Measuring sub Pf capacitances

[jusanother]

I have bought some nasty Chinese 1.3Ghz video transmitters and receivers (due to a lack of alternatives). As a rule I usually whip the case off such items just to check the construction, usually the machine assembled bits look fine but anywhere a human has been involved (connectors, shields, thru hole parts, bodge wires, etc.) the quality can go down hill dramatically. On one of the receiver tuners there is a component missing, looked like it had been knocked off the board. On opening another identical tuner it looks like a capacitor, I have removed it and tried to measure it but the capacitance is so low I am looking for a way to verify it.

I measured it using one of these by Phil Rice VK3BHR and it comes up as 0.6pF, it is repeatable but god knows how accurate this meter is at this level of capacitance. (Buying a 0.6pF cap and checking it would be a fair comment)

I considered buying a Mastech MS5308, I know overkill for one measurement but it doesn't look like the accuracy would be the best. This post is the nearest I can find, it is just a breakdown of the official spec not an actual test.

So the question is what tricks are there to figure out the value of this capacitor given it's potentially low value ? I have a digital scope, multimeter and other basic equipment. This simple Femto Farad circuit looks interesting.

I also realize that there is potential for this value to be a calibrated/compensated for value but I don't know enough about tuner topology to figure that out so I was going for the get it as close as I can and try it approach. Plus the only trimmed component I can see in the tuner is an air cored inductor and in several tuners the trimming looks very similar, which granted may be a good or bad sign. Good - the construction is so tight the trimming is all similar, bad - they just make it look like they trimmed something but the device never gets powered, granted the latter is more likely.

[RadioNerd]

You could build an LC resonator (tuned to 20 MHz or so) with a wire loop coil and a few 10pF resonator capacitance... the shift in resonance frequency will tell you the value of the unknown capacitor when you add it in parallel to the resonator capacitor.
To measure the resonant frequency you can exite the resonator using another coil loosely coupled (i.e. not too close) to the main coil.
You will need a signal generator for that, though.

[Terry01]

There are quite a few videos on YouTube on how to measure the value of a cap with a scope.

Do you live near any other members on this site who have an LCR meter or DMM that can measure down to pF? If your going to the bother to buy an LCR meter for just 1 measurement it may be easier and less expensive to post the cap to another member who can measure it for you.
Hope you get something sorted buddy. 

[Kleinstein]

Measuring small capacitance is not that difficult. The tricky part is more in how to hold / connect the capacitor than in measuring the relatively small AC current. The parasitic capacitance towards the capacitor can be in 0.1 pF range.  So the capacitance not only depends on the part but also on the layout around the part.

The usual bodge solution to get 0.6 pF is to have 2 strands of the flat cable and than use about 1 cm per pF, thus about 6 mm.  This also makes a nice trimmer. In some cases a piece of insulated wire on top of a track is another option.

[jusanother]

@Terry01 I have watched a few videos on measuring capacitance with a scope, most of them don't venture into the single pF region and I did read mention that the probe capacitance might be a limiting factor which you would have to compensate for, just not sure if that would work given the probes capacitance is going to be 20-30 times larger than what I am measuring ? As to buying a meter for one measurement, what can I say, he who dies with the most tools wins, right ? I hadn't thought of posting the component to someone more suited basically because I don't know anyone, but it's an excellent idea, I just need a willing helper. I do have a Knight  K-240C LCR meter but the measurement is lost in the noise, the DIY meter produces more repeatable measurements.

@ RadioNerd I had read about such a delta observation practice and although I don't own a signal generator I think it's a more sensible purchase than a LCR meter.

@ Kleinstein So with twisted strands I could at least check my current measurement ?

So at least you guys have confirmed it's not a totally trivial task and pointed me in some useful directions, thanks !

[Wolfgang]

Hi,

I do it on a VNA. I take an SMA flanged socket and solder the component from center to flange. To normalize, I use a new connector without anything attached.
The capacitance can be read from a Smith chart then.

Like here:
https://electronicprojectsforfun.wordpress.com/componentology/

[jusanother]

Interesting link, I had been considering one of the XAVNA's strangely enough. Never crossed my mind to use it for this task but as you say it can be done.

[qu1j0t3]

I measured it using one of these by Phil Rice VK3BHR

Does anyone know how to contact Phil? All the resource links (images, source code) on that site are now 404.
TIA

[jusanother]

Weird, just checked them 2018.11.06 00:02 GMT and they are all working. Check em again, if not I can download and share.

[qu1j0t3]

Ah, I see what the problem was... I was looking at the old version, not v2. I didn't realise there was a v2! Double thanks.

[seebeck]

If you want to measure a 0.xpF capacitor, you need to use a RF LCR meter such as Agilent 4287A (3GHz).

[G0HZU]

You could also do it with a UHF oscillator. eg make a negative resistance oscillator up at a GHz or so that looks like -10R in series with a couple of pF. Then the addition of the 0.xpF cap across another external cap (in series with a tiny resonator inductor) will change the frequency of the oscillator slightly. It wouldn't be difficult to characterise it if you bought a few 0.xpF caps of known value. It would cost about £1 in parts and be quick to make if you made an ugly prototype but a neater version would go in a nice test fixture.

[bd139]

It’s extremely difficult measuring capacitors that low without expensive kit due to fixture/probe and even placement capacitance. I genuinely wouldn’t bother.

I would buy a few small caps around the estimated value and make measurements once they are substituted in and pick one that has the desired outcome. This of course assumes you have measurement equipment to cover the desired outcome.

G0HZU’s method is probably most accurate (that’s what I use) but that still suffers from oscillator drift and temperature effects. You have to leave some oscillators an hour or more after soldering to settle down. Even the placement of the fixture on the bench can be a problem!

Sometimes working out how to avoid making the measurement is more cost and time effective

[Wolfgang]

It’s extremely difficult measuring capacitors that low without expensive kit due to fixture/probe and even placement capacitance. I genuinely wouldn’t bother.

I would buy a few small caps around the estimated value and make measurements once they are substituted in and pick one that has the desired outcome. This of course assumes you have measurement equipment to cover the desired outcome.

G0HZU’s method is probably most accurate (that’s what I use) but that still suffers from oscillator drift and temperature effects. You have to leave some oscillators an hour or more after soldering to settle down. Even the placement of the fixture on the bench can be a problem!

Sometimes working out how to avoid making the measurement is more cost and time effective

In these cap ranges, a super-well-defined geometry is everything. I would say that measurements below half a pF without a precision test fixture are unreliable. If it has to be exact, you need a VNA with APC-7 attached precision fixtures. AND you need a big wallet

[PA0PBZ]

I wonder if the cap was removed during 'trimming' because it was no needed/worked better without. Did you ever check the receivers performance?

[wraper]

I wonder if the cap was removed during 'trimming' because it was no needed/worked better without. Did you ever check the receivers performance?

Exactly, on the photo it does not look anything like knocked off. It was just desoldered.

[jusanother]

I wonder if the cap was removed during 'trimming' because it was no needed/worked better without. Did you ever check the receivers performance?

Exactly, on the photo it does not look anything like knocked off. It was just desoldered.

I think that photo was from the second tuner I removed the cap from to test. The original tuner with the missing cap had very definitely been knocked off, you could clearly see the component outline in solder. Whether it was knocked off as part of the trimming procedure didn't occur to me, I forget how rough some Chinese manufacturing can be. Another member here used a DER EE DE-5000 to measure the cap in question and got it at around 1pF (my meter reckoned 0.6pF), this appeared to work when re-fitted although I haven't tested the unit to the limits or against a factory "good" one.

[jusanother]

You could also do it with a UHF oscillator. eg make a negative resistance oscillator up at a GHz or so that looks like -10R in series with a couple of pF. Then the addition of the 0.xpF cap across another external cap (in series with a tiny resonator inductor) will change the frequency of the oscillator slightly. It wouldn't be difficult to characterise it if you bought a few 0.xpF caps of known value. It would cost about £1 in parts and be quick to make if you made an ugly prototype but a neater version would go in a nice test fixture.

Apologies for asking but my RF kungfu is weak, do you have an example schematic you could point me at ?

[G0HZU]

You could also do it with a UHF oscillator. eg make a negative resistance oscillator up at a GHz or so that looks like -10R in series with a couple of pF. Then the addition of the 0.xpF cap across another external cap (in series with a tiny resonator inductor) will change the frequency of the oscillator slightly. It wouldn't be difficult to characterise it if you bought a few 0.xpF caps of known value. It would cost about £1 in parts and be quick to make if you made an ugly prototype but a neater version would go in a nice test fixture.

Apologies for asking but my RF kungfu is weak, do you have an example schematic you could point me at ?

Sure, but do you have something that can measure frequency up at 1GHz?

The ideal thing would be a spectrum analyser but a cheapo USB SDR dongle (with a simple RF probe antenna)  that can work up at a GHz and give a slow scan of maybe 800-1000MHz would be adequate I think. You would also need some caps to calibrate it with although this isn't strictly necessary if you build it right. If you don't have the above frequency measuring device then there isn't much point making the circuit

It would take just a few minutes to make it and test it but you would need a decent RF transistor (eg BFR91 is easy to work with but a BFR93 SMD would be OK). Also a decent 1pF and 1.5pF SMD cap and a bit of spare PCB and a couple of basic resistors at maybe 1k and 47k (don't have to be SMD). It would also need an SMD inductor of about 33nH but you could make this yourself.

It should give about a 50MHz shift in frequency with 0.4pF added so it would be OK to solder the test cap in place as long as you don't mind waiting for a couple of minutes for it to cool. Otherwise, you risk pinging the SMD test cap into outer space if you press it in place with an insulating tool.
It should be good enough to measure caps at 1GHz across several pF to maybe 0.2pF with good results. If you have an SDR or a spectrum analyser I'll post up the circuit and maybe build an example for you to copy. It works fine on a simulation and should work well in reality as it's only 1GHz. Total cost maybe £1.

[jusanother]

I do have a cheapo SDR and a SSA3021 spectrum analyser (call it a splurge into the land of learning RF), so your help will be gratefully learned !

[G0HZU]

Here's the circuit so you can see if you have these parts. The transistor needs to be something decent and if you can get a genuine BFR91 it will be easy to work with because it is in a nice pill package. The other parts are non critical but the caps need to be SMD. The resistors don't nee to be SMD. C5 in the circuit is the cap under test. The ground connections need to be very direct and because you only need this for one task there is no need to make a proper PCB.

Can you get hold of an old school BFR91 transistor?

Don't build it until I've made one to show you how to do it easily and neatly. Don't expect lab grade precision but you should be able to get a good idea of the capacitance of your cap for a very low cost in time and parts. If you need to buy a few parts then maybe best to buy a few SMD caps in 0.2pF steps but you probably don't need to go to this extreme. Maybe just buy a few test caps, maybe 1pF, 0.5pF and 0.2pF.

Note that it runs from a negative supply of -9V. It is done this way to keep the circuit very simple and easy to make on a bare sheet of copper PCB.

[G0HZU]

It's probably easiest if I build one, test it and pop it in the post to you because we are both in the UK? The build cost to me is nothing. I have loads of surplus RF parts here.

[jusanother]

If your sure that would be great. I was just about to post a link to eBay for the BFR91's as neither RS nor Farnell have them but I am guessing you knew that already

[G0HZU]

Yes, it's hard to get genuine BFR91s nowadays. I have a large bagful of them that are over 25 years old. Give me a day or two to make a tidy version and have a play with it. I've also got plenty of 0603 caps in 0.1pF step sizes here.

[jusanother]

Brilliant, what can I say, thank you.

[G0HZU]

As I'm making it I've remodelled it with a tighter 'ugly construction' layout and I also modelled it in SPICE. The tight (unconventional) layout means it will have less parasitic capacitances and so it will give a bigger shift in frequency for (say) 0.4pF added.

As it is so easy to make I've built the first one on a scrap bit of PCB. I tried to be clever with the 1pF cap C2 by making it as a glued down PCB pad that had 1pF self capacitance. This makes it easy to solder the test cap. But I think this may be unreliable when soldered a few times. So I will try and dremel a pad into the PCB and use a proper SMD 1pF cap for C2.

But the image below shows the way to make a quick and dirty version of this crude (and fairly nasty) negative resistance oscillator. SPICE predicted just under 100MHz shift but I got about 120MHz shift with a 0.4pF ATC 600S cap added. But the frequency of the real oscillator was as expected at about 1GHz. I think my homemade 1pF cap pad is probably a bit less than 1pF because of the extra thickness of the smear of glue. So I get more shift than the model predicts.

[G0HZU]

I tested it again with a different analyser so I could grab a screenshot and the result below is with and without the 0.4pF cap. There is a bit of shift in the 'without' frequency because this should have been back at the CF of the analyser after removing the 0.4pF cap. The little 1pF PCB pad is moving a bit with heat stress so using this pad for C2 was a bad idea.

I'll try again tomorrow after cutting out a pad in the main PCB. I should have done this the first time but I was in a hurry

The oscillator is very tame and can be picked up and it doesn't shift much when on a span this wide. It also cools and stabilises very quickly after being prodded with the iron. It only moves about 10-20MHz when heated at C2 with an iron. So this is not an issue really.

[jusanother]

Can you show me a close up of the PCB arrangement you made to duplicate C2, it's not quite clear on the photo ?

[G0HZU]

See the latest image below. I decided against cutting a slot in the top foil of the main PCB as it would probably cause stability problems as it means making the bottom side of the PCB a subtle part of the oscillator.

So I got some Rogers 4003C PCB material in 0.06" thickness and made a fixture as in the image below. Because the little Rogers board is double sided I reflowed it onto the PCB as if it were an SMD component. So no glue needed as it is now soldered down quite firmly.

I also cut a fixture slot in it to suit an SMD 0603 cap and grounded the other side. I've also added some supply smoothing (but not much!) and a reverse polarity protection diode.

The stability is now excellent and the phase noise isn't bad either. Considering that this is a crude negR oscillator it has fairly good phase noise at about -114dBc/Hz at 100kHz offset. Probably 14 dB cleaner than a Siglent spectrum analyser at this offset. But close in the phase noise and jitter is poor. This is because it isn't phase locked and also because the supply isn't smoothed very well.

The thicker fixture standoff PCB means even less capacitance in C2 and so the shift for 0.4pF is just under 150MHz. But it returns back to 1.063GHz +/- about 5MHz each time I remove a test cap.

So I think it is OK and fit for purpose. i.e. it should be adequate to make a one off measurement of an unknown SMD cap that is somewhere around 0.6pF. I'll try and calibrate it tomorrow with some accurate SM caps

[jusanother]

So the first version had a small single sided pcb glued to the main pcb to form C2 ? Or was it just a square of copper foil glued to the main PCB ?

The second version has a small double sided PCB reflowed to the main PCB to form C2 ?

[G0HZU]

Yes, that's right. See below for the crudest possible model for this oscillator. The transistor has been replaced with a negative resistance and its self capacitance in series. This is C4 and R3.  The 39nH inductor is the total series inductance between ground and the base deep inside the BFR91. So it will be the 33nH of the SMD choke plus a few nH.

C2 is the shunt capacitance of the Rogers fixture PCB. I'm guessing it is around 0.5pF with strays etc.

With the model below the oscillator will oscillate at whatever the series network below is resonant at. You could work this out with an excel spreadsheet if you are bored and make it such that C5 varies across 0.1pF to maybe 3.3pF.

This will give you some idea what to expect in terms of calibration. I'm not sure calibration with real caps will be much more accurate than this crude model as many SMD caps have a tolerance of +/- 0.1pF.

But hopefully a quick play with the model below will take away some of the mystery of how this quick and dirty negative resistance oscillator circuit was designed to meet your requirements

Just work out the series equivalent of (C2+C5) and C4 is. The find the frequency this is resonant at with 39nH. (about 900MHz?)

Then remove the C5 cap (0.4pF) and recalculate. You should get something around 1050MHz. This is the concept of the design. You get a big frequency shift for a tiny change in capacitance but the fixture has to be very solid mechanically to prevent errors.

[G0HZU]

To give an idea of results with the real circuit:

With nothing at C5 it oscillates at 1063MHz .
With 0.4pF it oscillates at 918MHz.
With 1pF it oscillates at 798MHz.
With both 0.4pF and 1pF in parallel it oscillates at 756MHz.
When the caps are removed again it oscillates at 1062MHz. So hardly any change in the fixture after all the soldering.

This is reasonably close to the model prediction and this is with some decent/accurate ATC 600S 0603 caps. I'm being lazy and only allowing about 30 seconds cooling time but the heat from the iron doesn't make it shift very much now the fixture is improved.

[jusanother]

I'm not sure what to say, thank you. What an effort both in construction and explanation. Are you still planning on posting it ? I've also ordered some BFR91s from eBay, they can't come in wrong. From a UK source and listed as genuine, no one lies on eBay right ?

[G0HZU]

Yes I can still post it. I've updated my forum settings to allow a PM from you so can you PM me an address to send it to please?

Let me know on here if the PM gets blocked in some way.

[G0HZU]

One thing I forgot to show (sorry!) is that the inductor in the simple model above has some parallel capacitance hidden in the model. So it isn't a fixed inductance over frequency.
This means that a 33nH inductor won't look like 33nH up at 1GHz because of this capacitance. The inductance will slowly get bigger across 800MHz to 1100MHz.

So this makes it a bit harder to calculate the resonant frequency by hand. I was lazy and did it with the above model in a simulator and it calculates the resonant frequency for me and it corrects for the self capacitance of the inductor.

It's best to let the simulator handle the crude model I posted up earlier because of the self capacitance of the inductor model. It's also possible to use the manufacturer's s parameter data for the 33nH inductor and the results should be fairly similar. Sorry, I should have mentioned this earlier.

[G0HZU]

I did a calibration on it after tweaking the 33nH soldering slightly because it was too close to the test PCB PAD. So the 0pF frequency with no test cap is now 1072MHz.

I calibrated it using caps from this Kemet kit:

https://uk.farnell.com/kemet/cer-eng-kit-34/rf-microwave-capacitor-kit-0603/dp/2456895

I've attached the caps I used to the little test PCB as you can see in the image below. I've also revised the model to show the internal capacitance of the 33nH inductor and added the stray inductance as a second inductor to improve the accuracy of the model.

The little Rogers 4003C pad capacitor C5 is 4mm x 5mm in size and 1.5mm thick. The PCB dielectric is 3.38 so the capacitance is about 0.4pF here but there will typically be another 0.1pF in strays due to the physical layout. So C5 is 0.5pF in the model.

See below for a cal chart of the real oscillator vs the prediction from the tweaked model. It's quite close and I don't know how accurate the Kemet caps are. The spec says 1% but I don't think that applies to values below 1pF. Hopefully they are within 0.05pF but they should be within 0.1pF.

Note that your first attempt at a PM to me bounced and I lost the message. Can you try again?