The real part of the load impedance is rarely equal to the transmission-line impedance. In most cases, we have to transform the real part of the impedance as well.

For example, load impedance represents a series connection of a resistor and a nH inductor at 1 GHz. To match impedance to the transmission-line impedance , we first normalize the load impedance to transmission-line impedance.

This impedance is shown in Figure fig:PointSC.

#### SWR circle

Then, we identify an SWR circle that this impedance is on, as shown in Figure fig:SWRfor25Ohm. The point where the SWR circle intersects the green circle is of interest because the real part of the input admittance is equal to one . This second point, where , will give us the length of the line that we have to add to the load impedance.

#### Length of the line that will transform the real part of load impedance

To find the length of the line that will transform the real part of to , we identify the position of the load impedance , and the input impedance at the Wavelengths Towards Generator (WTG) scale. The reason we picked impedance is because the real part of the admittance is equal to one . Load impedance is at , and the input impedance is at . The difference between these two positions gives us the length of the line . In electrical degrees, this length is approximately . The input admittance to the line is now .

#### Adding a lumped-element to remove the susceptance

The final step is to add a susceptance that will remove the imaginary part of the input admittance . We see that to get the final admittance of , numerically, we have to add an admittance of . This represents an inductance. Since we are adding the two admittances , they have to be in parallel (as we know that when elements are in parallel, we add their admittances).

#### Other possible solutions

Graphically, there are several different mixed or transmission-line impedance matching circuits that we can make for a specific impedance. For example, for impedance , , there are four different circuits that we can make, as shown in Figure fig:MixedVariety. In this paragraph, we used the green path on the Smith Chart, with intermediate admittance .