Multiport Square Law Detectors: Responsivity Matrix Model and Direct Determination of the Optimum Injection Regime

A generic matrix model for the responsivity of millimeter-wave (mmW) and sub-THz square law detectors is proposed. The model is valid for any number of ports and takes the biasing conditions into account, the power distribution, the phase shifts between ports, and the frequency dependence of the detector response. The proposed approach is experimentally validated up to 67 GHz on an AlGaN/GaN high-electron-mobility transistor (HEMT). It could, however, be used for other types of detectors, including diodes and CMOS detectors. In addition, a reliable mathematical method is presented, allowing the direct determination of the maximum attainable responsivity and the associated optimum excitation. This method avoids a computing time-consuming evaluation of the above quantities by constrained optimization and thus provides an efficient way to evaluate the performances of a square law detector only based on its dc and S-parameters characterization.