RF Electronic Devices and Systems

# Transmission line circuit for mismatched load and generator

Let’s consider the most general case of a circuit, where we have the arbitrary loads Z1, Zand an arbitrary generator.

The input impedance of the terminated transmission line is . The voltage on the line $V\left(z\right)={V}_{0}\left({e}^{–j\beta z}+{\Gamma }_{l}{e}^{–j\beta z}\right)$ . To receive the voltage of the generator we must take into consideration is the reflection coefficient of the generator. The standing wave ratio here is $SWR=\frac{1+|{\Gamma }_{L}|}{1–|{\Gamma }_{L}|}$ . So the power delivered to the load is: where ${Z}_{in}={R}_{in}+j{Z}_{in},{Z}_{2}={R}_{2}+j{Z}_{2}$.

1. When the load is matched to the line, ${Z}_{in}={Z}_{0},{Г}_{l}=0$ and .

2. When the load is matched to the line, ${Z}_{in}={Z}_{2}$ the load power is

3. Assuming that the generator impedance is fixed, the condition $\frac{dP}{d{Z}_{in}}\to 0$ leads to the maximum power delivered to the load.

The conjugate matching condition is . This condition is conjugate matching, that leads to the maximum power delivered to the load for a fixed generator impedance . Figure 1 depicts the general case of transmission line circuit for mismatched load and the generator.