Modeling the baseband output envelope of a Microwave detector

The current state-of-the-art for the calibration of wave spectra containing spectral lines that lie on a harmonic grid (f₀, 2f₀...) relies on the well-established step recovery diode method. The challenge in narrow band modulated measurements resides in the calibration of the instrument´s phase distortion for such signals. A crystal detector (HP 420C,) is studied as a candidate reference element for the phase calibration of the large-signal network analyzer (LSNA) for modulated excitations as the detector translates the envelope of the RF-signal to IF frequencies. A realistic crystal detector itself will introduce phase distortion, hence the identification and validation of a parametric black-box model of the detector was undertaken. 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. In the first part of the paper the model extraction is discussed. 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. Therefore the physical representation of the model structure is translated into its differential equation in section 4. By means of this equation the low frequency output envelope is computed for RF input signals and compared to the measured envelope in section 5.