Implications of finite clock transition time for LPTV circuit analysis

Modeling linear periodically time-varying (LPTV) circuits is challenging due to the presence of frequency translation. Many approaches have been proposed that simplify the analysis and provide intuition into the operation of these circuits. It is critical to select the proper model when designing LPTV systems: too complex, and intuition is lost; too simple, and numerical accuracy degrades. This work shows how a conversion matrix-based model can be used for mixer-first receivers with complex feedback in the presence of finite switch transitions. This model accurately predicts S11 below -10 dB for all tested transition times, in contrast with prior models, which are shown to be invalid with transitions beyond 2% of the clock period. As a design tool, this approach models gain, harmonic rejection ratio, and noise figure within 0.1 dB of simulation with switch transitions even at 5% of the clock period.