# Two-port network parameter measurement using an LCR meter

I was wondering if it's possible to find the admittance parameters of a pi two-port network experimentally using an LCR meter.

For the network shown below, we have $$\begin{bmatrix} I1\\ I2 \end{bmatrix} = \begin{bmatrix} Y1 + Y2 & -Y1\\ -Y1 & Y1 + Y3 \end{bmatrix} \begin{bmatrix} V1\\ V2 \end{bmatrix}$$ So, if we short-circuit $$\Y3\$$ ($$\V2 = 0\$$), and connect LCR meter between nodes a and c, we measure admittance $$\Y1+Y2\$$, i.e. element $$\y_{11}\$$. Similarly, if we short-circuit $$\Y2\$$ ($$\V1 = 0\$$), and connect LCR meter between nodes b and c, we measure admittance $$\Y1+Y3\$$, i.e. element $$\y_{22}\$$.

However, I don't see how can we get $$\Y1\$$ since $$\Y1 = \displaystyle-\frac{I2}{V1}\$$(when $$\V2 = 0\$$), and I don't have access to measure either current or voltage but only impedance/admittance using the LCR meter.

Does anyone know if that's possible? If so, how do we proceed? Also, can a network analyzer help with this task? Maybe through the use of S-parameters?

P.S: I'm working with a low frequency (100 Hz - 10 kHz).

I was wondering if it's possible to find the admittance parameters of a pi two-port network experimentally using an LCR meter.

The answer is yes you can.

You can measure the impedance across each port with the other one shorted, this gives m1=Y1+Y2 and m2=Y1+Y3, then you can short a-b and measure across one port, this gives m3=Y2+Y3, and then Y1 = (m1+m2-m3)/2 and the rest is easy.

I was wondering if it's possible to find the admittance parameters of a pi two-port network experimentally using an LCR meter

Whether we talk about admittance parameters or impedance parameters; the problem is that you can find two of the four parameters by measuring impedance (or admittance) but, you can't find the other two. Consider the impedance parameters: -

• $$\Z_{11}\$$ can be found by simple measurement
• $$\Z_{22}\$$ can also be found by simple measurement

But you can't directly measure $$\\frac{V_1}{I_2}\$$ or $$\\frac{V_2}{I_1}\$$ so, you can't infer $$\Z_{12}\$$ or $$\Z_{21}\$$.

Whether its Y, Z or S parameters, two of the parameters relate to impedances or admittances and the other two parameters relate to the gain or transfer function of the 2-port network.