Would the tuner in series with the VHF radio effect its SWR?
It doesn't have to. The circuit can be designed to match 50 ohms to 50 ohms with
a range of Q values. It can also be made somewhat adjustable in case the antenna
doesn't present a perfect 50 match in the first place.
...how do I go about designing the circuit?...
I know there are a number of filter design programs around. I'll have to ask some
of the other hams here at work what they would recommend. You can do the
matching by hand on a Smith Chart, and formulas for the common L and pi networks
used to be in the Handbook. I'm sure some of the other posters on this board can
make recommendations as well.
But for someplace to start, try W9CF's tuner simulator applet available online here:http://fermi.la.asu.edu/w9cf/tuner/tuner.html
This implements a standard T-network antenna tuner, which is the same circuit you
would use for VHF side of the circuit. (If you go into the setup window and set the
maximum inductance to 3uH it makes it easier to gauge the small values from the
positions of the knobs, since the readout is only to the nearest 0.1uH.)
For a circuit that does NOT transform the impedance, expect both capacitors to
have the same value. A standard value such as 10pf or 27pf should work. (Smaller
values will increase attenuation of the 11m signal, but may have a little more loss.)
In this case, using 10pf for both capacitors, we get minimum SWR at about 0.065uH.
In practice you'd use a pair of fixed capacitors and an air core coil, then spread or
squeeze the coil turns slightly to get minimum SWR with a 50 ohm load on the output
of the network. (If you need it adjustable, then replace one of the capacitors with
a trimmer, and adjust both that and the coil for minimum SWR.)
The 11m side is a bit more difficult because it uses series coils and a shunt capacitor,
but you can use the same tool just by reversing the sign of the reactance for each
component. So if the circuit calls for a coil of 1.1uH, for example, you'd convert that
to reactance (~200 ohms) and instead use a capacitor with -200 ohms reactance (which
should be about 33pf if you want to check your math.) You'd also need to change the
sign of the input reactance.
Seems to me that the modeled load impedance was about 4-j500 ohms on 11m, so if
you set the frequency to 27MHz and enter 4+j500 as the load impedance in W9CF's
tuner simulator you can see the effect of various component values. (The Autotune
button comes in handy to get you close, then you can experiment with standard fixed
values for one or both capacitors.) In this case one of the capacitors is at maximum,
which is a clue that a simple "L" network will probably work as well for this impedance.
Personally I'd probably choose to transform the impedance in two steps, perhaps from
5 ohms up to 15 or 20 ohms (depending on what gives a convenient capacitor value)
and then a second stage from that to 50 ohms. With two "L" networks, this is the
same as the "Pi-L" output circuit used in some tube transmitter output stages, and
you should be able to find the equations for that, though any design charts probably
won't go down to 5 ohms. But if you consider each stage separately then it isn't
difficult to do the math by hand.
That won't tell you everything you need to know, but might get you started in some
interesting directions at any rate.