powdered iron or ferrite cores. If carefully made, RF
transformers can be used over a wide bandwidth of 10:1,
such as from 3 MHz to 30 MHz or from 150 MHz to
1,500 MHz. RF transformers are available for receiving
and small-signal applications of a few milliwatts to high
power transmitting units.
L-C Impedance Matching
An alternative to transformers are the L-C circuits or
networks shown in Figure 5. These networks are
composed entirely of reactive components (inductance
and capacitance). The combinations of reactances
transform voltages and currents at one side of the network
to a different combination at the other by sharing stored
energy as circulating voltages and currents. This electrical
juggling act only works when the reactances have the
right values, and that only occurs at one frequency since
reactance depends on frequency.
While four types of circuits are shown in the figure,
there are many variations of each, and even other different
circuits. Each of the networks is named for the letter which
the arrangement of components resembles: L, pi (π), or T.
Any of the Ls in the figure could be replaced by a C and
vice versa, with the resulting circuit being able to
transform different combinations of impedance.
The L network is very simple and works well for
matching values of impedance that aren’t too different.
(The more different Z1 and Z2 are, the higher the
amplitudes of the circulating voltages and currents, and the
higher the losses in the circuit components.) Each variation
of the L network is capable of matching half of the
possible combinations of input and output impedance. The
remaining combinations can be matched by turning the
network around. There is no dedicated input or output!
A calculator program (see the sidebar) determines
values of L and C that create the impedance match. Out of
the four L networks with one L and one C, two of the
circuits will “work.” (For the other two circuits, no values of
L and C are possible.) Of the two possible circuits, you can
select the values of L and C that are most practical, the
least expensive, or whatever is most suitable to your needs.
Figure 6 shows a high power L network that can
handle more than a kilowatt of RF power at 3. 55 MHz.
Other L networks might handle only milliwatts of power.
The pi and T networks act like two L networks
connected back-to-back. For example, if the series
inductor of the pi network is replaced with a pair of
inductors — each having half the original value — it is easy
to see the input and output L networks. Similarly for the T
network, the shunt inductor can be replaced with two
double-value inductors in parallel, creating two back-to-back L networks. Why go to all that trouble when a
simpler L network will do the job?
Remember that as the input and output impedances
get farther apart, the circulating voltages and currents get
larger. Another change is that the bandwidth over which
the impedances can be considered matched shrinks. As
the impedance ratio (also referred to as the network Q)
increases, these two effects can make an L network
impractical — particularly at transmitter power levels.
Pi and T networks are used to convert the
impedances more gradually, putting less stress on the
60 March 2016
Online Network Calculator
There are many network calculator programs, such as the
Microwaves 101 ( www.microwaves101.com) and RF Café
( www.rfcafe.com) websites. My favorite, though, is a web page by
John Wetherell that calculates L and C values for 16 different
networks ( home.sandiego.edu/~ekim/e194rfs01/jwmatcher
/ matcher2.html). Enter the source and load impedance, then look at
all of the choices for doing the job.
FIGURE 6. This L network is an example of the series-C
shunt-L network in Figure 5B. Made from a heavy-duty coil
and vacuum variable capacitor, it can easily handle 1 kW of RF.
FIGURE 7. The
transformer (or Q
section) at A uses a
transmission line to
match Z1 and Z2 by
setting up reflections
with the right phase
to cancel all
reflections from Z2.
At B, two 12th wave
sections match Z1
to Z2 without
requiring a special
transmission line. (Graphic courtesy of the American Radio