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DC Model and Parameters

  We now look at a model which we use to analyse the DC operation of a transistor in a circuit.

The ratio of collector current to base current is defined as

$$\beta = \frac{I_C}{I_B} .$$ (85)

This is a very important parameter which will be used often. Related to this is the ratio of collector to emitter currents:

$$\alpha = \frac{I_C}{I_E} .$$ (86)

From (83) you can easily work out that

$$\beta = \frac{\alpha}{1-\alpha} .$$ (87)

Typically, $\alpha$ is close to 1, so that $\beta$ is large. Common values might be $\beta$ 20 to 400 or more, and $\alpha$ say 0.99.

We will use the model shown in Figure 100. The BE branch is like the practical model of a forward biased diode, and the current gain relating base and collector currents is modelled by a current controlled current source.

  

Figure 100: DC equivalent circuit model for an npn transistor, with V_BE=0.7 V.

The DC model is only valid when the transistor is operating in its active region.

Spice uses a more complex model that can describe saturation as well.

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