Figure 2-5 shows an example for matching to 50Ω, and the following figure is an example of the
transformation using a different network.Figure 3-1. Matching to 50Ω
The following list provides a guideline on the transformation process (assuming ideal
conditions):
ZL has an assumed impedance of
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:
With the transformation from the shunt element,
the new admittance is reached, as represented in the following
equation:
As the next matching element is in series
orientation, the admittance must be transferred back to an impedance level using the
following equation:
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:
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 3-2. Example Application Circuit
for 50Ω Matching
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