# Transfer function and voltage probes

I have two questions. I have the following filter circuit: 1) How can I find the transfer function?

(I think):

$$\text{H}=\frac{\text{Z}_2+\text{Z}_3}{\text{Z}_1+\text{Z}_2+\text{Z}_3}$$

2) When I have two voltage probes (+ and -) what do I measure? I think:

$$\text{V}_{\text{probe}}=\text{V}_{\text{Z}_2}+\text{V}_{\text{Z}_3}$$

## 2 Answers

The transfer function (unless there is a load on the output) is simpler than your equation because Z3 can be regarded as a short circuit between the top of Z2 and the output. In effect you have a potential divider formed by Z1 and Z2.

If you have a load then the TF is more complex because you have to take into account the potential divider formed by Z3 and the load AND the impedance this creates in parallel with Z2.

In all of this I am assuming the input feeds Z1 and the output is at Z3.

So, the TF is simply $\dfrac{Z_2}{Z_1+Z_2}$ when the output is unloaded.

• So what does my transfer function look like? – jkall Nov 18 '16 at 10:49
• @jkall I've added the TF – Andy aka Nov 18 '16 at 10:51
• So it doesn't matter that Z_3 is a combination of a series capacitor and coil? – jkall Nov 18 '16 at 10:53
• If the output is just an open circuit (never true in reality) then it doesn't matter what Z3 is made from because there is never any current passing through it. – Andy aka Nov 18 '16 at 11:00
• As Andy said, if there’s a load at the output (this circuit looks like a motor LCL filter) then the Z3 component matters. If it’s a signal circuit, the right side is probably high-impedance. The voltage probes in the question indicate that. – vindarmagnus Nov 18 '16 at 11:26

What you have shown is a two port. Given that, its characteristics are defined by this matrix; $Z_{21}$ is the forward transfer impedance. This is what I would guess is what you are looking for. $Z_{21}$ is found by setting $I_2$ to 0 (open circuit) and solving for $V_2/I_1$.

You can find out more in this Two Port Lecture.