Measuring sub Pf capacitances

[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?