Transistors

Models

Devices like diodes and transistors are non-linear devices. This means that the mathematics to solve them can become very complex. Solving circuits with these elements is often done by using computer simulation software (i.e. SPICE).

In order to be able to analyse circuits containing transistors, models have been developed that replace them with a number of linear components, like resistors, voltage and current sources, capacitors and inductors. This allows approximating the behaviour of the transistor while still only utilizing easy to solve linear components. Depending on the type of circuit one of several models can be chosen to work with. Most models can be used in a simplified or extended version to account for more advanced concepts such as the Early effect and Miller effect. In many cases these effects do not have a substantial impact on the behaviour of the circuit and can be safely removed from the model, thus making the circuit a lot more easy to solve.

Diodes

The image below shows how a diode can be modeled as a simple voltage source or as a voltage source and a resistor to approximate its real behavior.

The voltage source approximates the voltage drop of the diode, whereas the resistor accounts for the small resistive loss causing a higher voltage drop with higher currents. Using the actual Shockley equation is in most cases highly unpractical; in many cases for example one would not know all the parameters for the equation. Computer simulation software has predefined parameters for known (popular) diodes, and thus can do very accurate simulations. In the professional scene, vendors have models of their products available for use in simulation software.

Bipolar Junction Transistors (BJT)

For BJTs, several models are available depending on the type of usage.

DC models

For determining the DC operating point, the following model is used when the transistor is in forward-active mode:

This model can be used to perform a DC analysis of the circuit, with relative simplicity. Note that I have seen the value of Vbe being set to either 0.6V or 0.7V. This is likely based on the perspective of the teacher. For circuits where a relatively high base current is common a higher value is probably assumed compared to applications witch usually employ lower currents. In some practical amplifier circuits I have studied, the base current is often just a few micro amps, and actual values of Vbe are just shy of 600mV.

TODO: add models for other transistor modes (saturation and cutoff) + explain how to determine

AC models

For AC circuit analysis, there are different models available. Both models presented here are simplified. That is they are not for very high frequency analysis, where parasitic capacitances and special physical effects of the transistor come in to play.

The models here as so called small signal models, which means that they assume the transistor is operating on a DC bias point that is properly setup and is much higher than the AC signal that is in superposition on top of the DC bias. For amplifier circuits this is the case.

However, for normal usage, they are quite accurate. Most circuit theory I have seen utilize these simplified models, and I have used them to successfully predict real world circuit behaviour with success.