Q of parallel tuned circuit

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

April the 1st?

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

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.

Cool!

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

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 correct answer.....

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

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

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.

Please keep us informed of your experiments. Highly interesting.

John

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 receiver.

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

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, and really help yourself.

--
 Thanks,
    - Win

(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 work to transfer audio from a receiver to headphones wirelessly.

Just a thought. Good luck.

John

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

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

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

PS: The comments about frequency vs minimum wore diameter is 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?