Understanding the Concept of RLC Matching Circuits

Why matching circuits are needed?

As we know that in RF systems maximum power delivery is the main objective while designing a circuit and to maximise the power delivery with minimum loss, matching networks are created. Read understanding the need of matching networks.

The main goal of RLC circuit is designing matching circuits. We have a circuit as shown below with R_s as the source impedance and R_L as the load impedance. So in order to have maximum power transfer in a circuit R_L should be equal to R_s. As we read before in the maximum power concept that to have maximum power transfer in a circuit, the load impedance Zl must be matched to the complex conjugate of the source impedance Zs*.

Assuming that we do not have equal resistances in this circuit therefore, we would need matching circuit which has only reactive elements like L & C. With this matching circuit maximum power can be delivered to R_L. The input of the matching circuit should be R_s as Z_in should be equal to conjugate of source impedance Zs* however, we assume that we have only real part therefore R_in=R_s

In previous section input impedance using Quality Factor and Resonance in RLC circuits we calculated the input impedance Z_in using RLC circuit which is equal to:

Here, Qp means quality factor of C and R_L. In order to make this circuit as matching, Z_in should be equal to R_s. So we have to design LC in order to reach this matching.

We know the load resistance R_L and the working frequency w. The only thing we have to change is C. When we change C we also have to change L. In previous section input impedance using Quality Factor and Resonance in RLC circuits we read that in method 2 when Q_p² was not higher than 1, L was calculated as:

Now that we can calculate w, RL & C, L can be calculated using the above equation. L & equivalent C in this parallel circuit are in resonance so the only thing left here is R_s. We have to say that the imaginary part of Z_in is equal to 0. Designing this matching circuit the output resistance can be transferred to input of the matching circuit by dividing it with 1+ Q_p². In summary, we have designed L & C so, the equivalent matching circuit can be shown as:

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