Problem 32-1    Source:   Problem elaborated by the author of the site.

In the circuit shown in Figure 32-01.1, determine the parameters "Y".

Solution of the do Problem 32-1

The Y parameters are given by the following equations:

It is calculated Y₁₁ making V₂ = 0, that is, a short circuit. Therefore, we must connect a current source I₁ on the input port. In the Figure 32-01.2, we chose I₁ = 3 A (only a convenient value) in such a way what I₂ = 2 A and the current across the 4 ohms resistor is equal to 1 A. Then, V₁ = 4 volts. Therefore, with this data we can calculate the following parameters:

Repeating the process, to calculate Y₂₂ and Y₂₁ we must have V₁ = 0, that is, an input short-circuit (port 1). Let us place a current source at the output (port 2) with a convenient value, for example 4A. Thus, a current of 1 A will be circulated by the resistor of 6 ohms , generating a voltage V₂ = 6 volts. And in the 2 ohms resistor , will pass a current of 3A. Therefore, I₁ = - 3 A. The modified circuit and the values of the variables can be seen in the Figure 32-01.3. Note that in he resistor of 4 ohm will not pass current due to the short circuit at the input.

As can be seen, Y₁₂ = Y₂₁ and with this we conclude that the circuit is PASSIVE or RECIPROCAL.

Alternative Method

Another way to solve the problem by knowing in advance that it is a circuit PASSIVE or RECIPROCAL, would be to compare it with the model seen in item Theory. Always remember that the admittance (Y) is the inverse of the resistance (R) and vice versa.

By direct comparison, we realize that:

And also that:

Doing in a similar way for the other branch, we have:

Therefore, we conclude that: