# Small Signal Model for transistors

1. Jul 7, 2013

### nebbione

Hi everyone, at my university (Computer engineering) we are studying the small signal model, but i didn't understand the practical application, i mean, why and when should it be used ?

For example at home i usually make electronics circuits, so i wanted to know how can i use the small signal model in my experiments ?

And when to use the large signal model ?

Thank you,

2. Jul 7, 2013

### Staff: Mentor

The small-signal model tells you the AC characteristics around a biased point. It is used when you need the AC characteristics (gain, impedance) of the transistor so that you can calculate the AC gain or impedance of the circuit that incorporates that transistor.

3. Jul 7, 2013

### nebbione

And what's the difference between large signal model?

4. Jul 7, 2013

### dlgoff

http://ecee.colorado.edu/~bart/book/book/chapter5/ch5_6.htm

5. Jul 7, 2013

### carlgrace

The issue is that it is VERY difficult to calculate things like gain, bandwidth, and distortion directly from first principles. You end up with Volterra series which are notoriously difficult to deal with.

By making some assumptions (the main one being the signal is small enough not to change the device's operating point) you can make the calculations MUCH easier, and also more insightful.

In practice you use the small-signal model whenever you can, and the large-signal model when you must.

6. Jul 7, 2013

### Staff: Mentor

The characteristic curves of a transistor are very nonlinear. Its β varies with IC, its VBE varies exponentially with IB, etc. The small signal model is a linear approximation that works well for small excursions around a fixedpoint, and allows much easier analysis & design. See below.

The best idea is to think of the diode's exponential curve. For small excursions around a point on that curve, we can represent the exponential's behaviour as a DC voltage source in series with a fixed resistor, we have linearised the characteristic. The resistor value needed? It's determined as being equal to the slope of the exponential at that operating point.

Suppose you see that your transistor's collector current is 100mA when its base current is 1mA. You'd probably say its β = 100. But then you notice that for a collector current of 115mA the base current needed is 1.3mA. So it seems β here is only about 90? But when designing for small changes, we say IC changed by 15mA when IB changed by 0.3mA, giving a small signal β = ΔIC / ΔIB = 50

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