Problem 78-10    Source:    Problem 13-30 - page 537 -    SADIKU, Mathew & ALEXANDER, Charles -    Book: Fundamentos de Circuitos Elétricos - Ed. McGraw Hill - 5ª edição - 2013.

Determine the input impedance, Z_in, by replacing the linear transformer of the previous problem, for its equivalent circuit "T".

Solution of the Problem 78-10   

To solve this problem we must remember the theoretical part studied in item 2.5. So, let's reproduce below the "T" circuit and its respective equations.

Note that the above equations relate to inductances and not impedances. However, if we multiply all of them by ω, the equations automatically turn into impedance relations. That way, we can write:

With this information we can design the equivalent circuit, as we can see in the Figure 78-10.3.

Now we can calculate the impedance value on the right side of the circuit, which we will call Z₁, and given by:

We can easily see that this impedance is in parallel with the j10 inductor, resulting in a equivalent impedance of:

And to find the value of Z_i, just add the value of Z_eq with the rest of the circuit. Like this:

As a final result we obtain:

Note that this result is exactly the same as the previous problem, ( Problem 78-9 ) when we use the impedance reflection technique.