Numerical modeling and uncertainty analysis of transistor noise‐parameter measurements

SUMMARY This paper provides an overview of the use of noise parameters as a numerical model to represent the noise characteristics of transistors, particularly in the context of a Monte Carlo evaluation of the uncertainties in noise-parameter measurements. The Monte Carlo also relies on a numerical model of the measurement process, in order to generate simulated measurement results, and this numerical model is also reviewed. Copyright © 2014 John Wiley & Sons, Ltd. Received 24 July 2014; Revised 30 October 2014; Accepted 9 November 2014 Models for the noise properties of transistors must, of course, respect the laws of physics, but beyond that, their validity is established by comparison to measurement results. Some parameter that characterizes the noise behavior is measured as a function of frequency or the physical temperature of the device, and the model predictions are compared with the results of those measurements. The parameter(s) that are chosen for measurement and comparison are typically taken from an effective-source or a type of black-box model of the transistor that is based on a few general properties (basically that the device is a frequency-preserving, linear two-port) and that is general enough to encompass any detailed model for the internal workings of the transistor. Any meaningful comparison of model predictions to measurement results requires some knowledge or estimate of the uncertainties in the measurements. If one truly has no idea of the uncertainty in the measurement, it is impossible to confirm or disprove any model. In practice, the ‘estimate’ often is merely a qualitative ‘feel’ for roughly how accurate the measurements are, but obviously a quantitative estimate from a solid analysis is preferred. Because of the complexity of most noise-parameter measurements, the most viable approach to uncertainty analysis is a Monte Carlo analysis. Such an analysis requires both the measured values of the noise parameters and a numerical model for the measurement system and process. This paper presents the basic effective-source or black-box models that are used to parameterize the noise characteristics of transistors, and it then reviews the numerical model for the measurement process that is employed in a Monte Carlo treatment of the uncertainty analysis. In the next section, we provide some basic background information and definitions for those more familiar with numerical modeling than with transistor noise measurements. The section after that presents two black-box