Problema 33-3    Source:    Problem created by the site's authors.

In the circuit shown in Figure 33-3.1 determine:

a) the "h" parameters:

b) check its equivalence with the use of   Table 30-01 with g parameters

Solution of Problem 33-3

Item a

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

To solve this problem we will present an alternative technique, using the equations taken from the circuit, without the need to introduce voltage or current sources at input or output ports. We transform the equations into a form similar to the equations that describe the quadripole. In this way, by equating the coefficients that accompany the variables, we obtain the parameters of the quadripole. Let's do the calculations.

Using the circuit shown in Figure 33-3.1 and using Kirchhoff's law for meshes, we obtain:

Working algebraically eq. 33-03.4, we obtain:

Agora façamos a malha identificada como I₃ na figura acima.

And from the circuit we find that I_x = I₂ + I₃. Substituting this value into eq. 33-03.6, we obtain:

Replacing eq. 33-03.7 in eq. 33-03.5, we obtain:

Now comparing this equation with the equation eq. 33-03.2, we can easily see that the coefficients that accompany the variables I₁ and V₂ will be the values of h₂₁ and h₂₂. Soon:

To calculate h₁₁ and h₁₂ we will work algebraically eq. 33-03.4, obtaining :

Therefore, replacing eq. 33-03.9 in eq. 33-03.3, we obtain:

Replacing the value of I₂ given by eq. 33-03.8 in the above equation and, after some algebra, we obtain:

Solving this equation, we obtain:

Comparing this equation with eq. 33-03.1 we find the values of h₁₁ and h₁₂, or:

Item b

To find the g parameters we will use   Table 30-01   to get: