"dave.harper" wrote in message
ups.com...
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?

For the L-C resonator itself, the falloff will be 6dB per octave (doubling of
frequency) once you're well outside of the center (tuned) frequency. The 3dB
bandwidth will be determined by the Q of the circuit, and this is often not
particularly well defined during the design stage -- often a well-defined
bandpass filter somewhere "down the line" (e.g., at an IF stage) will
ultimately define what the radio receives.

The 6dB/octave drop comes from just looking at the impedance or transfer
function of an LC(R) resonator -- you'll end up with an s^2 (frequency
squared) term in the denominator of the equation.

(different combinations of L and C will tune to the same frequency, but
is the gain the same?)

No, although for low Q resonators, it's often pretty close.

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. Is it to increase
the range of your radio's coverage? Or because the gain at certain
frequencies is better with different C/L combinations?

They're usually trying to match the impedance of the LC circuit to the input
impedance of "the next stage" (i.e., a transistor amplifier) to maximize power
transfer. So, while it's not really "gain" (we haven't amplified anything
yet -- this is more like a resistive divider), the output will be higher with
different C/L combinations.

Generally speaking, most relatively simple AM receivers are really only
intended to pick up relatively strong, nearby transmitters. As such, you can
get away with an awful lot of "cut and try" when it comes to designing the
circuit (largely ignore matching impedances, Q's, etc.) and still obtain
acceptable results.

---Joel