Problema 35-1    Source:   Adapted from problem 19-6 - page 808 -    SADIKU, Matthew N. O. , ALEXANDER, Charles K. -   Book: Fundamentos de Circuitos Elétricos - Mc Graw Hill - 5ª edição - 2013.

In the circuit below determine the parameters "ABCD".

Solution of the Problem 35-1

Os parâmetros "ABCD" são dados pelas seguintes equações:

By making I₂ = 0, we can determine the parameters A and C. A voltage source or a current source is placed in the input port. It was decided to place a current source of value I₁, as shown in the figure below.

From the circuit, since we have adopted I₂ = 0, there will be no voltage drop on the resistor of 10 ohms. It is also possible to notice that in the 20 ohms resistor will circulate the current I₁. Then, by making the mesh in the direction indicated by the arrow red, in the figure above, V₂ is:

On the other hand, by making the mesh in the direction of the violet arrow, in the figure above, the current I₁ will circulate through the 5 and 20 ohms resistors. Therefore, the input voltage V₁ will be equal to:

With this data, it is possible to calculate the values of A e C.

To calculate the values of B and D, we must do V₂ = 0 , that is, the output port must be short circuited.

Making the right mesh, in the direction indicated by the arrow green, it is determined a relation between I₁ and I₂. Then:

Working algebraically this equation:

But, from equation of the quadripole we know that:

Comparing the last two equations, we conclude that the value of D is:

On the other hand, making the left loop of the circuit in the direction of the arrow orange, we get:

Remember that I₁ = - (5/4) I₂. Then, replacing in the above equation and working algebraically the expression:

From the equation of the quadripole it is known that:

In this way, we conclude that:

To conclude, let's write the equations of this quadripole.