The circuit in question doesn't appear to be in the PDF. You need to use
a lot of caution with Lankford's theories. I don't want to get into a
pissing contest, so I will leave it at that.
Push pull with transformers goes back to the tube days. It is a
convenient scheme to kill 2nd harmonic distortion while at the same time
biasing the single sex amplifier.
Take the center tap and tie it to a positive voltage. Feed the other two
inputs to the transformer with a differential signal. You have blocked
DC from the output, restoring a ground referenced single phase. (as
opposed to differential) output.
These active whips are prone to picking up electrical noise. Fine if you
live in the boonies. Not so good for urban dwellers.
If the antenna is just a wire in the air, I'm not sure what good it does
to capacitively couple the input. Who cares if some DC is floating on a
wire just poking in the air.
While some people think of transformers are bandlimiting devices, note
that all those coupling caps have series inductance. There is no free lunch.
Just meditating out loud, if you were to go push pull with a ferrite
antenna AND you are winding it yourself, you could avoid the biasing
resistors by putting a center tap in the antenna itself, then tie that
center tap to an appropriate bias voltage. I haven't seen this done, so
their may be a gotcha with that scheme, but the science is good.
Generally you will get a lower noise circuit if the input device is an
amplifier rather than a buffer.
Lanksford's input stage is essentially a push pull buffer, but I don't
see that cancelling 2nd harmonics like a push pull amp. But for a whip,
which is a single ended input, I don't see a way to get a differential
input. Not true for a ferrite antenna.
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