# Matching to a Given 50Ω Impedance

Figure 1 shows an example for matching to 50Ω, and the following figure is an example of the transformation using a different network.
Figure 1. Matching to 50Ω

The following list provides a guideline on the transformation process (assuming ideal conditions):

• ZL has an assumed impedance of ZL=(RL+jXL)Ω
• A parallel component changes the impedance on the conductance circles (mirrored Smith Chart). Therefore, the easiest way to handle parallel components is to convert them to the admittance level by the following equation:
YL=1ZL=(GLjBL)S
• With the transformation from the shunt element, the new admittance is reached, as represented in the following equation:
Y1=(G1+jB1)S
• As the next matching element is in series orientation, the admittance must be transferred back to an impedance level using the following equation:
Z1=1Y1
• The serial component can make changes in the impedance level. As the component has no resistance, it only influences the imaginary part of the complex impedance. Therefore, the real part must be already at 50Ω and the following equation gives the impedance at Z1:
Z1=(50jX1)Ω
• The transformed impedance after the serial component is ZS = 50Ω
Note: Consider following the rules of admittance deployment if the impedance transformation is done in the Smith Chart (without a network analyzer). The following figure shows an example application circuit for a 50Ω matching network. The antenna already has the target impedance so that the complex impedance ZL can match to the target impedance.
Figure 2. Example Application Circuit for 50Ω Matching