What are the characteristics of a quadripole circuit element?

Question

I'm reading Music, Physics and Engineering (H. Olson 1967), and contains models of musical instruments as electric circuits, i.e. uses the analogies between electrical circuits and mechanical (mass-spring-dashpot) systems. (The idea is that the reader will be more familiar with the electrical circuit representation.)

In some of these systems he uses (without defining) a "quadripole" circuit element. A specific instance is to represent the sound board of a guitar (or other string instrument).

I've seen some vague references that it performs some sort of amplification, but I would like to known a reasonable approach for mathematically representing it's effect within an electrical circuit.

Another possibility is that the term "quadripole component" has fallen out of favor, and there is some other more modern name for this type of thing.

Answer 1

A "Quadripole" is a "four-terminal network", if the currents through pairs of terminals are equal, it becomes a "Two-port network".

If you post a schematic containing a quadripole, I could probably tell you if it is a two-port network or not.

The equation for a two-port network is: $$ \begin{bmatrix}V_1\\V_2\end{bmatrix}= \begin{bmatrix}Z_{11} Z_{12}\\Z_{21} Z_{22}\end{bmatrix}\begin{bmatrix}I_1I_2\end{bmatrix} $$