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I spent the afternoon building a spreadsheet to calculate the reflection coefficient and phase angle required for different values of reactance and capacitance. It was quite interesting to test different scenarios.

The reactance of a 470 pF capacitor at 3.4 MHz. is 100 ohms. If the measured ESR at this frequency was 0.2 ohms the Q would be 500. If the ESR measured was 0.4 ohms the Q would be 250. The reflection coefficient and phase angle for the Q = 500 case would be .9984 and 53.12996 degrees. For Q=250 the reflection coefficient and phase angle are .99681 and 53.12952. The difference between the two is .00159 and .00044 degrees. A graph showing the calculated resistance with these reflection coefficients and angles is attached.

One can see that even a slight error in measurement drastically affects the R calculated so it is not possible to measure high Q capacitors with a NanoVNA using the S11 method.

However if we have a low resistance and vary the frequency the capacitive reactance can be calculated with reasonable accuracy because the reflection coefficient and phase angle change must faster than the case above. See the attached graph for an illustration. This is why earlier plots of calculated capacitance were quite close to what is expected for the DUT.

Roger

Another fairly crude form of verification would be to place a large resistor in parallel with the cap and see if the Q curve changes as expected. Also, it would be worthwhile extending the frequency range. Maybe test up to 50MHz to see how the VNA copes with a decent 470pF ceramic cap up at VHF. Also, try and find someone who will let you play with a decent (fairly modern) lab VNA to compare results. Obviously, I'd expect the lab VNA to have the edge over the nanoVNA here.

On Fri, Feb 19, 2021 at 09:42 AM, Manfred Mornhinweg wrote:

using the test jig I published, several days ago

Hi,

I can't find your jig. Could yo re-publish?

Thank you, larry

The reflection coefficient phase angle should hardly change at all with the big change in Q of the 470pF cap from 300 to 3000 at 10MHz. It will change a tiny, tiny fraction of a degree. That's why I said it doesn't really change. Are you sure you are calculating for the the reflection coefficient? This is what the nanovna bridge measures.

One test to see how valid a measurement of Q was would be to measure the Q vs frequency of a single high Q capacitor and then measure the Q vs frequency of two identical caps in series. Obviously the connections need to be tight but I think the Q curves should be the same. If this happens then it adds confidence to the measurement.

The point I'm trying to make is that the -112deg phase measurement doesn't
really change if you could magically alter the Q of the 470pF cap across a Q
of 300 to 3000 as it was being measured on the VNA.

Well, it does change! I just did the maths. But I have to concede that the phase change seems to be less important than the amplitude change.

The nanoVNA just has to be
able to measure something like -112deg at 10MHz to let you know that it is a
470pF capacitor at 10MHz.

No, it also needs the amplitude! When the amplitude changes while the phase stays constant, the part has a different capacitance and of course also a different resistance.

We really always need to consider the vectorial value - that's why the thing is called a VECTOR network analyzer, after all! I was horrified a while ago when I looked for online reflection coefficient calculators, and found several that consider impedance to be a scalar value!!!! Fortunately there are also some that correctly take impedance as a vector, and allow to enter both dimensions of it.

And then of course the NanoVNA needs the calibration values, to remove the line length effect and other minor things. After all, a bare bones pure capacitor causes a -90° reflection, but the line length can turn this into anything, such as your -112°.

What the NAnoVNA does, for S11 based measurements, is placing the part under test plus some line length in a 50? resistance bridge, feeding a test signal into it, running two direct conversion receivers, one for the driving signal and one for the bridge imbalance signal, digitize the two audio outputs from the receivers, and then process that digital data. It can basically measure three things: Reference amplitude, imbalance amplitude, and the phase difference between the two signals. Everything has to be derived from this. I trust that the maths used in the software are correct, but the results are bound to the linearity, stability and noise of those circuits. When we connect a capacitor, the imbalance of the bridge is very large, so both the reference and the imbalance signals are large, and should be easy to measure. But the phase difference, which contains not just the noise of the mixers and ADC but also the phase noise of the oscillators, might be harder to measure accurately. That's what I meant in my post Whether or not I'm right, is of course a different matter... I cannot be the judge on that.

Anyway, regardless of whether the phase or the amplitude is more critical in any given case, I think we agree on the fact that the NanoVNA's accuracy and/or resolution in measuring them is insufficient for directly measuring the Q of high quality capacitors. Which is a pity, but fully expected, and shared with many much more expensive instruments. When I bought the NanoVNA, I expected far less measuring range than it actually has, so I'm still happy with it, even if it cannot plot the Q of a good capacitor over frequency, with reasonable accuracy!

Manfred

Absolutely, you do have to be able to measure the angle of the reflection coefficient otherwise you wouldn't know it was a 470pF cap. But measuring this angle is very easy for the nanovna. The hard bit is measuring the magnitude of the reflection coefficient. From a mag / angle measurement of 0.999 / -112deg it is possible to compute the Q of the 470pF cap at 10MHz.

The point I'm trying to make is that the -112deg phase measurement doesn't really change if you could magically alter the Q of the 470pF cap across a Q of 300 to 3000 as it was being measured on the VNA. The nanoVNA just has to be able to measure something like -112deg at 10MHz to let you know that it is a 470pF capacitor at 10MHz. It's the 0.999 'mag' number that changes with the change in Q.

I prefer to think in terms of amplitude and phase, R and X, rather than in reflection coefficient. Anyway, to measure the Q of a component it's necessary to measure both its reactance and resistance, or at least the ratio between the two. I don't see how a VNA could directly measure the ratio, since there is no tap between the R and X parts of a component! So the VNA needs to measure a two-dimensional value, like amplitude and phase.

Rather than delving deeper into VNA theory, which is not yet one of my strengths, I want to report about my next test: I tried to measure a capacitor in series with a crystal. Attached are the clean impedance plot of the crystal alone, and of the crsytal plus capacitor in series. The crystal is a common cheap 10MHz microprocessor clock crystal, while the capacitor is the same as before, the 470pF 1% dipped silver mica.

Assuming that the small difference in impedance at the lowest point is the ESR of the capacitor at 10MHz, simple maths tell that the capacitor has a Q of 160 at 10MHz. Hardly credible. Is my logic wrong, or are all my mica capacitors bad?

I tried several other 470pF capacitors in series with the crystal. Supposedly high Q ones like polystyrene, also NP0 ones. The result was interesting: In each case I got either the same Q value as for the mica capacitor, or an infinite Q! Which of the two values I got depended more on contact pressure than on capacitor type.

Clearly it seems that the NanoVNA's resolution is insufficient for this kind of measurement, even using the crystal in series. And of course contact resistance is important.

I do think it's more intuitive in this case to think in terms of the ability to measure the magnitude of the reflection coefficient rather than looking at resistance and reactance.

For example, at 100kHz a 485pF capacitor with ESR 0.58R, -3282R reactance might appear (to some) to be still within in the reaches of the nanovna as the Xc and ESR numbers don't look that scary at first glance. But if you look at the reflection coefficient it is about mag 0.9999946. It would be pointless to even think about trying to use the nanoVNA (or a regular lab VNA) to measure this reflection coefficient.

As I mentioned earlier, a fairly good VNA will begin to struggle above a reflection coefficient of mag 0.998. Across the HF band a really good lab VNA can often measure to 0.9995 but the result will be getting quite jagged and noisy. See below for a plot of a 100k chip resistor taken with my nanoVNA. The VSWR will be 100,000/50 = 2000. The mag r will be (2000-1)/(2000+1) = 0.999

You can see that my nanoVNA is really struggling to measure the 100k resistor across LF to 20MHz as the trace is quite jagged. This measurement of mag r = 0.999 probably represents an indication of the upper limit for the magnitude reflection coefficient that my nanovna can measure.

If you limit the VNA to this (very noisy) reflection coefficient of 0.999 at 10MHz I think you end up with a Q limit of just under 1000 for the nanoVNA for a 470pF cap at 10MHz. If a really high Q 470pF cap was tested this would produce a very jagged Q curve at 10MHz but I think it would show a Q trace somewhere in the region of 1000 at 10MHz if you visually averaged it. The above assumes the nanoVNA is in good condition and is running decent firmware and the calibration kit and test fixture are good. Obviously it would be better to use other means to measure the Q. I haven't used my nanoVNA for critical s11 measurements like this before because I would normally use other methods but I think the above example is representative of what it should be able to achieve in this case. If I have grossly overlooked something I'd be interested to know what it would be.

I think the nanoVNA measures the reflection coefficient of the network under test so I don't see how it can fail to measure the phase angle of the reflection coefficient with good results in this case. If it was getting this wrong it wouldn't even be able to indicate the capacitance of the 470pF capacitor across this range. I think the nanoVNA will probably max out at a reflection coefficient of about 0.999 / -112deg at 10MHz for a really high Q 470pF capacitor. This is a Q of nearly 1000 at 10MHz although the Q curve will look very jagged and noisy as this is right at the limit of the instrument. The phase angle of the reflection coefficient isn't critical in this case?

Alan,

The vna measurement just can't quite make it. The approach that did work and
correlated well with practice in design was to build a cavity resonator and
embed the cap under test in series with the Tline resonator.

Using a cavity would be roughly equivalent to my idea of using a crystal in series with the capacitor to be tested. With the crystal being suitable at HF and low VHF, and the cavity at high VHF and through microwaves.

But these methods just give the capacitor's Q at a single frequency. In some cases that's all one needs, of course, but in other cases it would be highly desirable and instructive to see a curve of Q over a wide frequency range.

Manfred

Manfred's plots of the 2000pF 'Hi Q' capacitor (on the EFHW transformer
thread) obviously had a problem somewhere with the test setup or maybe his
2000pF capacitor was faulty?

Everything is possible. But I do think that the main cause of the Q inaccuracy is the limits of the NanoVNA. It's just very hard to measure a very small resistance when it's in series with a very much larger reactance.

To rule out a faulty capacitor, and calibration problems, I just made a new measurement. The guinea pig this time is a 470pF, 1%, dipped silver mica capacitor made by Sangamo, new from the bag, never used. I let the NanoVNA warm up for one hour, then erased the old calibration, made a fresh calibration with averaging over 8 measurements, then connected my capacitor with very short leads and measured with long averaging. The resulting Q curve, and also the RX curves are attached. I measured from the low end to 30MHz, because much beyond that the reactance is so small that the job gets even harder for the NanoVNA.

As you can see, the Q curve is far too low again. Leaving aside the huge inaccuracies at the low frequency end, where the reactance of such a small capacitor shoots through the roof (or rather the floor, this being negative reactance), it's just not possible that such a mica capacitor has a Q in the range of 60 to 270 over the HF range. It must be MUCH higher.

The RX curves show clearly that the NanoVNA measures a higher resistance at lower frequencies, where the reactance gets high. This suggests that the NanoVNA cannot measure the phase angle of the reflection with enough precision. Which is no surprise, given how critical this phase measurement is: A phase of 90 degrees would be infinite Q, while a phase of 89.94 degrees is a Q of around 1000, and a phase of 89.42 is a Q of 100. To make a reasonably accurate measurement of capacitor Q, a VNA needs to be able to measure the phase of the reflection with an accuracy of at least one hundredth of a degree! I think that we cannot expect such performance from the NanoVNA, and not even from much more expensive VNAs.

What I would love to learn is some trick to get around this limitation, so I can plot a valid Q curve over frequency for a capacitor.

Manfred

On 3/21/21 1:18 PM, jmr via groups.io wrote:

I think it's a bit optimistic to hope that a VNA could measure that component with a basic s11 measurement. I did a few quick sums and at 100kHz, a 485pF capacitor with ESR 0.58R, -3282R reactance, (Q of 5655) will have a reflection coefficient of something like mag 0.9999946. I did some tests on my nanoVNA a couple of days ago with a test load consisting of an ATC 100B 39pF porcelain cap in series with a 1R 1% 0805 SMD resistor.

The aim was to see how well it could measure the Q of this network across the 2-30MHz HF band. This cap will have a similar reactance magnitude as a typical handwound toroid using either Micrometals 2(red) or 6(yellow) material and this is why I chose these component values to put in series. Things generally get difficult for a modern VNA when the magnitude of the reflection coefficient creeps above about 0.998.

The plot below shows the theoretical Q curve in green for 1.02R in series with 39pF. The blue trace is for the Q measured with the nanoVNA and the Q was also measured with a lab VNA and this is the brown trace. The nanoVNA does OK until the Q goes above about 200 and then it gets very noisy. This is a plot taken with no averaging on the nanoVNA. I've improved my cal kit definitions since I took that plot so I'll try and find the RC network and measure it again. It isn't a perfect yardstick because the ESR of the 1R resistor will tend to creep up slightly with increasing frequency and the ATC cap probably has an ESR of 0.02R across the HF bands. However, I think it is a useful test.

When the reflection coefficient magnitude is 0.998, that implies you need to be making the I/Q measurements with an accuracy better than 0.1%? - as you say, that gets challenging.? Considering it just as a SNR thing, it corresponds to an SNR of 60 dB - that is, voltage noise of 0.001 relative to 1.

On Mon, Mar 22, 2021 at 10:01 AM, DiSlord wrote:

After reset calibration, select 8mA output (CALIBRATE->POWER->8mA) and after
made calibration (this mode used in 0.8). This also reduce noise on measure.

I can't really see any difference on my device when leaving this set to auto or when setting it to 8mA as you describe.

/Andreas - SA0ZAP

Well not quite, John.

DiSlord has released v1.0.50 now.? :-)

Mike - M0MLM

------------------------------------------------------------------------
*From:* John [mailto:k9ka@...]
*Sent:* Monday, 22 March 2021, 12:05 pm
*Subject:* [nanovna-users] Problem with Dislord V1.0.45 Solved

Hi Group,

I finally got my H4 VNA running with Dislord's V1.0.45. My solution was to first load Huygen's V1.0.45, which worked, and then follow up by loading the Dislord V1.0.45 which is now working on my unit. I can't explain why this worked, but there must have been something in firmware that was not set right. Anyway I am now happy with the latest features on my VNA.

73, John, K9KA

On Sun, Mar 21, 2021 at 11:12 PM, <sunkan@...> wrote:

This is how it looks on my device now using the 1.0.50 firmware (performing
same calibration procedure as described above).

I think it looks better, but the 0.8.0 firmware still seems to perform the
best on my device.
I don't know if this test is the best way to verify the performance of an
individual device?

Thanks for all your work on improving the firmware.

/Andreas - SA0ZAP

After reset calibration, select 8mA output (CALIBRATE->POWER->8mA) and after made calibration (this mode used in 0.8). This also reduce noise on measure.

Looking at the notes you have a fix in the H4 version "-For H4 now allow 7 save slots H - fix tupo on average (now noise floor more better)" Do you recommend upgrading my H4 version from 1.0.45?

1.0.50 version fix some bugs after 1.0.45 (hang on load from empty slot in some cases)

This is how it looks on my device now using the 1.0.50 firmware (performing same calibration procedure as described above).

I think it looks better, but the 0.8.0 firmware still seems to perform the best on my device.
I don't know if this test is the best way to verify the performance of an individual device?

Thanks for all your work on improving the firmware.

/Andreas - SA0ZAP

On Sun, Mar 21, 2021 at 05:56 PM, jmr wrote:

I tried to repeat Roger's test of a 'Hi Q' 470pF cap with my nanoVNA and
managed to see an indicated Q that was very noisy (as expected) below 10MHz.
At 10MHz it was probably averaging a indicated Q of 2000 with the nanovna. By
20MHz the indicated Q dipped below 800 and the trace was still very noisy but
it was easier to spot the average.

Manfred's plots of the 2000pF 'Hi Q' capacitor (on the EFHW transformer
thread) obviously had a problem somewhere with the test setup or maybe his
2000pF capacitor was faulty? I'd expect the nanoVNA to perform better than
that across the HF bands if given a fighting chance with a decent 2000pF test
capacitor. Obviously, the nanoVNA can't measure the Q of the 2000pF cap down
at lower frequencies but it should perform reasonably well across the HF bands
for example.

In Roger's case, a decent 470pF cap is probably best tested across 5MHz to
20MHz. Below this the nanoVNA will increasingly limit the measurement and it
becomes meaningless to even try measuring the Q of the cap much below 5MHz
unless it is not a high Q cap.

It turns out the old cap in my parts bin that was marked HiQ was not a high Q cap. I found out afterwards doing a Google search that HiQ was a trademark of AeroVox corporation some years ago for their ceramic capacitors. This particular cap was a large (3/4") ceramic disc cap with a high voltage rating. Not much of a high frequency performer as it turns out but the test still showed that it could not give the same results as my DE-5000 LCR meter at 100 kHz.

I don't believe that testing a "real high Q" 470 pF cap from 5 to 20 MHz. on a NanoVNA will work very well. The reactance at 5 MHz. is 67 ohms and at 20 MHz. 17 ohms ohms. Even to measure a modest Q of 300 the capacitor ESR will have to be .223 ohms for 5 MHz. and .057 ohms for 20 MHz. At 5 MHz. the results will be marginal and at 20 MHz. not good at all. But if someone has results that show otherwise I would be interested in seeing them.

Roger

I think the usual way to measure component Q with an S21 measurement is to place the cap in series with an inductor and then put this in shunt as an acceptor circuit to ground. Then measure the notch depth at resonance. If it was first done with a cap of known lower Q and then re-measured with the high Q test capacitor then it would be possible to work out the Q of the high Q cap by comparing the notch depths and doing a few calculations. This method does rely on having accurate test port impedances (usually 50R) or errors can creep in.

The other way to do it with S21 would be to arrange the network as a parallel resonant circuit and measure the change in 3dB bandwidth when the known medium Q resonator cap is swapped for the high Q test cap. There are probably other methods but I use these two methods here quite often when measuring (very) high Q inductors. Care is needed with this method as it is easy to introduce unwanted loading (or subtle Q multiplying) of the resonator.

If you don't ask, you won't find out they say. So here goes, could
capacitor Q be measured using the S21 method?

Richard, K8CYK

On Sun, Mar 21, 2021, 5:56 PM jmr via groups.io <jmrhzu=
[email protected]> wrote:

I tried to repeat Roger's test of a 'Hi Q' 470pF cap with my nanoVNA and
managed to see an indicated Q that was very noisy (as expected) below
10MHz. At 10MHz it was probably averaging a indicated Q of 2000 with the
nanovna. By 20MHz the indicated Q dipped below 800 and the trace was still
very noisy but it was easier to spot the average.

Manfred's plots of the 2000pF 'Hi Q' capacitor (on the EFHW transformer
thread) obviously had a problem somewhere with the test setup or maybe his
2000pF capacitor was faulty? I'd expect the nanoVNA to perform better than
that across the HF bands if given a fighting chance with a decent 2000pF
test capacitor. Obviously, the nanoVNA can't measure the Q of the 2000pF
cap down at lower frequencies but it should perform reasonably well across
the HF bands for example.

In Roger's case, a decent 470pF cap is probably best tested across 5MHz to
20MHz. Below this the nanoVNA will increasingly limit the measurement and
it becomes meaningless to even try measuring the Q of the cap much below
5MHz unless it is not a high Q cap.