Application to Transistor Modeling and Circuits

Abstract

The typical introduction to spectral techniques covers linear passive RLC circuits and potentially leaves the impression that active devices, such as MOSFET transistors, work with a different logic. While it is true that active devices are nonlinear, that alone does not preclude them from riding on the spectral techniques wagon! We all have seen the small signal model of transistors, which is an RC network with some controlled sources. Since this simplification, around a DC operating point, results in a passive linear network, the transistor small signal model should abide by the rules and techniques under spectral and convolution umbrella! As such this chapter shows how to extend our analysis of transfer functions to transistors. We start by reviewing the basis behind the large signal operation of the MOSFET to get the IV characteristics and then introduce the small signal model. In the low-frequency version, the small signal model includes only resistors and current sources; in the high-frequency version it also includes parasitic caps. Add to that the load cap and we end up with a multi-branch RC circuit just like we’ve been dealing with all along. We experiment with a few simple MOSFET circuits, derive the operating point, then the small signal model comprised of output impedance and input/output transconductance both of which depend on the MOSFET terminal voltages. Then we derive the system transfer function, such as output voltage versus input one. Knowing the solution in the frequency domain we are assured a time version thereof via inverse transforms.