Noise considerations when determining phase of large-signal microwave measurements

Abstract

Advances in microwave instrumentation now make it feasible to accurately measure not only the magnitude spectrum, but also the phase spectrum of wide-bandwidth signals. In a practical measurement, the spectrum is measured over a finite window of time. The phase spectrum is related to the position of this window, causing the spectrum to differ between measurements of an identical waveform. It is difficult to compare multiple measurements with different window positions or to incorporate them into a model. Several methods have been proposed for determining the phase spectrum such that multiple measurements can be effectively compared and utilized in models. The methods are reviewed in terms of the information required to determine the phase and compared in terms of their robustness in the presence of measurement noise.

The Random Component of Mixer-Based Nonlinear Vector Network Analyzer Measurement Uncertainty

“…For many applications, such as fitting models and aligning signals, it is important to know the covariance matrix corresponding to the measurements. The covariance matrix can be used to weight a cost function when fitting models, used to weight the signal alignment problem [4] or give uncertainty bounds for the measurements.…”

“…where is the phase of the transformed forward pseudowave , is the transformed reference channel. 4 The covariance matrix given by (18) will be called Covariance Model 1. This model assumes the receivers operate as described in Section III-A and the measurements are independent with equal variance.…”