LC oscillator sensitivity analysis

Add it to an equal amplitude reference frequency or two and use the interference beats patterns to work out the frequency difference.

Classic trick once you have a rough period and an estimate of error on that is to run for long enough to get a max cumulative error of 1/4 cycle and then knowing it was an exact number of cycles refine the estimate.

--
Regards, 
Martin Brown

Frequency can only be as accurate as the time you are allowing for the measurement. Are you trying to get a cw measurement or the value of the frequency while in sweep mode

A long T-line and a bv source configured as a multiplier would give you a delay discriminator, which can do a pretty good job if you filter the output. The good news is that you average over many cycles, which gets rid of the adaptive step size funnies.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC 
Optics, Electro-optics, Photonics, Analog Electronics 

160 North State Road #203 
Briarcliff Manor NY 10510 

hobbs at electrooptical dot net 
http://electrooptical.net

I can make fairly large changes to part values, and then zoom up one cycle of oscillation, or maybe a few, and use the cursors to show me period and frequency, and then calculate sensitivities. That assumes, well, linearity of my non-linearities. Tedious, but it will mostly work.

I'm running a time step of 1 ps. The defaults are obviously goofy.

One big nasty is the tempco of the FR4 PCB capacitances. Guarding is a remote possibility.

I'd still like you to review this for us, when I can get organized enough.

--

John Larkin         Highland Technology, Inc 
picosecond timing   precision measurement  

jlarkin att highlandtechnology dott com 
http://www.highlandtechnology.com

You have to do a whole run per time, so the delay discrim ought to work fine. "Long" doesn't have to mean a million cycles--it's being done in floating point after all. Ten or twenty cycles should be lots.

Sure, sounds like fun.

Cheers

Phil

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC / Hobbs ElectroOptics 
Optics, Electro-optics, Photonics, Analog Electronics 
Briarcliff Manor NY 10510 

http://electrooptical.net 
http://hobbs-eo.com

I put these statements in the sim:

.meas t1 find time when v(tank_p,tank_n)=0 cross=1 td=100u .meas t2 find time when v(tank_p,tank_n)=0 cross=4001 td=100u .meas f_tank param 2000/(t2-t1)

The td=100u is to skip the startup time of the oscillator. The 2000 cycles was arrived at after I kept increasing the number until the measurement stabilised. There are still some rounding-error issues in there I think.

I was using a max time step of 500 ps, which is about as much as I could tolerate. There is probably some optimum combination of time step and number of cycles, but I didn't spend much time trying to find it after the other problems became apparent.

The real limitation of this approach is that the LTSPICE inductor doesn't accurately model core losses, and how they change with current and temperature (it just has a parallel resistance). The manufacturers don't often quote this anyway, so I had to buy lots of samples and measure them.

If you're using an air-cored inductor, of course, a lot of these issues go away, but you still have to deal with skin effect and dielectric loss in the FR4, and the dependence of these on temperature.

On top of all of the above, it turned out that our first choice of inductor was also sensitive to humidity, it looks like the wire insulation is hygroscopic and the stray capacitance drifts over a period of hours or days. That one caused a lot of head scratching.

Our application is trying to measure small changes in capacitance, about

1-2 pF with an offset of ~ 150 pF, so small changes in parasitics can completely screw up the measurement.

This stuff is a lot harder than anybody imagined at the start of the project. Good luck...

LTSpice offers the John Chan model of a hysteretic inductor, which may be m ore realistic.

"The other non-linear inductor available in LTspice is a hysteretic core mo del based on a model first proposed in by John Chan et la. in IEEE Transact ions On Computer-Aided Design, Vol. 10. No. 4, April 1991 but extended with the methods in United States Patent 7,502,723. "

I didn't have any trouble digging the parameter out of the data sheet for t he core I was using

.

Sounds like a job for a Blumlein bridge.

Centre-tapped transformers wound with twisted pair (and certain amount of a ttention to detail) offer a 1:1 ratio that is accurate to about one part in a billion.

Ratio transformers are somewhat more flexible, but the precision goes down to about one part in ten million.

These are a few of the many interesting facts you can find in

The Kibble is the guy whose name got recorded in the Kibble balance

--
Bill Sloman, Sydney

That's cool. I haven't used .meas. I'll have to learn that.

I'm running 5 ps time steps, for a 1 us run, which seems good enough. Smaller steps don't seem to change my frequency. The LT Spice default step delivers nonsense.

I'll be using a high-Q Coilcraft air-core inductor. I do wonder how it interacts with the PCB copper planes.

Skin effect shouldn't much affect my 125 MHz Colpitts oscillator, but FR4 is a horrible capacitor.

I have also been experimenting with measuring risetimes of short microstrips on FR4, between two SMA connectors. We have an ongoing debate here about when it's necessary to pay for exotic laminates.

I used one coil that was wound on a plastic coil former. It looked very nice but it slowly changed inductance as the coil tension made the thermoplastic flow. The time constant was months. The short-term fix was to bake all the inductors to relieve the stress. The long-term fix was to buy something else.

Yes. I'm doing an instant-start, instant-stop, phase-locked oscillator, with a goal of 1 ps RMS jitter on every edge. Pray for me.

--

John Larkin         Highland Technology, Inc 

The cork popped merrily, and Lord Peter rose to his feet.  
"Bunter", he said, "I give you a toast. The triumph of Instinct over Reason"

It's a diabolically cheap and nasty approach to precision timing.

Exorcism is the kind of prayer mode that would be appropriate.

Use two time-to-digital converters to locate the leading and trailing edges with respect to the edges of a stable and continuously running clock - I w as looking at a clock running at 800MHz when I did it, thirty years ago, bu t that was driven by a manager who wanted something that he could make sill y claims about when he was selling it.

This approach gets expensive when you want it to deliver up edge-to-edge ti mes at MHz rates - fast A/D converters aren't cheap - but it does lend itse lf to frequent auto-calibration.

Obviously you have to pay for a fast, stable low jitter oscillator, but the se are off-the-shelf parts (if not all that cheap).

--
Bill Sloman, Sydney

You mean this one?

(bottom of page)

I had a quick play with it, using the example example model in the second link. I don't have time to look into it in any more depth right now, but worth adding to the toolbox.

I'm using 1210 surface-mount inductors from the likes of TDK, Murata, Wurth. I think one of the Murata ones had a SPICE model but it didn't include non-linearity or behaviour over temperature. The other vendors just have bare data sheets with 'typical' values or impedance curves at room temperature. Measuring the parts ended up being quicker than trying to model them.

[snip]

Custom magnetics would be an absolute last resort for this one. The whole PCB is about the size of a stick of gum, none of the cores I can find would fit. Plus this is an area I have very little experience of, throwing another steep learning curve into the mix at this point wouldn't endear me to my boss.

I do have a reference capacitor, being measured by an identical circuit, and doing the ratiometric stuff in software, which works well enough to correct the temperature drift. The humidity drift is a harder problem, mainly because it takes so much longer to measure.

[snip]

I did consider an air-core inductor, but I need a few tens of uH, and it wouldn't fit in the product. Also there is no overall shielding in this one apart from the PCB ground plane, and I can see it would end up becoming a Theremin.

Cool. That is a much straighter line than I would expect. Was that done using a DMM?

I've never done anything high enough frequency to have to worry about dispersion etc. But the FR4 was definitely part of the humidity drift problem. None of the PCB laminate vendors we approached would commit to the orders-of-magnitude lower moisture absorption we were asking for, so we're sticking with FR4 for now.

It turns out the customer can accept nulling out the drift at the start of each day, they have a lot of other measurements where they have to do this so it's not too big a deal. It's a lot easier to hit than our originally planned 12 month calibration interval.

Ouch. You'd need to identify the core material.

Perhaps, but getting stuck with complicated job and a half-baked scheme to tackle it is the kind of thing that inept bosses do to their subordinates.

There are some fairly compact cores designed to be integrated with printed circuit windings

You might be able to integrate one of them into a fairly compact solution (and a compact solution is the kind of thing bosses do promise their customers, and have trouble backing away from).

Bridge circuits - particularly one-to-one bridges - don't have that kind of problem.

--
Bill Sloman, Sydney

Very good data, John. Thanks. I did some analysis to try to understand your ppm results on the right hand side of your graph. I can't come up with the same numbers. Did you perhaps mean 89pF rather than 99pF?

Not a big deal in any case. I just want to know if I understand it correctly.

Did you get any tempcos? Most air-wound inductors have positive TCs in the roughly +100 PPM/K range. But if the coil is stretched by the FR4 TCE, that has an effect too.

I'm about to learn some more about that.

I had to wind my own air-core power inductors, to tolerate skin-loss heating. #14 wire wound on a reference Sharpie.

--

John Larkin         Highland Technology, Inc 

The cork popped merrily, and Lord Peter rose to his feet.  
"Bunter", he said, "I give you a toast. The triumph of Instinct over Reason"

I used my faithful AADE capacitance meter. I have a Boonton 72 too.

I should measure microstrip and stripline prop delay vs temperature too. I have a kitchen-sink 4-layer proto board coming up soon, so I can throw in some test traces for that. And a couple versions of my Colpitts. And a couple of LTM8078 tests in lieu of having a Spice model. The Spice model ETA remains unknown; LT Spice is in turmoil.

I'm going to try guarding/bootstrapping the critical node of my oscillator by an inner-layer PCB plane patch driven from the emitter of the Colpitts transistor.

Our newer designs self cal every powerup, or startup from idle, so they accept whatever frequency the oscillator wants to run at. That eliminated piston caps and worries about long-term drift.

It's interesting to phase-lock an arbitrary-frequency triggered LC oscillator to a 10 MHz OCXO. I invented one scheme and on a good day, with lots of coffee, I can still mostly understand how it works.

--

John Larkin         Highland Technology, Inc 

The cork popped merrily, and Lord Peter rose to his feet.  
"Bunter", he said, "I give you a toast. The triumph of Instinct over Reason"

Did I mess that up? That would be bad, but FR4 isn't consistant anyhow.

Looks like roughly +750 PPM.

I bought a special-made reel of 3.3 pF caps with specified TC of -4700 PPM (measured close to -5000, not bad shootin') to compensate my LC and CCRO oscillators. First article, I pad one of these with an NPO to fine-tune the overall TC.

--

John Larkin         Highland Technology, Inc 

The cork popped merrily, and Lord Peter rose to his feet.  
"Bunter", he said, "I give you a toast. The triumph of Instinct over Reason"

Single-layer coils obey the approximate relation

L = a**2 N**2/(9a + 10b),

where L is in uH, a is the mean radius in inches, and b is the length in inches.

You can use that to choose a coil form material so that the increase in length balances out the increase in diameter.

There's probably some value at which B&W Miniductor stock has zero tempco--the plastic expands 10 times more than the copper, which stretches out the coil.

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs 
Principal Consultant 
ElectroOptical Innovations LLC / Hobbs ElectroOptics 
Optics, Electro-optics, Photonics, Analog Electronics 
Briarcliff Manor NY 10510 

http://electrooptical.net 
http://hobbs-eo.com

No, it is not bad. It doesn't make that much difference. I was just checking my understanding. Great info, sir.

That's what I came up with. Thanks for the confirmation.

That's great! Love to see your data. Thank you.

[snip]

[snip] Sort of. We don't have an LCR meter, I should probably try to do something about that.

What I did was test the various inductors on the PCB in an environmental chamber, so what you get is the combined tempco of the L and the C, which is more relevant to my application but possibly not as useful to anyone else. The last spin of the board used a TI FDC2212, which measures the resonant frequency to an effective accuracy of about 250 Hz.

I'll dig out the numbers and post them on Monday if they're likely to be of any use.

We did rent an LCR meter for another project years ago, big HP boat-anchor of a thing, I forget the model number now. Something similar would definitely help here.