Q measurement methods

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Itsu

Re: Q measurement methods « Reply #25 on: 2026-04-27, 09:31:46 »

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Quote from: Verpies on 2026-04-25, 22:35:25

So add a low-ESR cap to your parts order before it ships on Monday.
I have been pretty happy with Murata ERB series capacitors that have 40mΩ ESR at 3MHz.

I had some 270pF SMD caps: kemet c1206h271jggact250 which suppose to be low ESR, so I measured one to be 269.8pF and an ESR of 7.5 Ohm at 100kHz (my max).
I tested it with the T200-2 core with the 40 turns 1mm diameter wire measured L= 18.82uH and DCR of 0.065 Ohm (100kHz) and a single turn input loop from the FG.

Result is:

270pF SMD cap, 500mVpp input voltage, Fres 2204kHz at 19.9Vpp output voltage with -3dB points (19.9V x 0.707 = 14Vpp) at High 2210.2kHz, low 2196.6kHz = 13.6kHz difference with a Q of 2204 / 13.6 = 162

I also used a big variable air capacitor set to 270.2pF which measured an ESR of 2K at 1kHz, but that was lowered to 3 Ohm at 100kHz.

Result is:

270pF Air cap, 400mVpp input voltage, Fres 2174kHz at 15.6Vpp output voltage with -3dB points (15.6V x 0.707 = 11Vpp) at High 2182kHz, low 2165.6kHz = 16.4kHz difference with a Q of 2174 / 16.4 =132.5

So the ESR of the capacitor is a major factor for a good Q result.

Those Murata ERB series capacitors look even better, so worth a test with them.

I don't think comparing this measurement result with the ones done before is valid, so i won't list them here.

Itsu

« Last Edit: 2026-04-27, 14:55:11 by Itsu »

gyula

Re: Q measurement methods « Reply #26 on: 2026-04-28, 20:47:00 »

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Indeed, we cannot compare the previous Q measurement results with this new result because both the coil and the tuning capacitor affects the resulting Q value. So in this case the capacitor was to blame for the miserably low Q values.

We can trust in the Amidon toroidal core specifics, namely for the T200-2 type, it has Q=425 at and around 2 MHz (N=40 turns, 20uH, awg #18), this has been tested during the decades and proved correct data.

So a good quality tuning capacitor is needed, with a Q > 1000 but preferably even higher Q like 2000-3000. These are expensive, unfortunately.

I attached the graph on the Q values of the T200-2 core from its data sheet.

At 2 MHz the 20 uH coil on this core has an inductive reactance of X_L=251.3 Ohm and has a Q=425. Its total loss resistance (core + wire) is r = X_L / Q i.e. r = 251.3 / 425 = 0.59 Ohm

So the ESR of a tuning capacitor should be way below than this, preferably around 0.1 - 0.2 Ohm at 2 MHz so that it should not ruin significantly the coil Q. Reverse calculating the Q for such a capacitor would give a Q = 251.3 Ohm / 0.1 = 2513 or 251.3 / 0.2 = 1256

Then the Q value of the LC parallel circuit at resonance will be 425 x 2513 / (425 + 2513) = 363 or 425 x 1256 / (425 + 1256) = 317 (The resulting Q can be calculated like the resulting resistance of paralleled resistors.)

Gyula

Q measurement methods

Screenshot 2026-04-22 AMIDON.png (335.88 kB, 1048x782 - viewed 69 times.)

Itsu

Re: Q measurement methods « Reply #27 on: 2026-04-28, 21:46:32 »

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Gyula,

thanks for the clear explanation, so we should aim for a Q of >300 at least.

The problem is to find a good enough (low ESR) capacitor, preferable one from which we can measure the ESR at the resonance frequency of the LCR circuit, in our case around 2240kHz (40 turn coil on a T200-2 core with a parallel capacitor).

There are procedures to measure the ESR of a capacitor, but only at its self resonance frequency which often is much higher than our LCR resonance frequency.

Like my variable air capacitor set to 270pF which measures an ESR of 0.7 Ohm at 15.7MHz self resonance frequency.

That is nice to know, but does not say anything about the ESR of it at 2240kHz.

I have some low ESR SMD capacitors on order, so it probably will be a trail and error method to find the correct one.

Itsu

gyula

Re: Q measurement methods « Reply #28 on: 2026-04-28, 22:00:43 »

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Well, you can use a series LC circuit too, either using the nanoVNA which has 50 Ohm terminations at its RX-TX terminals (and no coupling caps), measuring S21 at the bottom of the notch and look the ESR in the table a youtuber guy links to.
or you could use the the 50:1 step down transformer as referred to in the HP Q meter, also in series LC connection, scope probe would be hooked up across the tuning capacitor.

Lets hope the ordered capacitors will have an ESR of < say 0.2 around 2-3 MHz.

EDIT: You wrote:

Quote from: Itsu on 2026-04-28, 21:46:32

... so we should aim for a Q of >300 at least.

Well, in fact we should aim for as high a Q value as we can achieve with practical components (considering design goals for our LC circuit, of course).

Gyula

« Last Edit: 2026-04-28, 23:07:57 by gyula »

Itsu

Re: Q measurement methods « Reply #29 on: 2026-04-29, 10:04:58 »

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Gyula,

Quote

Well, you can use a series LC circuit too, either using the nanoVNA which has 50 Ohm terminations at its RX-TX terminals (and no coupling caps), measuring S21 at the bottom of the notch and look the ESR in the table a youtuber guy links to.

Good idea, you are talking about this video: https://www.youtube.com/watch?v=lO97K8th_uU and this chart at the 11-minute mark:

So using my nanoVNA on the SERIES LCR circuit of the 40 turn coil on the T200-2 core and the 270pF variable air capacitor, i get these graphs:

The upper graph is the S21 Log Mag sweep pointing to a series LCR resonance of 2300kHz at -23.02dB which according to the above chart points to around 2 Ohm.
The bottom chart shows in red the real resistance R at series resonance as 1.83 Ohm.

As the used method is for measuring / calculating the ESR of a capacitor ALONE, i am not sure if the measured 2 / 1.83 Ohm values are the ESR of the capacitor alone or that it could include also some other resistances.

But it clearly shows that some improvement is possible, so we now have something to compare with

Quote

or you could use the the 50:1 step down transformer as referred to in the HP Q meter, also in series LC connection, scope probe would be hooked up across the tuning capacitor.

I am working on this 50:1 step down transformer using my big T520-2 core, so we would have another means to compare results.

Itsu

gyula

Re: Q measurement methods « Reply #30 on: 2026-04-29, 12:19:36 »

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Hi Itsu,

I think the 2 Ohm or so ESR you got includes that of the coil losses too.

Because the coil's total ESR gives about 0.59 Ohm (core + wire loss) as I calculated from the data sheet in Reply #25, I think if we substract this from the 2 Ohm, we can
receive the approximate ESR of the capacitor, i.e. 2 Ohm - 0.59 Ohm = 1.41 Ohm. So it looks like the variable cap has around 1.4 Ohm ESR at this frequency.

Thanks for your efforts.

Gyula

Verpies	Re: Q measurement methods « Reply #31 on: 2026-04-29, 12:48:55 »
Group: Administrator Hero Member Posts: 4856	Quote from: Itsu on 2026-04-29, 10:04:58 So using my nanoVNA on the SERIES LCR circuit ... Measurement #2 in shunt-through mode ?

Itsu	Re: Q measurement methods « Reply #32 on: 2026-04-29, 14:03:58 »
Group: Moderator Hero Member Posts: 4848	Quote from: Verpies on 2026-04-29, 12:48:55 Measurement #2 in shunt-through mode ? Yes, correct

Itsu	Re: Q measurement methods « Reply #33 on: 2026-04-29, 15:22:57 »
Group: Moderator Hero Member Posts: 4848	Here i tested the earlier in post #25 measured (Q = 162) 270pF SMD capacitor kemet c1206h271jggact250 which suppose to be low ESR: As the higher Q predicts, it has a lower ESR than the variable air capacitor (its Q was measured to be 132.5). -29.57dB at series resonance (2222kHz) with an ESR according to the chart of 0.85 Ohm. Itsu

Itsu

Re: Q measurement methods « Reply #34 on: 2026-04-29, 21:57:26 »

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I finished my 50:1 T520-2 toroid with 0.8mm diameter magnet wire and which measures 49uH : 0.66uH and a DCR of 0.198 Ohm : 0.031 Ohm.

I hooked up my FG to the 50 turn primary and the 1 turn secondary to the series T200-2 40 turn coil and my 270pF variable air capacitor.

I hooked up the scope across the variable air capacitor.

The frequency was set to resonance which was 2223kHz.

The result can be seen here:

Blue is the FG input signal acros the 50 turn primary
yellow is the signal across the 270pF variable air capacitor.

Using the Fres / bandwidth (-3dB) method for calculating the Q i get 2223 / 10.4 = 213.7

Itsu

gyula	Re: Q measurement methods « Reply #35 on: 2026-04-29, 22:00:54 »
Group: Tech Wizard Hero Member Posts: 1385	Itsu, did you have a 50 Ohm resistor across the primary coil? I assume you had. Thanks! Gyula

Verpies	Re: Q measurement methods « Reply #36 on: 2026-04-29, 23:02:25 »
Group: Administrator Hero Member Posts: 4856	Quote from: gyula on 2026-04-29, 22:00:54 Itsu, did you have a 50 Ohm resistor across the primary coil? I assume you had. If the cable connecting the FG to the primary winding was 10cm long then the 50Ω resistor was 10cm away from the primary winding, because the FG's output is terminated with an internal 50Ω resistor.

gyula

Re: Q measurement methods « Reply #37 on: 2026-04-29, 23:26:20 »

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Quote from: Verpies on 2026-04-29, 23:02:25

If the cable connecting the FG to the primary winding was 10cm long then the 50Ω resistor was 10cm away from the primary winding, because the FG's output is terminated with an internal 50Ω resistor.

Hi Verpies, yes but both in the HP4342A and in the W7ZOI paper the 50 turn primary coil has a 50 Ohm termination, establishing a 25 Ohm impedance across the primary coil. The turns ratio is 50:1 and the square of 50 is 2500, so the 25 Ohm impedance created across the primary coil (by the 50 Ohm resistor + the generator 50 Ohm output impedance in parallel) create 25 Ohm / 2500 = 0.01 Ohm secondary output impedance. They mentioned 0.001 Ohm output i.e. 1 milliOhm for the secondary coil output impedance but IMHO it is a typo.

What is your understanding on this? I attached the Figure from the W7ZOI paper.

Gyula

Q measurement methods

Screenshot Coil Q measurement W7ZOI.png (51.14 kB, 743x450 - viewed 40 times.)

Itsu

Re: Q measurement methods « Reply #38 on: 2026-04-30, 09:32:38 »

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Quote from: gyula on 2026-04-29, 22:00:54

Itsu, did you have a 50 Ohm resistor across the primary coil? I assume you had.

Thanks!

Gyula

Gyula,

no i did not have that, as i also expected this to be the FG input resistor.

But i added one across the primary which changed some things in the created voltages, see screenshot (FG input was set to 5V sine wave p2p in both cases):

Blue trace again the input signal across the primary (and 50 Ohm), which is now higher.
Yellow trace is across the variable air capacitor set to 270pF still, at resonance (almost the same) we here now have a lower voltage.

But the Q seems almost the same with 215.9 using Fres / bandwidth (-3dB) method (2224 / 10.3).

Itsu

gyula

Re: Q measurement methods « Reply #39 on: 2026-04-30, 11:20:19 »

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Hi Itsu,

Thanks. As I see this, the additional 50 Ohm across the primary coil made the impedance across the primary coil to be 25 Ohm, the nearly 2.5 Vpp you measured across it means that because the FG output set to 5 Vpp is halved.

Without the additional 50 Ohm across the primary coil, the stepped down FG 50 Ohm output impedance should appear as 50 Ohm / 2500 = 0.02 Ohm in series with the series LC circuit, while with the added 50 Ohm the output impedance of the transformer
should appear as 0.01 Ohm.

From the present ESR values of the L and C components points of view this additional 0.02 or 0.01 Ohm means a quasi negligible additional loss this measurement method represents, this explains why there is small difference between the Q values 'without' and 'with' the additional 50 Ohm. Now it seems the ESR of the capacitor ruins the operating Q which would be over 400 with this toroid core.

Would you mind checking the stepped down voltage amplitude across the secondary coil? Because the turns ratio is 50 to 1, the nearly 2.5 Vpp from the primary coil should appear across the secondary coil as nearly 50 mVpp.
The secondary coil voltage is labelled as "e" in W7ZOI's schematic. The ratio of this "e" voltage to the voltage across the capacitor labelled as "E", so (E / e) should give the same or very close Q value to that of the 3 dB method.

You can increase the FG output to a higher value so that the stepped down secondary voltage should be higher than 50 mVpp.

Gyula

Itsu

Re: Q measurement methods « Reply #40 on: 2026-04-30, 12:26:18 »

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Gyula,

thanks for the information.

Without changing anything else since the above screenshot, i added a 3rd probe across the 1 turn secondary, see purple trace:

It is around 200mVpp, so much higher than expected.

If i increase the input voltage from the FG to 20Vpp i get the following result:

Not much better.

Perhaps i need to put things on a ground plane PCB, so all grounds are at the same point (now grounds are mostly via the scope probes).

Itsu

gyula

Re: Q measurement methods « Reply #41 on: 2026-04-30, 12:54:00 »

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Thanks. Well, the total circuit inside the HP4342A Q meter includes additional structural solutions which are understandably not present in your setup.

We can see photos from the original HP4342A meter in this HP Journal, see it from page 10 https://hparchive.com/Journals/HPJ-1970-09.pdf In page 14, Figure 5 shows the tuning capacitor with the connection posts on top to which the unknown coils are to be hooked up.

Anyway, it is good the 3 dB method with this setup i.e. feeding the series LC via a very low source impedance reveals much better LC circuit Q than the previous ones you have tested.

Gyula

Magluvin

Re: Q measurement methods « Reply #42 on: 2026-04-30, 17:10:12 »

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Quote from: Itsu on 2026-04-27, 09:31:46

I had some 270pF SMD caps: kemet c1206h271jggact250 which suppose to be low ESR,

Itsu

you can get a better ESR by putting low ESR caps in parallel.

Soundstream amplifiers claimed an ultra low ESR cap bank at the input of their amps. the caps were already labeled low ESR.

mags

Q measurement methods

Screenshot 2026-04-30 120859.png (1337.38 kB, 1366x768 - viewed 48 times.)

Itsu	Re: Q measurement methods « Reply #43 on: 2026-04-30, 19:45:16 »
Group: Moderator Hero Member Posts: 4848	Thanks Mags, i have some "47pF Murata ERB series capacitors" on order that suppose to "have 40mΩ ESR at 3MHz" and which i want to parallel 6 of them to get to around 300pF. Itsu

Itsu

Re: Q measurement methods « Reply #44 on: 2026-04-30, 21:23:51 »

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Instead of the variable air capacitor set to 270pF, i used some very small (0402)

smd capacitors of 47pF and put 6 of them parallel measuring 285pF, and they suppose to be very low ESR.

So i tune for resonance frequency using the FG which turns out to be at 2126.3kHz.

FG input is again 5Vpp.

The results are here:

So we have in:

blue; input across the 50 Ohm resistor
purple; the signal across the 1 turn loop
yellow the signal across the fixed 285pF capacitor.

Using the Fres / bandwidth method i have for a Q: 2126.3 / 7.3 = 291.2

Here a picture of the cleaned up (ground plane used) setup used:

Itsu

gyula	Re: Q measurement methods « Reply #45 on: 2026-04-30, 22:08:43 »
Group: Tech Wizard Hero Member Posts: 1385	Itsu, very good result. Thanks, Gyula

Verpies	Re: Q measurement methods « Reply #46 on: 2026-04-30, 23:16:38 »
Group: Administrator Hero Member Posts: 4856	Quote from: Itsu on 2026-04-30, 21:23:51 Here a picture of the cleaned up (ground plane used) setup used: I can't see the annotated single loop on that photo. If I can't see it then it is too small. Consider using a very thick wire for it. Like the pencil-thick speaker wire... or a slice of copper pipe. You will cross 300 then.

Itsu	Re: Q measurement methods « Reply #47 on: 2026-05-01, 20:16:28 »
Group: Moderator Hero Member Posts: 4848	The single loop is of the same 0.8mm diameter magnet wire as the primary 50 turns coil. But i see it could be better to use a thicker wire there as we are dealing with very low impedances, so i will see what i can do. Itsu

gyula

Re: Q measurement methods « Reply #48 on: 2026-05-01, 20:54:35 »

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Yes, a thicker secondary wire used for the secondary single turn coil of the matching transformer will reduce the present loss in the 0.8 mm piece of wire. The improvement will be small though, I think.

In the present setup the ESR of the tuning capacitor represents the highest loss, after the coil. When the new capacitors arrive, hopefully they will have lower ESR than the present cap assembly that establishes the Q=291 now.

Gyula

Itsu

Re: Q measurement methods « Reply #49 on: 2026-05-01, 21:44:18 »

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Gyula,

to avoid any confusion, the 6 parallel 47pF SMD capacitors i am using now instead of the variable air capacitor are the newly ordered ones.
But they are not the " Murata ERB series capacitors" verpies had recommended as they seem to be obsolete, and instead i was directed to this substitute: GJM1555C1H470FB01D which are also 47pF smd (very small 0402 type) capacitors with LOW ESR.
No indication on how low the ESR is however, but better than the variable air capacitor.

Itsu