Efficiency optimized distributed transformers for broadband monolithic millimeter-wave integrated power amplifier circuits

This paper revises the efficiency optimization equations for magnetic-transformer-based power combiner/divider impedance transformation networks (e.g., distributed active transformer). It evaluates their usability for high millimeter-wave frequencies, where the distributed behavior of a transformer and its loss become relevant. As is demonstrated, the standard optimization equations do not lead to an optimum result. To enable the optimization of distributed transformers, an extended lumped equivalent circuit model is proposed and used for the derivation of new optimization equations. The novel equations enable the design of magnetic transformers with maximum efficiency. To demonstrate the performance that can be achieved with optimized distributed magnetic transformer networks at millimeter-wave frequencies, measurement results of an R-band (i.e., 170-260 GHz)/H-band (i.e., 220-325 GHz) power amplifier (PA) are presented. With an output power of approximately 6.2 dBm at 260 GHz, the amplifier is among the state of the art for mHEMT PAs operating in this frequency range. With its relative 3-dB bandwidth of 29%, however, it surpasses all those reported mHEMT PAs to date.