reactive matching

Reactive matching is another form of impedance matching that can be used to match a load impedance to a transmission line. Reactive matching involves adding capacitive or inductive elements in series or parallel with line.

The problem with reactive matching is that at high frequencies it becomes difficult to fabricate discreet inductive or capacitive components. Connecting such an element introduces a lot of fringing which can drastically effect the performance of the circuit. For this reason, stub tuners and quarter wavelength transformers are more commonly used. Reactive matching, as with other matching techniques, is generally fairly narrow band; the distance the element is placed from the load depends on the wavelength of the signal being carried.

Like other impedance matching techniques, reactive matching can be solved using the venerable Smith chart.

1. Normalize the load impedance by dividing it by the characteristic impedance of the transmission line.
2. Plot the impedance on the Smith chart. Use your compass to draw a circle around the center of the Smith chart at the same radius as the impedance you just plotted.
3. You have four options for solving this problem:
1. shunt inductance
2. shunt capacitance
3. series inductance
4. series capacitance
4. For the series cases, start from the impedance and rotate toward the generator. It will intersect the circle of unit resistance at two points.
5. At the point on the top half of the Smith chart, you are at 1 + jA, where A is positive. For impedances, the top half of the Smith chart is inductive, so you have to add a capacitance of -jA to cancel out the inductance. Note the distance from the load impedance to 1 + jA. Multiply that by the wavelength to get the distance from the load that you have to add your series capacitance of -jA.
6. At the point on the bottom half of the Smith chart, you are at 1 - jA. For impedances, the bottom half of the Smith chart is capacitive, so you have to add a impedance of jA to cancel out the capacitance. Note the distance from the load impedance to 1 - jA. Multiply that by the wavelength to get the distance from the load that you have to add your series impedance of jA.
7. For the shunt cases, the procedure is much the same. The only difference is that you must convert the impedance to a admittance by rotating it a quarter of a wavelength (half way) around the Smith chart.
8. From the load admittance point, rotate around the circle you have plotted until you cross the 1 + jA circle (the circle of unit resistance). You will cross this circle in two places. Note the electrical distance traveled and multiply by the wavelength to get the distance your shunt element must be from the load.
9. If you at the upper point, then you have a capacitance you have to cancel out by adding a shunt inductance (for admittance, the top half of the Smith chart is capacitive and the bottom half is inductive). At the bottom point, add a shunt capacitance to cancel out the inductance.

A good understanding of what happens to a impedance or admittance as you rotate along the Smith chart, and remembering that for series elements you sum impedances and for parallel (shunt) elements you sum admittances is all you really need to solve reactive matching problems.