Franclim F. Ferreira, Pedro Guedes de Oliveira, Vítor G. Tavares

Circuit transformations method

The circuit transformation method is a procedure to evaluate amplifier circuit parameters gain, input and output resistances) through simple transformations based on the application of the basic circuit theorems ( Thévenin, Norton, etc.).

The method has been published in the IEEE Transactions on Education, vol. 42, pp. 212-216, August 1999:

"Using Circuit Transformations for the Evaluation of Amplifier Parameters"

that may be retrieved in .pdf format, here.

Note: The use of this article is subject to the copyrights of IEEE. Therefore, any non personal use should get the express agreement of IEEE (Copyrights and Trademarks - copyrights@ieee.org).

The application of this method is especially interesting when, for a “pencil-and-paper” analysis, we want to get in a fast and easy way, reasonably approximated values of the circuit parameters.

The main aspect of the procedure is the progressive reduction in the number of elements in the circuit, until we have a circuit in a canonical form so that we can evaluate the parameters by simple inspection.

Therefore, the first step is the resolution of trivial series or parallel of existing resistors. For example, in the circuit on the right, it seems obvious to put R₁, R₂ and r_p in parallel.

When we do it to R₁ and R₂ there is no problem but, in what concerns r_p we should be cautious because its current is the controlling parameter of the current source b i. So, before proceeding to the parallel, we should transform i = v_i / r_p so that

There are many situations where we have a Norton configuration in series with a resistor (or a Thévenin configuration in parallel) and the application of the Thévenin's (or Norton's) theorem may simplify the circuit.

Another situation that occurs frequently requires the application of the source absorption theorem (both in its dual forms). The circuit in the figure represents a typical situation.

The existence of one resistor where we have the sum of two known currents may be transformed through the use of the Miller’s dual theorem, as we can see in the following example:

The previous example can be seen as a feedback circuit: the resistor 3.3 kW provides the feedback. However, there are feedback circuits that are not as easy to solve as this one, as it is the case of the example on the right.

The circuit may be transformed with the equivalent two-port network technique, applied to resistor 3.3 kW seen as a the two-port network:

Let’s now make the changes in the circuit:

Naturally, other situations may occur where the application of the method is not evident and it requires some practice. You may see an animated use and a guided example of the application of this method.