A Statistical Evaluation of Detection Response of an Electric Field Probe Loaded With Nonlinear Diodes for Modulated Signals

Abstract

To improve the calibration uncertainty of an electric field probe loaded with diodes to modulated signals, an approximate method for evaluating the detection response using the probability density function (pdf) of the envelope amplitude of an actually transmitted modulated signal waveform is proposed. In this article, we focus on the high-strength modulated signals and evaluate the effect of the nonlinearity of the transmission system on the probe gain. First, the equivalent circuit parameters of an electric field probe are estimated using an unmodulated signal and then used to simulate the probe gain for the amplitude-modulation (AM) signal. The probe gain for the modulated signal deviates considerably from that for the unmodulated signal, depending on the modulating frequency and modulation index of the AM signal, especially when a large incident voltage is applied to the equivalent circuit simulating the probe. Moreover, we propose two approximate expressions using the pdf to obtain the fluctuation range of the detection response of the modulated signal. One is an approximate expression that considers the equivalent circuit parameters of the probe. The other one is an approximate expression for the modulated signal with slow envelope variation. These two expressions are found to give a good approximation of the asymptotic value of the probe gain for an AM signal with fast and slow envelope variations, respectively. By applying these approximate expressions, the upper and lower limits of the gain variation of the probe for the AM signal are obtained. As an application to actual communication signals, integrated services digital broadcasting terrestrial (ISDB-T) signals and single-carrier frequency-division multiple access (SC-FDMA) signals are demonstrated as examples. It is shown that the probe gain in the saturation region increases as the signal bandwidth or peak-to-average-power ratio (PAPR) increases, which can be understood similar to the probe response to AM signals.