EEE 51 Transistor Models

In EEE 41, you studied the fundamental concepts of how transistors can be realized using semiconductors, specifically, the two most popular transistors currently in use: the bipolar junction transistor (BJT) and the metal-oxide field-effect transistor (MOSFET).

In EEE 51, we want to be able to use these transistors (as well as other semiconductor devices such as diodes) to design and implement useful electronic circuits. This means we have to be able to describe, and eventually predict, the behavior of the terminal voltages and currents of these devices. We can accomplish this by using transistor models.

Large Signal Transistor Models

The large signal transistor models allow us to describe the electrical behavior of the transistor, when a voltage or current is varied over its allowable range. Here, we can see how varying the terminal voltages (and currents) determine the operating region of the transistor. Since there are many combinations of voltages and currents available for us to choose from, it is convenient to standardize which terminal voltages/currents we can use. This makes it easy to compare different transistors, as well as to systematically analyze and design electronic circuits based on these transistors.

The standard large signal transistor characteristics that we use are (1) the transfer characteristics, (2) the output characteristics, and (3) the input characteristics. Note that these models are normally considered as DC or low-frequency models, where we assume that the transistor parasitic capacitances are still negligible.

Transfer Characteristics

Transfer characteristics usually implies an input-output relationship, similar to the transfer function of a two-port network. But where are the input/output terminals or ports of a transistor? As we will see later on, one of the main goals of electronic circuits is to amplify signals (i.e. voltage, current, etc). Thus, it is convenient to choose the input-output terminal pair of a transistor that is commonly used to provide the largest amplification. In the BJT case, it is the common-emitter configuration, and in the MOSFET case, it is the common-source configuration.

The BJT Transfer Characteristic:

The BJT common-emitter (CE) configuration is shown in Fig. 1. We define the “input” signal as the base-emitter voltage, $V_{BE}$, and the “output” signal as the collector current $I_{C}$. Therefore, we can model the the BJT transfer characteristic using

$I_{C}=I_{S}\cdot \left(e^{\frac {V_{BE}}{V_{T}}}-1\right)\cdot \left(1+{\frac {V_{CE}}{V_{A}}}\right)$

(1)