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Inductor Q Measurement
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Andrew Kurtz
I am neither a programmer nor trained in electronics, but I am having a great time using my nanoVNA-H4 with my homemade crystal radio. I measure S11 using only CH0, and the results I get for Smith chart, inductance, and reactance seem about right and work well when I use them for things like predicting tuned frequency given a know capacitance.
However, I believe I have no way to estimate Q = X / R for my coils, because R is quite low and may vary between -2 and 5 ohms. That variability may not be all that bad for a $90 instrument, but it can’t be used for Q! I am hoping you EE types may suggest a workaround for getting a decent Q estimate. Here is a totally made up example of what someone may suggest: "R gets quite high at frequencies way higher than those the coil will be used at. At those high R values, the error is less. Take that number, and “everyone knows” equation XYZ for skin effect is quite accurate, so use equation XYZ to back-calculate R at lower, practical frequencies. Now you can estimate Q reasonably well." |
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Andrew Kurtz
Great, thanks! I can see that your article addresses the issue nicely, but it also uncovers so many questions a non-EE like me has:
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- I am guessing a “trap network” is a series resonant circuit, but I’m not sure. - I don’t know what constitutes a “high Q variable capacitor” which your method requires. - When X is 0 at resonance, I get that Rs is all that is left of impedance… but why is that in parallel with the termination resistance? - Indeed, is “termination resistance” simply the built-in resistance of the meter? - What is a “notch” and why is there an attenuation depth when series resonance provides a lack of attenuation? - Couldn’t I simply measure the series resonant circuit with the VNA and get a Rs reading directly, but would it be any better than what I get off the coil alone? Indeed, possibly related to my third point above: I have never understood why X / Rs = Rp / X. I have played with hypothetical cases, and it seems to not work. Andy On Oct 11, 2021, at 9:24 AM, alan victor <avictor73@...> wrote: |
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- I am guessing a “trap network” is a series resonant circuit, but I’m not sure.
YES, IT IS A SERIES TRAP NOT A PARALLEL TRAP BUT IT IS IN SHUNT WITH THE OUTPUT, CH1. SO THIS IS A S21 MEASUREMENT. IN AFFECT YOU ARE USING THE VNA AS A SPECTRUM ANALYZER-VOLTMETER AND TAKING A MEASUREMENT OF THE NOTCH DEPTH. IF THE SERIES R OF THE LC NETWORK UNDER TEST IS SMALL, SAY ON THE ORDER OF MILLI-OHMS, YOU WOULD BE SEEING Q's ON THE ORDER OF 300 OR GREATER. THE MEASUREMENT PROCESS IS JUST THAT OF A VOLTAGE DIVIDER. - I don’t know what constitutes a “high Q variable capacitor” which your method requires. IF THE Q OF YOUR COIL IS ASSUMED TO BE 300 OR MORE... YOU ARE GOING TO NEED TO FIND A C LARGER THAN THAT! AIR VARIABLES LIKE BC BAND ARE PRETTY GOOD AND THEIR ARE SOME CERAMIC CAPS THAT HAVE Q'S GREATER THAN 500... SEE AVX CAPS - When X is 0 at resonance, I get that Rs is all that is left of impedance… but why is that in parallel with the termination resistance? AGAIN, RS IS IN SHUNT WITH THE LOAD, 50 OHMS, BUT ITS VALUE IS SO SMALL, THAT THE NOTCH DEPTH CREATED IS THAT OF A VERY SMALL SHUNT R. THE END RESULT IS THE NOTCH DEPTH IS DIRECTLY CORRELATED TO THE Rs OF THE LC NETWORK AT RESONANCE. - Indeed, is “termination resistance” simply the built-in resistance of the meter? YES, 50 OHMS. - What is a “notch” and why is there an attenuation depth when series resonance provides a lack of attenuation? SERIES RESONANCE PROVIDES A LACK OF ATTENUATION IN THE SERIES MODE. BUT THIS HAS IT CONFIGURED IN THE PARALLEL MODE! - Couldn’t I simply measure the series resonant circuit with the VNA and get a Rs reading directly, but would it be any better than what I get off the coil alone? YES, BUT THE NUMBERS ARE SOME ARE DIFFICULT TO DISCERN. THIS IS AN INDIRECT WAY TO GET TO A NUMBER WITH SOME IMPROVED ACCURACY. KEEP IN MIND, IF THE FIXTURE LOSSES OR R VALUES ARE NOT SMALL, YOU WILL NOT OBTAIN CORRECT ANSWER. Parallel Q is the same as series Q at a single frequency. Google the concept of a series to parallel conversion. There you will find the proof and the math. It is not hard, but will require your familiarity of complex numbers. |
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Andrew, my coil program might interest you. It calculates inductance and Q for solenoids made of solid or Litz wire. It models a number of wire alloys and form dielectrics, dielectric ribs or ridges, coil leads, and polygonal coil shapes. The program can automatically maximize coil Q while keeping inductance constant.
To validate accuracy, the documentation compares calculated values with hundreds of inductance and Q measurements made with an HP 4342A Q meter on dozens of coils of widely varying size and shape. For the coils from my own junk box, average error magnitude is 2% for inductance and 5% for Q. The program runs in Windows and is free. Brian |
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Brian, thanks very much for the link to your program. It seems to run fine
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under Wine in Linux. Dave On Mon, Oct 11, 2021 at 7:10 PM Brian Beezley <k6sti@...> wrote:
Andrew, my coil program might interest you. It calculates inductance and Q |
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Thanks for the feedback, Dave. I didn't mention that COIL is a Windows console program. I gather that wineconsole is necessary. I forgot to mention that a user should first read README.TXT. COIL evolved from a DOS program I wrote 25 years ago. It does not have the usual Windows user interface. Many features are inscrutable, but they are explained in the documentation.
Brian |
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On Mon, Oct 11, 2021 at 09:21 AM, Andrew Kurtz wrote:
That "-2" suggests to me that you're not actually reading 'Resistance' there. Resistance should be positive, but Reactance can be in negative ohms. Since high Q _requires_ low R, it's going to be difficult to get good, low resistance connections to your coil - do you solder the cable from the NanoVNA directly to the coil leads/terminals? Any mechanical variability in the metal-to-metal contact there will certainly affect the Q value. says "The Q, or quality, factor of a resonant circuit is a measure of the “goodness” or quality of a resonant circuit. A higher value for this figure of merit corresponds to a more narrow bandwidth, which is desirable in many applications. More formally, Q is the ratio of power stored to power dissipated in the circuit reactance and resistance, respectively: Q = Pstored/Pdissipated = I2X/I2R Q = X/R where: X = Capacitive or Inductive reactance at resonance R = Series resistance. This formula is applicable to series resonant circuits, and also parallel resonant circuits if the resistance is in series with the inductor. This is the case in practical applications, as we are mostly concerned with the resistance of the inductor limiting the Q." Therefore, you could try measuring a resonant circuit, with, as has been mentioned, a high quality capacitor like an air-insulated variable or a mica capacitor to make the resonant circuit. It might be worthwhile to do some research on the Q or quality of various types of capacitors, to ensure that you get a good one. This is an interesting question/'problem and I've often wondered myself about determining the Q of a component or circuit. I've had lots of training and experience as an electronic technician (and ham radio operator), but none in the advanced types of math needed for engineering. -- Doug, K8RFT |
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On 10/12/21 6:05 AM, DougVL wrote:
On Mon, Oct 11, 2021 at 09:21 AM, Andrew Kurtz wrote:Depending on how the conversion from reflection or transmission coefficient (gamma) to R+jX is done, a coefficient with magnitude >1 will result in negative R.R is quite low and may vary between -2 and 5 ohms.That "-2" suggests to me that you're not actually reading 'Resistance' there. Resistance should be positive, but Reactance can be in negative ohms. If you're measuring low impedances (so |gamma| is close to 1) then noise or roundoff errors in a measurement can wind up with gamma>1 |
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Brian, thanks for the background information on COIL I have gotten many
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features to work under Wine in Linux and it is very useful. I may have spoken a bit too soon in implying everything would work with Wine. However, I need to brush up on Wine and to try COILS on a Windows machine to see what I may be missing. Thanks again! Dave On Tue, Oct 12, 2021 at 8:47 AM Brian Beezley <k6sti@...> wrote:
Thanks for the feedback, Dave. I didn't mention that COIL is a Windows |
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Gary Rondeau
Quick and dirty method... Just measure the self resonance of your coil. If you calibrate the nVNA to your fixture and then just run the S11 sweep up high enough on the coil, you will undoubtedly see a resonant peak. At low frequency you can determine the inductor, L. (the nVNA saver software will do this for you) The frequency of the peak tells you the self resonant parasitic capacitance, C. From the magnitude of the the resistance, R, measured at self resonance, and the calculated self resonant impedance, Z=sqrt(L/C), then Q will be R/Z.
This procedure also shows you explicitly when parasitic capacitance becomes important -- which it often does! |
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Hi Brian,
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Thanks for reminding all about COIL. It takes a little getting familiar with it since you use an interesting GUI interface, but I got the handle on it.? Is there a way to input the coil inductance, fix the physical parameters and come up with the required turns. It didn't seem like it. It's still very useful - thanks again. Regards...Bill - N6GHz On 10/12/2021 05:47:39, Brian Beezley <k6sti@...> wrote:
Thanks for the feedback, Dave. I didn't mention that COIL is a Windows console program. I gather that wineconsole is necessary. I forgot to mention that a user should first read README.TXT. COIL evolved from a DOS program I wrote 25 years ago. It does not have the usual Windows user interface. Many features are inscrutable, but they are explained in the documentation. Brian |
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Bill, I'm not sure this does what you want, but try it: Set frequency, coil diameter, and wire gauge. Click on Turns for turns/inch and set the value you have in mind. Then vary coil length with the mouse wheel until you get the desired inductance. It's really fast if it's what you need. The only thing I truly automated was Q optimization.
Brian |
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Andrew Kurtz
Yes, R cannot be < 0, but my interpretation is simply that the -2 is error in some small number like, say 1 or 2 ohms. I will admit that many of you experts talk about how you attach your DUT very carefully, solder it, sometimes have to throw it away when done testing, and all this sounds bizarre to a non-EE who is simply playing with crystal radio. My nanoVNA attaches to my DUT via 2 alligator clips which are on little connectors (BNC maybe?) which screw into the VNA. I recognize that I am accepting error, even though I do my calibration at the same alligator clips, but except for R, I am convinced that the error I am accepting is negligible when my interest is 0.5 to 25 MHz, picking up AM signals. (I welcome any insights if you think I am wrong.)
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Andy On Oct 12, 2021, at 10:05 AM, Jim Lux <jim@...> wrote: |
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On 10/12/21 11:20 AM, Andrew Kurtz via groups.io wrote:
Yes, R cannot be < 0, but my interpretation is simply that the -2 is error in some small number like, say 1 or 2 ohms.exactly. Let's say the gamma measurement is +/- 5%.? If you convert gamma = 1.05 (angle = 0) you get -2050 ohms and Mag S11 = 0.4238 dB If you convert gamma=0.95, you get 1950 ohms and mag S11 = -.4455 dB Here's some examples (excel attached if you want to fool with it yourself).? For any coil with a reasonably high Q (>100), your DC resistance might be pretty low, especially if the reactance is something like 100 ohms.? In such a case, gamma is VERY close to 1, so small uncertainty in the measurement will result in negative resistance Z = Z0*(1+gamma)/(1-gamma) Z0 50 gamma mag gamma ang complex Z Zreal Zimag 0.5 0 0.5 150 150.0 0.0 0.5 90 3.06287113727155E-17+0.5i 30+40i 30.0 40.0 0.95 0 0.95 1950 1950.0 0.0 0.99 0 0.99 9950 9950.0 0.0 1 0 1 #NUM! #NUM! #NUM! 1.01 0 1.01 -10050 -10050.0 0.0 1.05 0 1.05 -2050 -2050.0 0.0 0.95 90 5.81945516081595E-17+0.95i 2.56241787122207+49.9342969776609i 2.6 49.9 0.99 90 6.06448485179767E-17+0.99i 0.50249987374375+49.9974748750063i 0.5 50.0 1 90 6.1257422745431E-17+i 50i 0.0 50.0 1.01 90 6.18699969728853E-17+1.01i -0.49750012375625+49.9975248750062i -0.5 50.0 1.05 90 6.43202938827026E-17+1.05i -2.43757431629014+49.9405469678954i -2.4 49.9 gamma = (Z-Z0)/(Z+Z0) R X Z Q gamma gamma mag gamma angle 0 500 500i #DIV/0! 0.98019801980198+0.198019801980198i 1.000 11.42 1 500 1+500i 500 0.97981005617555+0.197940625729906i 1.000 11.42 2 500 2+500i 250 0.979422565531214+0.197859946815246i 0.999 11.42 -1 500 -1+500i -500 0.980586447755754+0.198097471880064i 1.000 11.42 -2 500 -2+500i -250 0.980975331346312+0.198173631809246i 1.001 11.42 0 100 100i #DIV/0! 0.6+0.8i 1.000 53.13 1 100 1+100i 100 0.595270216649472+0.793587810491231i 0.992 53.13 2 100 2+100i 50 0.590680100755667+0.787153652392947i 0.984 53.12 -1 100 -1+100i -100 0.604870574953633+0.80638658172728i 1.008 53.13 -2 100 -2+100i -50 0.609882964889467+0.812743823146944i 1.016 53.12 I will admit that many of you experts talk about how you attach your DUT very carefully, solder it, sometimes have to throw it away when done testing, and all this sounds bizarre to a non-EE who is simply playing with crystal radio. My nanoVNA attaches to my DUT via 2 alligator clips which are on little connectors (BNC maybe?) which screw into the VNA. I recognize that I am accepting error, even though I do my calibration at the same alligator clips, but except for R, I am convinced that the error I am accepting is negligible when my interest is 0.5 to 25 MHz, picking up AM signals. (I welcome any insights if you think I am wrong.) |
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Andrew Kurtz
Yes, that article and Alan’s explanation were very helpful. I realize that I had a misunderstanding of where a “parallel” resistor would be, and how a resonant circuit can be tested via shunt reflection versus transmission shunt through versus transmission series through. I had even gotten the impression that nanoVNAs really work best in reflection on CH0 only, not so much transmission from CH0 to CH1 even though that is available. For the record, I have been able to calculate that X / Rs = Rp / X exactly!
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Andy On Oct 11, 2021, at 6:51 PM, Kerry <planningpower@...> wrote: |
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Andrew Kurtz
That program sounds wonderful! The only problem is that my computer is a Mac, and I bet it won’t handle it. I know someone might say “O just get Python and change XYZ while uploading ABC from Github….” and I might as well be listening to Greek. I have not yet succeeded in getting my nanoVNA data other than by hand-typing it into Excel because I can’t get nanoVNAsaver to run. Any way to get your Coil program working on a Mac?
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Andy On Oct 11, 2021, at 7:00 PM, Brian Beezley <k6sti@...> wrote: |
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