Problema 33-4    Source:    Problem 18.7 - page 781 -    NILSSON & RIEDEL -    Book: Electrical Circuits - 10th edition - Ed. Pearson Education do Brasil - 2016.

Select the values of R₁, R₂ and R₃ in the circuit shown in Figure 33-4.1 so that h₁₁ = 4 Ω, h₁₂ = 0.8, h< sub>21 = - 0.8 and h₂₂ = 0.14 S .

Solution of Problem 33-4

The parameters "h" are given by the following equations:

Note that in the problem statement we must select values for the resistors. This way, we will select a value for R₁. Let the value be:

Initially, making V₂ = 0, that is, putting port 2 in short circuit, we can determine the value of h₁₁. In this case, R₃ will be eliminated from the circuit. Then, the resistors R₁ and R₂ will be in parallel. And their parallel must be equal to h₁₁ = 4 Ω. Soon:

Carrying out the calculation, we determine the value of R₂, or:

On the other hand, if I₁ = 0 the value of h₂₂ can be calculated. In this case, we need to calculate the parallel between (R₁ + R₂) and R₃. This way, we have:

As h₂₂ = I₂ / V₂, then inverting the previous equation and replacing the known resistors by their respective numerical values we have:

Solving this equation, we find the value of R₃, or:

Naturally, these are not the only values that satisfy the problem statement. It depends on the initial value. For example, if R₁ = 24 Ω then R₂ = 4.8 Ω and R₃ = 9.499 Ω. These values also satisfy the requirements of the problem. Check it out!!!.