# Q of parallel tuned circuit

Discussion in 'Electronic Design' started by Albert, Apr 1, 2005.

1. ### AlbertGuest

I need to have an estimate of the Q for a parallel tuned circuit
consisting of a 10 microhenry air wound coil and an 8.2 microfarad
electrolytic cap.

Coil parameters are below.

DC Resistance 0.16 Ohms
Wire Gauge 24 AWG
Wire Diameter 20.1 mils (1 mil = .001 in)
Coil Length 1 in
Coil Inner Diameter 0.5 in
Coil Outer Diameter 0.54 in
Average Turn Diameter 0.5 in
Wire Length 6.02 feet
Copper Weight 0.01 pounds
Turns 46
Levels 0.92
Turns/Level 49.75

The circuit will feed into an mk484 AM radio chip (or it's very
similar brother, the LMF501) which has an input impedance of (about)
100 K ohms.

I'm sure this is easy to do, but I can't figure out how the ac
resistance of the cap impacts the Q calculation.

Thanks,

A

2. ### Charles SchulerGuest

April the 1st?

3. ### Bob LiesenfeldGuest

8.2 uF? This works out to a resonant frequency of about 17KHz. Does
this have to do with the "insta-fence" project?
In any event, the series loss resistance of the cap and the series
loss resistance of the coil must be converted to parallel form where
they can then be added using product over the sum method to get a total
loading resistance to calculate Q (not including the zin of the chip
which if is ~100K will probably be so much higher as to be unimportant).

Estimating the loss of the cap may be the more difficult of the two.
From experience with tanks down in the audio/vlf range I would not
expect a Q higher than about 50 if that. Many types of electrolytics
are very lossy. Perhaps you could change to a higher value of L and
less C to get away from the electrolytic?
None of the above includes any losses from a load such as an antenna
connected to the tank.
Hope this helps.

Bob

4. ### AlbertGuest

Thanks Bob, appreciate the info.

I used to work with active filters years ago, and we always used
polystyrene caps, matched with a simple C meter.

Not sure if they make them now and/or whether they go up in value high
enough.

You get the prize tho-you gave (by far) the best answer. Some thought
it was homework and another thought it was an April Fools joke.

Yes, it is for the Insta-Fence project. I returned the one I bought
because it was over priced and it was large and ate custom (single
source) batteries like candy (6 bucks a throw).

I threw together a really crude receiver... TL082 op amps, a ferrite
core loopstick antenna with about 14,000 pf of silver mica caps. It
resonated well at 17.8 Khz. With the existing transmitter, I roughed
out a couple of 15 hz active filters and took off running towards the
road (700 feet away). I used TL082's for the front end and also for
the 15 Hz active filters. The stock receiver from petsafe dies at less
than 100 feet. My homebrewed unit allowed me to cross the street and
go about 200 feet past that. So, I was very close to 1000 feet!!
Problem is, my prototype was too large and used way to much battery
power...but it demonstrated that a better receiver is possible and
easily doable.

I found the Temic U4224 vlf receiver chip, which is used in 'atomic'
clocks at 40, 60 and 77.5 Khz. If quartz filters are used, they are
very narrow band and sensitive. They draw 30 microamps, have a digital
output and built in AGC. But, I can't find any of these chips! They
company is well hidden, maybe they are only available in Europe?!

The mk484/lmf501 AM receiver chips also have agc, run on 1.5 volts and
they only draw 300 micromaps. They are 3 terminal devices, so they are
really small and easy to work with.

I had some idea for transmitters too. With the laptop soundcard, a
random loop antenna and generating 17.800 and 17.815 Khz, I managed to
hear the laptop 'transmitter' for 4 feet with the stock receiver and
about 80 feet with my homebrewed prototype.

Anyway, I'm well into phase II, which is making the receiver smaller,
lighter and more practical. I like using the air wound coil and the 8
uf cap because the coil is easy to build (not many turns). Going to a
lower value cap means winding a MUCH larger coil, which is why I asked
for Q values for the coil and cap in the previous message.

I had not planned on using a wire antenna, just the loop (small
ferrite or air coil).

I had really hoped that the low esr electrolytics would allow a decent
Q, they come is small surface mount packages too. I would like to
have a Q of 100, if that's possible. But, have no idea what I need to
do to make that type of Q.

I want to investigate using a ceramic filter or possible a quartz
filter in the front end, which will incur some losses, but will really
limit the out of band interference.

A

5. ### Bob LiesenfeldGuest

They make them but not in the uF range that I know of.
Hahahah. Yeah there is a lot of "Homework Help" stuff that shows up.
Excellent! This is how to best solve this type of problem. Try stuff and
try to extract the useful data.
I have used these chips and they are quite useful although I don't know if
it is exactly what you are after. Have you though of using opamps in an
active bandpass filter configuration for 17KHz? A coil (the larger the
better) could be used as an antenna feeding the first stage.
That magnitude of Q is going to be difficult to obtain in an L/C ckt at
that freq. Active filters again seem to me to be the approach to persue.

Keep me posted. Sounds like an interesting project.

Bob

6. ### AndyGuest

A trick question. If there is ONLY the inductance specified and
the capacitance specified in the circuit, the "Q" will be infinite.

As a practical matter, there would be resistance present, but this was
not part of the specification. Hence it becomes a trick question.

A million years ago, back in school, I had a prof that used to delight
in quesions like this. Some people would generate "volumes" of
discussion
on possible solutions and why the question was stupid, and others would
see right thru it..... and only waste 5 seconds in giving the

Happy April 1st to whoever posted this question !! :>)))

Andy (old, retired EE who still has a sense of humor)

7. ### John - kd5yiGuest

Hi, Albert -

The reactance of the coil at 17 kHz is only 1.07 ohms. You say the
resistance is .16 ohms, so the Q of the coil is only 1.07/.16 or 6.7.
Adding the capacitor will not improve your Q. You probably need to increase
your inductance, if you can do so without increasing the resistance much.
Larger diameter wire will help.

They make ceramic chip capacitors up to 22 uF these days. See Kemet in
Mouser. But, watch out for the temperature curves.

John

8. ### AlbertGuest

My friend,

This is not a joke, April Fools message or anything of that sort and
it's not a theoretical 'trick' question.
Your statement is absolutely true, but in real life, there is no such
thing as zero series resistance, so the series resistance value will
always be finite, hence the Q will always be less than infinate.

I am building a small, low power and easily transported 17.8 Khz

I asked for an approximate estimate of the loaded Q, so I can have a
starting place for the selectivity in the front end, which is a
parallel resonant circuit feeding a relatively high impedance receiver
chip.

Can you help with an approximate value using a modern low esr
electrolytic cap?

A

9. ### John - kd5yiGuest

<Albert> wrote in message

(snip)
(snip)

The unloaded Q of the coil is X/R. You need to get the inductance up and
keep the resistance down. If you go up in inductance, the required
capacitance goes down which will help the Q of the capacitor. And you can
try using ceramic chip caps.

Here is a thought that just occurred to me... what if your loop antenna
passed through a small toroid core which also had a secondary winding with
a lot of turns of small-gauge wire? It would basically be a transformer
with a physically big primary loop. I have seen something similar to this

Just a thought. Good luck.

John

10. ### Winfield HillGuest

Albert wrote...
I don't think you'll want to use a 8.2uF electrolytic cap for
resonance. Not only does it have a very unstable capacitance
value, it has a high esr. For example, consider a good bipolar
elec, with tan-d = 0.15, the esr = tan-d/(2pi f C) = 0.16 ohms,
which is as bad as your wimpy 0.16-ohm 10uH coil. (It's funny
how those two numbers are equal, is this a homework problem?)

First, I'd recommend that you use larger than #24 wire for your
coil. The skin depth of Cu is 2.6-in/(sqrt f) = 0.02" at 18kHz
(it's funny how #24 wire happens to be 0.02" dia). Considering
proximity effect, you need wire with a larger diameter, flat
strip, or paralleled windings, etc. Better yet, use litz wire!

Second, I'd recommend a film cap, instead of an electrolytic.
Along with using bigger wire, you could keep your total series
resistance under say 0.05 ohms. Then your Q = Xc / esr = 22.
But with such a low inductance at such a low frequency, you've
got a very low signal source impedance of only 22 ohms to the
amplifier! That's a good candidate for an input transformer!
If you stick with the #24 wire and 8.2uF electrolytic, you're
looking at a Q of no more than 5 or so, and a nearly useless
5-ohm Zsource too.

Actually, why not use a ferrite or laminated iron core in the
coil to raise the inductance, reduce the cap size, raise the Q,

11. ### AlbertGuest

Hi John, thanks for the help.

I understand about the Q of the coil now. And, I understand that a
smaller value cap will have less esr (and, therefore a higher Q).

I'm not sure how the Q or the cap and the Q of the coil combine though
(to make an overall Q for the tuned circuit.

I'm working on a 17 Khz receiver that will be magnetically coupled so
the antenna will be a coil (not a wire).

The manufacturer of one of the chips I might use cautions about using
a high Q coil because the bandwidth will be much to narrow and
temperature change becomes an issue then.

Since the receiver has to operate in 0 degree weather as well as 90
degree weather, I had hoped to use an air wound coil in the finished
product.

The receiver has to be small and use very low power, so the physical
size of the antenna matters alot...which is why I started with a 10 uh
coil and a higher value cap. It also needs to be somewhat omni
directional so I planned on having 2 coils mounted at 90 degree
angles.

If I use ferrite cores, the antenna coil can be much smaller tho-most
likely I can't get away from ferrite coils. Since the coil is a
receiving antenna, I can probably use high mu ferrite, which will make
the coil MUCH smaller.

Thanks so much for all the comments and have a great day.

A

12. ### AlbertGuest

I don't think you'll want to use a 8.2uF electrolytic cap for
OK, thanks Win,

I remember your assistance several years back regarding the
cockcroft-walton power supply I was working on then. Thank you again!
The supply was a complete success.

OK, you make alot of sense regarding the wire size.

The coil is part of a parallel tuned circuit that will also be the
antenna for a 17 Khz receiver I need. The receiver needs to be pretty
sensitive, but the spectrum down there is pretty noisy. So, the
bandwidth of the antenna has to be carefully considered.

The antenna coil has to be small and compact, as does the receiver
itself. But, one of the manufacturers of the chip I might use warns
against building a high Q antenna coil due to temperature issues. My
receiver needs to work from zero to 90 degrees F, so this is not a
trivial consideration. I had assumed (perhaps wrongfully) that air
dielectric would be more stable than ferrite.

OK, the receiver chip has around 100 K input impedance, so 5 ohms
feeding it would not result in good power transfer.

One question though.....

If I know the Q of the cap and the Q of the coil, how do I estimate
the Q of the combined coil and cap?

OK, since this isn't a high power situation, I don't have to worry
about saturation. So, I could use a very high mu ferrite, which would
keep the physical size of the coil down.

Can I use steel at 17 Khz? I thought steel modulation transformers
performed badly, which is one reason why they aren't widely used in AM
transmitters these days.

Can thin layers of steel be laminated to be low loss at 17 Khz?

Drop me a line when you can and thanks again.

A

interesting. The 17 Khz transmitter I bought had 9 inch coils and # 30
wire. The wire size is just a guess, but it's probably pretty close. I
compared the transmitter coils to some 30 gauge wire wrap wire I had
here, and the stuff is about the same size.

Is it possible that there is the possibility of better range by
winding equivalent inductance coils on the same sized forms, except
that larger gauge wire is substituted?

13. ### John - kd5yiGuest

Hi, Albert -

The Qs combine just like parallel resistors. Q(total)=1/(1/Ql + 1/Qc)
whether in parallel or series.

Yes, I understand that.
I think you will have some trouble getting a Q high enough for this to be a
problem, but I might be wrong. You have already said you wanted a Q of 100,
as I recall.

With a low Q, this is not a problem. And, I doubt you will get a high Q in
a small size without some heroic effort. But, I've been wrong before.

I'm not sure you understand what I proposed. Imagine a loop of (say) two
feet in diameter composed of one turn of wire. On the circumference of the
loop is a small toroid of (say) .5 inches inside diameter. Close wound on
the toroid is (say) 20 turns (or 50 or 100) of #30 wire.

Now you get a 20:1 increase in voltage or current. A 400 to 1 change in
impedance. Your very low impedance loop is now 400 times better at matching
a realistic input impedance.

Of course, this is hypothetical and I have very little to back it up except
for the example I gave in another post.

In any case, I wish you luck and I will follow your posts. They will be
educational, I'm sure.

John