Question

How can you calculate the input impedance of a network using Y-parameters?

Answer 1

To calculate the input impedance of a network using Y-parameters, you need to follow a few steps. First, let's understand what Y-parameters are. Y-parameters (also known as admittance parameters) are a way to characterize a linear two-port network. They relate the input current and voltage to the output current and voltage of the network.

In general, the Y-parameters are represented as follows for a two-port network:

[ I1 ] [ Y11 Y12 ] [ V1 ]
[ ] = [ ] [ ]
[ I2 ] [ Y21 Y22 ] [ V2 ]

Where:

I1 and I2 are the input currents at ports 1 and 2, respectively.
V1 and V2 are the corresponding input voltages at ports 1 and 2.
Y11, Y12, Y21, and Y22 are the four Y-parameters, representing the network's behavior.

To calculate the input impedance (Z_in) using Y-parameters, you can do the following:

Short-circuit port 2 (i.e., set V2 = 0) while keeping port 1 open (V1 ≠ 0).
Measure the current flowing into port 1. Let's call this I_in (the input current).
Now, the input impedance (Z_in) can be calculated as Z_in = V1 / I_in.

Here's the reasoning behind this calculation:

When port 2 is short-circuited (V2 = 0), the output current at port 2 (I2) will be zero.
Since I2 is zero, the equation simplifies to: [ I1 ] = [ Y11 Y12 ] [ V1 ]
[ ] [ ] [ ]
[ 0 ] [ Y21 Y22 ] [ 0 ]
or simply: [ I1 ] = [ Y11 Y12 ] [ V1 ]
[ ] [ ] [ ]
Now, you can calculate I_in (the input current at port 1) as I_in = Y11 * V1.
Finally, the input impedance (Z_in) is given by Z_in = V1 / I_in, which results in Z_in = 1 / Y11.

So, the input impedance Z_in is equal to the reciprocal of the Y-parameter Y11.

Keep in mind that this method assumes a linear two-port network and is valid for small-signal analysis. For large-signal analysis or nonlinear networks, other methods might be necessary.