# Physics of Bipolar Transistors

The bipolar transistor was invented in 1945 by Shockley, Brattain, and Bardeen at Bell Laboratories, subsequently replacing vacuum tubes in electronic systems and paving the way for integrated circuits.

In this chapter, we analyze the structure and operation of bipolar transistors, preparing ourselves for the study of circuits employing such devices. Following the same thought process as in Chapter 2 for *pn* junctions, we aim to understand the physics of the transistor, derive equations that represent its I/V characteristics, and develop an equivalent model that can be used in circuit analysis and design. The outline below illustrates the sequence of concepts introduced in this chapter.

## 4.1 GENERAL CONSIDERATIONS

In its simplest form, the bipolar transistor can be viewed as a voltage-dependent current source. We first show how such a current source can form an amplifier and hence why bipolar devices are useful and interesting.

Consider the voltage-dependent current source depicted in Fig. 4.1(a), where *I*_{1} is proportional to *V*_{1}: *I*_{1} = *KV*_{1}. Note that *K* has a dimension of resistance^{–1}. For example, with *K* = 0.001 Ω^{–1}, an input voltage of 1 V yields an output current of 1 mA. Let us now construct the circuit shown in Fig. 4.1(b), where a voltage source ...

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