Takashi Ohira
Figure 1 shows the rectifier circuit of this “Enigmas, etc.” column series. The RF voltage source has a purely sinusoidal waveform. However, the current ${i}_{s}{(t)}$ flowing into the circuit is distorted from a sinusoid because of the diode nonlinearity. We can decompose ${i}_{s}{(t)}$ into its Fourier series: \[{i}_{s}{(}{t}{)} = {I}_{o} + {\left[{I}_{P}\,\,{I}_{Q}\right]}\,{\left[\begin{array}{c}{\sin}\,{\omega}{t} \\ {\cos}\,{\omega}{t} \end{array} \right]} + {\cdots} \]
Figure 1. Single-series diode rectifier. Given the dc output current, can we calculate the RF input current?
where ${I}_{o}$ signifies the zeroth-order or dc term, ${I}_{P}$ and ${I}_{Q}$ stand for the orthogonal first-order components, and ${\ldots}$ denotes the second-order and higher order harmonics that follow. Assuming a nominal 50% duty operation, we can infer ${I}_{P}$ and ${I}_{Q}$ backward from ${I}_{o}$. Which among the following is equal to ${I}_{P}$?
(a) ${I}_{o}$ (b) $\frac{1}{2}{I}_{o}$ (c) $\frac{\pi}{2}{I}_{o}$ (d) $\frac{2}{\pi}{I}_{o}$
Digital Object Identifier 10.1109/MMM.2023.3284796