From: dave.harper on Jul 12, 4:12 pm

I had a couple of questions regarding recievers that I haven't been
able to figure out. I'd appreciate it if anyone could give me some
insight...

How well-defined is the gain for a cap-coil loop, like in an AM radio?
(i.e., how fast does the gain droppoff as you move up or down from the
'tuned' frequency?) Is it a function of L and C? Or just frequency?
(different combinations of L and C will tune to the same frequency, but
is the gain the same?)

"Gain" of a crystal radio depends on the bigness of the antenna.

If you are talking about a loop antenna on an AM [BC band]
radio, then it's a different story. The loop antenna on an
AM receiver is small/tiny/micro-stuff relative to the 200+
meters of AM BC wavelengths. The received signal VOLTAGE
is directly dependent on the number of turns in that loop and
the physical size of the loop.

A loop antenna is into what some folks call a "magetic antenna";
i.e., very small relative to wavelength, therefore it intercepts
only the magnetic part of the electro-magnetic wavefront radiated
by a transmitter. The more turns in that loop, the greater the
voltage induced in the loop.

A humungous-long wire is going to supply the greatest amount of
POWER to a crystal receiver. POWER drives the headphones. But,
the amount of power coupled in involves IMPEDANCE and that, right
away, gets into a complicated mess of more electrical rules.

Simple crystal receivers want to keep impedances very high at
both input, middle, and output. ["crystal" or piezo-electric
headphones are the best for that, next best is the highest
impedance magnetic headphones (2000 Ohms or higher) you can get]

For the typical parallel-tuned L-C input to a crystal set, the
inductor Q will make a difference. It must be as high as is
practical; Qs of 200 to 300 have been done. But, the Q of the
coil is dependent on a LOT of different factors which I noted
in the other message.


How come the coils on many of the CR schematics I've seen have multiple
tap locations? It seems that with a variable cap, you should be able
to tune to whatever frequency that's in your range.

Mostly, that is just old-time tradition! :-) [I kid you not]

The formula for resonance is: F^2 = 1 / (39.478 * L * C)

With F being frequency in Hz, L in Hy, C in Fd.

To check this out, a 2.5 mHy inductor and 1000 pFd capacitor
will be resonant very close to 100 KHz.

The maximum to minimum variable capacitance ratio is equal to
the square of the maximum to minimum frequency tuning ratio
desired. That's about IT.

"Taps" on a coil can be to select different inductance values
for resonance with limited-range variable tuning capacitors.
Note: Back in the prehistory of radio, like around the 1920s,
variable capacitors were expensive and not so easy to get. A
few old-time crystal sets "tuned" via lots of coil taps using
a fixed parallel capacitor. I had a Philmore crystal radio kit
back in 1946 that did that. Very cheap kit. It worked, so-so.

Presupposing a loop antenna that is resonated by a variable
capacitor, its "gain" is going to be greatly influenced by
its Q or Quality factor. The higher the Q, the greater the
voltage into the headphones. However, the Q may NOT be the
same over the approximate 3:1 frequency span of the AM BC
band. [again, too many variables as noted in other message]

The Q of that L-C circuit is going to be "spoiled" by the
impedance/resistance of the headphones. Those headphones are
in parallel with the parallel-tuned L-C circuit. The higher
the impedance/resistance of the headphones, the least effect
it will have on the Q of the L-C resonant circuit.

Somehow my browser failed to pick up your initial message so
this is a reverse-order answer. Sorry about that.