Maximum power with transformers

[Bromio]

Homework Statement

In Figure 1, the transform is perfect (k = 1). Calculate the maximum power which can be transferred to the load ZL. Design a dipole which that power can be transferred to.

Homework Equations

k = 1 --> n = sqrt(L1/L2).

Pmax = |V(rms)|/(4*Rg)

The result must be Pmax = 0.368 W approximately.

The Attempt at a Solution

I've eliminated the transform dividing current source maximum value (I = 1) by n = 0.5 and each impedance by n^2 = 0.5^2. Then, I've obtained the Thevenin equivalent of the circuit from ZL. Eventually, I've used the formula for Pmax. I've got Pmax = 0.380 W. OK.

However, the problem solution offers another way to solve it, which is shown in Figure 2. In this case, the maximum value for current source is 2, and, the elimination of the transform is done after getting the Thevenin equivalent circuit. I don't understand why the maximum value is 2. Why?

Thank you.

 

[KataKoniK]

Hello there,

Thank you for your post. It seems like you have made some good progress in solving this problem. I can offer some insight into why the maximum value for the current source is 2 in Figure 2.

In Figure 1, the transform is perfect (k=1) which means that the ratio of inductances L1 and L2 is equal to 1. This also means that the ratio of voltages across L1 and L2 is equal to 1. Therefore, the maximum value for the current source in Figure 1 is 1.

In Figure 2, the transform is not perfect (k<1) which means that the ratio of inductances L1 and L2 is less than 1. This also means that the ratio of voltages across L1 and L2 is less than 1. Therefore, the maximum value for the current source in Figure 2 needs to be greater than 1 in order to achieve the same voltage across the load ZL as in Figure 1.

I hope this explanation helps. Keep up the good work in solving the problem!