Stochastic approach to noise modelling of bipolar microwave transistors

To characterise the noise behaviour of transistors, different noise equivalent circuits are used. In these circuits the noise properties are modelled as noise voltage and current generators in order to design microwave devices for low noise applications. In this paper we present a stochastic approach to study the noise modelling of bipolar microwave transistors. Starting from experimental on-wafer measurements of the scattering and noise parameters of these bipolar devices, we obtain the corresponding Giacoletto model with the noise internal sources. We write down then the stochastic differential equations of the Giacoletto model for a short-circuited output in order to study the noise properties of these devices. The probability distribution of the output current is obtained. We give the analytical temporal behaviour of the second moment of the output current, assuming particular given correlation functions between the internal noise sources. From the power spectrum of the output current we obtain the behaviour of the noise figure as a function of the operating frequency. Our theoretical results are in good agreement with experimental ones. The present approach allows us to study the statistical properties of the output current for different statistics of the internal noise sources of the bipolar transistors (BJT and HBT)