# Can we think of an impedance or an admittance as a case for a transfer function?

We define impedance as the complex ratio of potential (voltage) over flow (current). We can describe it as how much a system "impedes" the flow according to a potential applied to it. But wouldn't it be better to think the other way around, as the resulting potential produced by a flow through the system?

This interpretation of impedance feels more organic with the topology of electronic systems. Once current flows through an element, it produces a voltage potential. The input is current, the output is voltage. This would turn flow into the input and potential into the output. Output/Input = Transfer Function.

This approach makes the concept of admittance, which is sometimes better applicable for mechanical systems, easier to manipulate. The input for a mechanical system is usually force and the output is velocity. Again, Output/Input = Transfer function.

I'm modelling transducers and it seems like transfer functions are a more general concept for describing the behaviour of a system that converts energy between domains (electrical<->mechanical).

But wouldn't it be better to think the other way around, as the resulting potential produced by a flow through the system?

No of course not; engineers usually think of the current flowing as a result of a potential being applied. However, it all depends on what your primary source is (more often than not voltage).

Can we think of an impedance or an admittance as a "special" case for a transfer function?

Not a special but an actual case.

• Wouldn't that be a contradiction then? Transfer function assumes that the denominator is an input and the numerator is an output. In the case of an electrical impedance, it is voltage/current which would mean that current would have to be the input. Also, you could think that what initially reaches the element, the input, is the current and due to it, a drop in voltage potential occurs. – RaiGon84 Mar 7 '18 at 14:28
• Notwithstanding the majority case of using conductance as a TF for an applied voltage with current as an output, I was using the only other question you raised (your title) to ensure I covered all your angles and if the source is current then the TF is impedance. For instance a transimpedance amplifier has a TF measured in ohms. A MOSFET has its TF as siemens because you apply volts and get out current. – Andy aka Mar 7 '18 at 14:32
• What initially reaches the element (IN ALL SITUATIONS) is a current field and voltage field both simultanously. – Andy aka Mar 7 '18 at 14:34

Ordinary admittances or impedances are response functions but they are not transfer functions.

Regardless of the usage in mechanical engineering, in EE a transfer function is a response function that describes the output at one port as a result of stimulus at another port of a device.

So admittances and impedances are not transfer functions. They are response functions for a single port only, and they don't transfer a signal from one port to another.

There are circuits called transimpedance amplifiers that transfer a signal from one port to another. They produce a voltage response to a current stimulus, so their transfer function is called a transimpedance.

But wouldn't it be better to think the other way around, as the resulting potential produced by a flow through the system?

An impedance does exactly this. It describes the voltage response to a current stimulus:

$$v = Zi$$

An admittance is the opposite, it describes the current response to a voltage stimulus:

$$i = Yv$$

In these equations the (initially) unknown or dependent values are on the left hand sides and they are calculated from the known or independent values on the right hand sides.

This interpretation of impedance feels more organic with the topology of electronic systems. Once current flows through an element, it produces a voltage potential.