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.

- Normalize the load impedance by dividing it by
the characteristic impedance of the transmission
line.
- 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.
- You have four options for solving this
problem:
- shunt inductance
- shunt capacitance
- series inductance
- series capacitance

- For the series cases, start from the impedance
and rotate toward the generator. It will
intersect the circle of unit resistance at two
points.
- 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.
- 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.
- 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.
- 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.
- 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.