This project will use conjugate matching to match a capacitive load of 50-j40 to a generator of impedance 25+j30. Since the generator impedance is complex, conjugate matching is required to match the network, as opposed to in situations of low frequency where the reactive components are negligible. In the example, an L network is used to match the generator to the load. Theoretically, differentiating the power and setting this equal to zero proves that maximum power is transferred when the resistance of the source and load are equal and the reactive portions are equal and opposite phase shift/sign.
The first step is to use the impedances given to calculate the actual lumped inductor and capacitor values to use for the network to work at 2 GHz. 25+j30 corresponds to a 25 ohm resistor in series with a 2.387732 nH inductor and 50-j40 corresponds to a 50 ohm resistor in series with a 1.98944 pF capacitor.
The following shows the schematic with the source, matching network and load.
Running the simulation with Data Display equations yields….
This shows maximum power transfer at the correct frequency of 2 GHz. The next step is to use the Smith Chart tool. A shunt inductor and series capacitor is used to form the L Network. Exact values can be typed in for these to get the impedance value Z = 0.5 +j0.6 which is the normalized equivalent source impedance (divided by 50).
With the capacitor and inductor values recorded, these values can be loaded into a separate schematic and compared to the original schematic results.
Conjugate matching is not achieved with this Smith Chart configuration so there is no peak at 2 GHz.
Alternatively, the Smith Chart tool can be used from the palette. From this point with the chart icon selected, the network can be created by selecting “Update Smart Component” from the Smith Chart tool window. These results show that it is important to select the proper design network for the specifications for optimal results.