Solution to the January/February Problem on Rectifier Efficiency [Enigmas, etc.]

The correct answer to the problem presented in the January/February 2018 installment of “Enigmas, etc.” is c. The circuit topology in question looks simple. One could analyze it with ease if only the voltage source were free of internal resistance. However, in this problem, the source has nonzero internal resistance, i.e., , 50X which is quite usual in RF systems. This makes the problem rather complicated. Actually, due to this resistance, the voltage waveform on inductor L is no longer sinusoidal but crucially distorted with multiple harmonic components. One may observe it on a circuit simulator such as SPICE. This nonlinear problem can be formulated in piecewise time intervals segmented by the turn-on and turn-off instances of the diode. Although this may sound a little tough, the circuit equation in each interval can be solved with a pencil and paper. The overall RF-to-dc conversion efficiency results in