signal frequencies. As the physical solution is unique, all the circuit elements are determined without any optimisation or any knowledge of the geometrical or process parameters of the device. To assess the effectiveness of the present method three HBT devices, with 2×25 μm², 2×20 μm² and 2×10 μm² emitter areas from two different foundries, are studied. Excellent agreement is obtained between the model and measurements up to 20 GHz and for all amplifier bias classes.