Time domain model validation of a nonlinear block-oriented structure

A crystal detector is studied as a valid candidate reference element for the phase calibration of the large-signal network analyzer (LSNA) for modulated excitations. However, one cannot use a crystal detector straightforwardly as a phase reference element, since a crystal detector inherently introduces phase distortions. Hence, the identification and validation of a parametric black-box model of the detector is needed. In this work, a nonlinear feedback model for a crystal detector is constructed: the model contains a low-pass filter in the feedforward path and a Wiener system in the feedback loop. The model is estimated from baseband data and needs to be validated for use with high-frequency signals: the model needs to be extrapolated to RF frequencies, which is quite an arduous task. The validation of the extrapolated model is performed using two approaches: (i) the RF narrow band modulated signal is applied to the extrapolated model structure and the output signal is computed; (ii) the physical representation of the model structure is translated into its differential equation and by means of this equation, the low-frequency output envelope is computed for RF input signals. The second approach requires a slight modification of the extracted model compared to the model used in the first approach, with respect to the function describing the static nonlinear behavior. The deviation between the modeled output envelope and the measured output envelope is evaluated for both approaches. The method (ii) that computes the output of the detector in the time domain by means of solving a differential equation that characterizes the identified nonlinear feedback model gives the overall best results for predicting the magnitude and the phase of the detector output spectrum and the amplitude behavior of the time domain output waveform. The mean deviation in magnitude between the modeled and measured envelope equals 2.6 dB. This approach significantly outperforms the first method (i) as the mean deviation between the phase of the modeled and measured envelope equals 8.2°