Theory

A silicon NPN BJT consists of a P-type silicon region sandwiched between two N-type silicon regions as shown in Fig.2.1. The P-type region, which is called the base, is very narrow. The N-type regions are called the emitter and the collector. The structure is actually two PN junctions which are in very close proximity to each other. At this point we will not concern ourselves with the physical details of how a BJT works, but we will give its equivalent circuit for amplifier operation.

  

Figure 2.1: BJT Basic Structure (NPN)

To function as an amplifier, the BJT is biased to operate in what is called the forward active region. In the forward active region, the base-emitter PN junction must be forward biased, while the base-collector junction must be reverse biased. BJT operation can be fairly complicated, but you can go very far without worrying about the details and consider a BJT in forward active to be a three-terminal device composed of a diode and a current controlled current source as shown in Fig. 2.2.

  

Figure 2.2: Large Signal Equivalent Circuit

Whenever we analyze or design circuits in this chapter, we will assume that the BJT operation is governed by its equivalent circuit, and analysis is performed by replacing the BJT circuit symbol on the left of Fig. 2.2 with the equivalent circuit on the right of Fig. 2.2.

The BJT then has three terminals, the base, collector and emitter, and thus three terminal currents, I_b, I_c, and I_e, which are defined in the Figure above.

In forward active, the collector current is equal to the base current times the current gain $\beta$ or $I_c = \beta I_b$, where $\beta$ is typically about 200. From Kirchoff's current law we have

I_e = I_c + I_b

Substituting $I_c = \beta I_b$we have

$$I_e = I_b( 1+ \beta )$$ (16)

Furthermore, the base current I_b depends on the base emitter voltage V_be. (Note that while this expression is very accurate, it does contain approximations which will be discussed later.)

$$I_b=I_S exp{\frac{V_{be}}{V_t}}$$ (17)

Where I_S is the saturation current which is a parameter like $\beta$ that depends on the specific BJT construction. Also V_t is the thermal voltage which is equal to $\frac{KT}{q}$ where K,T,q are Boltzmann's constant, absolute temperature and electron charge, respectively. At room temperature V_t=0.026V.