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?)

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?

Thanks in advance for any insight!
Dave

"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

Joel Kolstad wrote:

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

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.

Thanks for the response Joel. So if I understand correctly, Q is
basically an indicator of how well the LC circuit resonates? Could you
think of Q as the inverse of a dampening coefficient?

If so, I guess ideally you'd get the best Q with an iron-core inductor,
thick windings, and as few windings as possible?

Dave

dave.harper wrote:

Joel Kolstad wrote:


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

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.


Thanks for the response Joel. So if I understand correctly, Q is
basically an indicator of how well the LC circuit resonates? Could you
think of Q as the inverse of a dampening coefficient?

If so, I guess ideally you'd get the best Q with an iron-core inductor,
thick windings, and as few windings as possible?

Dave

If I may jump in....
The case of crystal receivers is somewhat different than a "powered"
radio in that you want to keep things at as high a Q as possible to
match the high impedance of the circuit. High Q is desirable in any
case but moreso in a crystal set.

After having established a good high Q with the LC configuration you can
count on the circuit/antenna loading it down somewhat so then it becomes
a matter of selecting appropriate diodes, decoupling the ant, etc. so it
always helps to start out with as much as possible.

Textbook Q of more C/less L is dictated simply by resistance. In
practice, at least for BCB xtal radios, the dielectric of the coil, skin
effects of the wire, interwinding capacitance are the key players.
Thats why certain coil dimensions, use of litz wire and certain winding
techniques can generally be counted on for the highest Q.

The Q of a coil, and/or complete circuit, will have a curve of its own.
With BCB, what is good at 600kc may be better at 800kc and
(relatively) terrible at 1600kc.

I've had good success with ferrite toroids approaching Q=400, although
ferrites are by nature very unpredictable Q-wise. This is as good as
one can expect with something like a 3-4" diameter coil of #18 wire on a
good coil form. OTOH, the toroid stops there. That same 4" coil wound
with 660-strand litz can get up into the Q=800 stratosphere with a
basket-wind technique.

There's always a downside. A big, hi-Q coil needs to be kept well away
from ANYTHING or else the Q will take a nosedive and then lead
capacitance starts biting you from the backside.

I find xtal sets fascinating. I've been radioing for 35-40 years and
never gained a full appreciation for L, C and Q until I got into DXing
with xtal sets. Logged 105 BCB stations in the competition earlier this
year including two in Brazil!

-Bill

From: "dave.harper" on Thurs 14 Jul 2005 18:55

Joel Kolstad wrote:

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

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.

Thanks for the response Joel. So if I understand correctly, Q is
basically an indicator of how well the LC circuit resonates? Could you
think of Q as the inverse of a dampening coefficient?

In a way, you might think that. For going to more advanced things
besides "simple AM receivers," I'd suggest thinking of Q as a
built-in LOSS element.

For parallel-tuned circuits, the loss can be modeled as a resistor
in parallel with the L and C. This equivalent resistor value is
the reactance of either L or C (they are equal at resonance)
multiplied by Q. A high Q indicates least loss in a parallel
circuit, a high value of equivalent parallel resistance.

But, for series-tuned circuits, the loss is equal to a resistor
in series with L and C. That resistor value is equal to the
reactance of either L or C divided by Q. A high Q in a series-
tuned resonance would have the lesser value of series resistance.

If so, I guess ideally you'd get the best Q with an iron-core inductor,
thick windings, and as few windings as possible?

Yes and NO. Q will vary by MANY things. Generally, physically
big coils will have higher Q, physically big windings will have
higher Q. Shape factor, like length versus diameter of a
solenoidal winding has an optimum value. Nearby shielding will
tend to reduce Q; one reason why toroidal forms have higher Q
than solenoidal or cylindrical windings.

CORE MATERIAL IS FREQUENCY SENSITIVE! "Iron core" has to be
defined. Power transformer laminations are okay at up to
about 10 KHz and then become more lossy with increasing
frequency. Special iron (tape shape, usually) is used for
higher frequencies in the supersonic range. At LF and higher,
various kinds of iron POWDER are used to enhance Q (within
their specified frequency range).

Q applies to capacitors also...and is affected by things like
plate area, plate material, dielectric if other than air, and
(to some degree) physical shape factors. Generally, though,
the Q of most resonating capacitors is 10 to 100 times larger
than inductors and can usually be neglected in most
calculations of tuned circuits. Inductor Q rules! :-)

For self-education, I'd suggest spending some time with a good
Q Meter and trying out measurements on various kinds of
inductors. That will probably give you the best Q picture in
your mind.

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.

dave.harper wrote:

Thanks for the response Joel. So if I understand correctly, Q is
basically an indicator of how well the LC circuit resonates? Could you
think of Q as the inverse of a dampening coefficient?

Just about exactly. You'll find the term "damping factor" (sometimes
"damping ratio" or "damping coefficient") often used in many situations
involving network analysis and control systems, usually represented by
the lowercase Greek letter zeta. And it's numerically equal to 1/(2Q),
so Q is exactly 1/2 the inverse of the damping factor.

When the damping factor is 1 (Q = 0.5), a second order circuit is said
to be critically damped.

Roy Lewallen, W7EL

wrote:

Before I start my rant, let me excuse myself to Len (who I highly
regard) for taking some issues to point on the actually-having-done-it
level.



"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.

Loop antennas do suck on a xtal set for that reason but "bigness" can
suck equally if not done right.



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.

You know how you read all those old texts about using nice glass
insulators and keeping the wire away from anything? In everyday
practice you can do pretty well what you please with wire antennas and
powered radios and notice very little difference. Once you get into the
realm of truly hi-z installations those tree leaves brushing against the
wire become noticeable.

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]

Acutally the best is a good matching xfmr and sound powered phones.
Those old 1920's 2k headsets are relatively deaf. But you did specify
"simple crystal receivers" and it that case it doesn't really matter.

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.

Q in excess of 1000 is readily achievable. 200-300 is a starting point
on a decent dx set.



How come the coils on many of the CR schematics


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

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

.....snipping here....

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.

Most of these old ckts relied on a 17 or 21 plate cap which was in the
400-500 pf range. They would tune the entire band at full tapping. The
tapping allowed a guy to really nitpick his tuning for two
reasons...ease of fine tuning and higher Q at the best combination.

"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.

I think you described the Philmore kit well. That was a toy.


My 4 cents worth.


-Bill

-ex- wrote:
Q in excess of 1000 is readily achievable. 200-300 is a starting point
on a decent dx set.

So what's a good inductance to DC resistance ratio for an inductor on
an xtal set? The one I wound is about 500uH, and I get a resistance of
3.2 Ohms.

Using the formula Q=2*pi*f*L/R, I get a Q for my coil of 981 (@1MHz).
But based on its performance, I KNOW it's not that good. I'm picking
up a couple stations at night, but just barely.

Dave

dave.harper wrote:


-ex- wrote:

Q in excess of 1000 is readily achievable. 200-300 is a starting point
on a decent dx set.


So what's a good inductance to DC resistance ratio for an inductor on
an xtal set? The one I wound is about 500uH, and I get a resistance of
3.2 Ohms.

Using the formula Q=2*pi*f*L/R, I get a Q for my coil of 981 (@1MHz).
But based on its performance, I KNOW it's not that good. I'm picking
up a couple stations at night, but just barely.

Dave

For BCB work the 'standard' is in the 220-240uh range for tuning with a
~365-400 pf cap. There's an (almost) infinite number of combinations
you can use if you want to split the band into segments which sometimes
has an advantage. But switches and tapped coils can also be Q-killers
once you get into the Q stratosphere.

In practice the coil Q is determined primarily by the form dielectric,
wire size, wire spacing, diameter/length ratio/neary coupling effects,
etc. R is far enough down the list that its generally not even
considered. When you do a DC measurement of coil R thats not
representative of the skin effects and true RF resistance, thats why the
textbook formula doesn't pan out.

If you want to make a fairly nice coil without getting into the expense
of litz, check out spider-web coils and rook coils. When done with say
16-18 ga wire, and diameters in the 4" range you can get a pretty nice
coil. With 166-strand litz (30-35c/ft) you'll note an improvement but
by that time its time to start thinking about a good hi-q ceramic
capacitor and circuit loading concerns.

The Rap-n-Tap forum is where to get some good info.
http://www.midnightscience.com/rapntap/ "Best coil" is a common topic!

-Bill