# Measurement and Modelling of the Noise Behaviour of Non-linear Systems Operating at RF or Microwave Frequencies

## Project Details

### Description

Measurement and Modelling of the Noise Behaviour of Non-linear Systems Operating at RF or Microwave Frequencies.

Alain Geens

An attempt was made to study the noise behaviour of mixers. The purpose of this study was to determine the properties of the frequency translated noise bands. Theoretically, this should be an effortless study. In reality however, a practical measurement problem arose due to strong mismatch of the out-of-band noise. Although it was possible to apply a correction for this mismatch, the correction term to resolve the problem was so large that it led to untrustworthy results. Hence, this approach was not used.
Due to the principle of non-linearity itself, a separated treatment of signal and noise (as is the standard approach in the linear case) is quasi impossible. This adds an extra dimension to the problem: the noise behaviour of a circuit becomes a non-separable function of the combination of signal and noise at its input.
As a first step in the theoretical approach, we chose to model an amplifier. A simple model, consisting of a linear main term and a cubic distortion was treated here. The effect of the non-linearity of the on the noise figure was studied for an input signal consisting of the white Gaussian noise and a continuous wave signal. Theoretically, the classical method to measure the noise figure showed to be invalid, and an alternative measurement method was proposed. The results were also verified experimentally.
The simple amplifier model was also used to theoretically predict the noise behaviour of an amplifier in compression. For non-linear systems it showed to be necessary to expand the concept 'Noise Figure' from a single scalar value to a two-dimensional curve, function of the input noise and the input signal. Theoretically, it showed that under certain circumstances, the non-linearity could lead to an improvement of the signal-to-noise ratio. This theory was also verified by practical measurements.
The latest developments are to predict the noise behaviour of the amplifier when bandpass filtered noise is presented at its input.
Acronym FWOTM116 Finished 1/10/98 → 30/09/02

### Flemish discipline codes

• Electrical and electronic engineering

### Keywords

• micro-waves
• non-linear system
• modelling
• microwaves
• measurement