# Misunderstanding of output impedance and linearity

When I read about Thevenin equivalent, it is mentioned it only applies to "linear circuits".

But I also see in texts and tutorials showing how to measure the output impedance of an actual device which is complex such as a power supply or a transducer. They measure the output impedance and equate the device to a single power/signal source with a single output resistance/impedance.

But these devices are composed of non-linear circuits. And the whole idea of Thevenin applies to linear circuits.

How come we can employ Thevenin in these devices conceptually? Is a power supply or a transducer a linear circuit?

You have to separate some things first.

Thevenin by itself has nothing to do with output impedance. Thevenin is just a method for "shuffeling around" sources and impedances (resistors) and represent them in a different way which is sometimes convenient. For example:

This only whorks for linear elements and therefore only for linear circuits.

Output impedance is also only defined assuming that a circuit behaves in a linear way. We can however define for example output impedance of a non-linear circuit by linearizing it around a certain operating point.

This is what is for example done for all transistor based circuits which have a (somewhat) linear behavior for small signals but have a non linear behavior for large signals.

For that large signal behavior we cannot define an output impedance but for the small signal behavior we can. And in case that results in an inconvenient circuit, we could use Thevenin to represent it in a different way which is more convenient.

• You mentioned small signal model, similar to this I think: pcbheaven.com/wikipages/images/trans_theory_1323438130.png But this is different than linear RCL circuits with current voltage sources. There is a dependent current source here. Is this circuit still linear?? Why? Commented Jan 2, 2017 at 12:07
• Indeed that is an example of a small signal model. A different circuit might have a different small signal model. Yes that circuit is still linear. Linear means, for all values of the input value, an X times increase in value gives an X times increased value at the output. The circuit behaves the same if you feed it 0.00001 V or 10000 V, Vout/Vin remains the same. An ideal dependent source where Out = A * In is also a linear circuit element. What would not be a allowed is a dependent source with a certain maximum output value. Or a x^2 like behavior. Commented Jan 2, 2017 at 12:31

The bad news is that there are no linear circuits in real life. Even resistors and capacitors exhibit a certain amount of non-linearity.

Anyway, the theory of linear circuits is very useful and powerful. For this reason non-linear circuits are approximated by linear ones in order to be able to apply concepts like transfer functions, frequency response and so on.

It depends on the circuit and the application how well this approximation works, sometimes it is necessary to use different linear models for various operating points to model a non-linear circuit sometimes it is sufficient to work with a single model.

Using linear models for non-linear circuits is done routinely so that people often forget about the fact that the approximation might only be valid for a certain operating point, e.g. when an AC simulation is made for a circuit that contains non-linear devices like transistors.