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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).

enter image description here

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2 Answers 2

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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.

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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: -

enter image description here

  • \$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.

The answer is therefore no.

can a network analyzer help with this task? Maybe through the use of S-parameters?

Some may and some may not. Read the brochure for the device.

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  • \$\begingroup\$ So, we can't do that even with a network analyzer! Say, by measuring S-parameters then converting them to Y-parameters? \$\endgroup\$
    – Likely
    Commented Jan 19, 2022 at 12:33
  • \$\begingroup\$ I cannot say what network analyser may or may not help here. I suspect some might and I expect some may not. I'm not an expert on network analysers @Likely. If you can extract S parameters and you know the reference impedance used then yes, you can convert to Y or Z parameters. \$\endgroup\$
    – Andy aka
    Commented Jan 19, 2022 at 12:36

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