Any complex source impedance can be matched to any complex load impedance by
two L network configurations. One will be a low pass (series L and shunt C)
while the other will be a high pass configuration (series C and shunt L) when
connected from source to load.
Some source/load values will result in 4 possible configurations. It depends on
the following two relationships between source and load impedances.
The real part of the load, when the load is in the equivalent series form, must
be less than 50 ohms, which is the usual source impedance. Simultaneously, with
the load expressed in the equivalent parallel form, the real part must be
larger than 50 ohms.
An easiest way to find all of this out is to download the free L matching
software 'LC Match' from RadioCom Corp which is easily found in the Google
search thingie.
For examples of all of the above, when matching a load of, say, 500 +j200 ohms
to 50 ohms at 14 mHZ, the two possible networks are:
1. series 185 nh, shunt 7 pf and which is a low pass network.
2. series 7 pf, shunt 231 nh and which is a high pass network.
If the load impedance when in series equivalent form is, say, 15 +j30, notice
that the 15 ohms real part is lower than the 50 ohm source. And notice that it
is larger than 50, it is 75, when the load is in the parallel equivalent form.
Therefore we would expect to see four possible configurations. And, sure
enough, these are:
1. series 402 nh, shunt 410 pf.
2. series 322 pf, shunt 196 pf.
3. shunt 347 pf, series 1604 pf.
4. shunt 372 nh, series 215 pf.
In the first example, the coil of 185 nh would probably be preferable to the
larger coil of 231 nh for lowest tuner loss. Actually there's not much
difference in this case.
In the second example, things are pretty much even. Note however, that two of
the possibilities require only two capacitors and no coils in the tuner.
Unfortunately, the capacitor values appear prohibitively high and therefore
difficult to come by. It's a toss up between solutions 1 and 4.
I am not certain but I believe that all popular antenna analyzer instruments
yield measurements in the series form but don't take my word for it. At any
rate the LC Match program requires load input in the series form.
As simple as an L C network appears, there are a few additional interesting
subtleties but I didn't want to complicate the issue too much. If the load
impedance is given as a parallel equivalent form, always transform to the
series form to check for the possibility of four networks. Actually, the best
thing to do is use EZNEC as the antenna modeling software, ARRL's TLW
Transmission line software and RadioCom's LC match software. These will give
you a comprehensive picture of your antenna system. Too bad there isn't ONE
program that combines all three elements and none that I know about that
calculates tuner losses; L, PI, T and others. What about that, you software
writers out there?
73, AL
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