Sensing small inductances

I have a power budget and a low supply voltage constraint (~3 volt) in the project so speeding that oscillator up to where the test inductors have a higher Q and I could just frequency count with a fast comparator into a fast uP is gonna be a problem.

I feel my options are either to a) use a trick to boost the intrinsic tank Q at lower frequency and use multiple measurements as Jan suggested in his post, or use a suggestion like yours and not try to make the DUT part of an oscillator circuit at all and do it indirectly.

the good news is that gain is pretty cheap and gotten a lot cheaper lately it seems, 20MHz RRIO CMOS op amps that go down to 1.8V supply, in duals or quads are under a buck in small quantity

I would do a moving average and math in software, do they even make that Motorola quadrature detector chip anymore?

Inductors are goofy parts, so it only makes sense to measure their inductance near the frequency they will be used at. An easy way to do that is to build an oscillator and measure the frequency. The stability is usually dominated by the inductor tempco, often in the

+100 PPM/K range or so for sensibly constructed air cores.

Try heating and cooling the inductor a bit to see if the inductance is actually changing.

Randy Rhea has written a lot about negative resistance oscillators.

A small USB thing could do the measurements, and then let a PC take over.

Analog Devices has some nice DDS synthesizers and differential-input analog multipliers, which would be another way to go. And the network analyzer chip that someone mentioned.

All it takes is a little trig. I have a nice trig textbook, printed in

1868. It was bought by George P Lents, for $1.25, in 1872.

Basically most, if not all oscillators can be analyzed using a series resistor at the input.

All oscillators can be analyzed using the Barkhausen criterion.

Sure. They have minimal inductance in the base, grounded emitters, multilayer pcbs with good ground plane, 50 Ohms in and out, good layout and bypassing, and so on.

I never said all Darlingtons oscillate. But I explained when you find one that does, why it is so difficult to kill the oscillation. I suspect part of the reason is the higher input impedance. The other reasons the base resistor kills the oscillation is a subject for further study.

the inductor in this case is functioning as a strain gauge/transducer (as opposed to resistivity strain gauge) so the circuit that it's in, is the capacity that it's being used in, as an indirect measurement of displacement

How do you get LTspice to plot in Cartesian coordinates?

Looks like he is analyzing a standard Clapp oscillator and omitting the base- emitter and stray capacitances.

Most, if not all oscillators can be analyzed with a resistor at the input. All oscillators can be analyzed using the Barkhausen criterion.

I meant this sort of thing:

Same thing. Emitters go to ground with recommended layout to minimize ground inductance. 50 Ohm environment. Multilayer pcb with ground plane and good layout prectises required.

Again, I never said that all Darlintons oscillate.

I found how to plot in Cartesian coordinates. Simple.

Your plot shows the impedance going negative above 10 MHz. I think that may be an artifact of your circuit. It sure doesn't look like a Colpitts to me.

I have carefully examined the input impedance under small and large signal conditions. I was unable to find any region that exhibited negative input impedance.

The term "negative resistance" is a complete misnomer. It has nothing to do with the classical definition of negative resistance, where the current decreases as the voltage increases. The term is simply ill-chosen.

The term merely illustrates the value of resistance needed at the input of an oscillator to kill oscillations.

That's interesting in a time-domain sim, with a 1 GHz 1 volt source. There is voltage gain at the right-hand end of the 50 ohm resistor, about 1.6 volts peak with a little phase shift. The generator clearly sees a negative resistor.

That's his circcuit. Try a Colpitts.

Any passive resonator that oscillates is seeing a negative resistance. Energy is conserved, and the resonator loss has to be made up for.

Where did you get that? Try measuring the input impedance of a Colpitts. It is always positive. The negative resistance is a complete misnomer. It has nothing to do with the voltage increasing and the current decreasing. It is only the resistance needed to stop oscillations.

The Barkhausen criteria states the phase shift has to be zero or multiples of

360 degrees, and the loop gain has to be equal to or greater than 1. No negative resistance is needed.

In a cc Colpitts, you control the energy loss by adjusting the emitter resistance and thus the energy delivered to the tank. In a Pierce, you adjust the resistance from the output to the tank.

See Oscillators.zip at

I don't know if it's entirely relevant but the Barkhausen criteria are necessary criteria for oscillation, but they don't imply that they are sufficient conditions.

I don't believe anyone's ever come up with a set of universal criteria that act as sufficient conditions for predicting oscillations, in all electronic positive feedback loop structures that it's possible to theoretically construct.

So whether negative resistance appears in some oscillating system or not, and whether it's required to be there or not for it to oscillate, likely depends entirely on the particular system.

That is to say the mathematical theory of large-signal periodic oscillations in electronic circuits is pretty complicated, there are a number of table-breaking books written on the subject, and at the very least I think it's difficult to make any un-qualified "all oscillators do this" or "all oscillators do that"-type statements about them.

Measure when and how? what the Colpitts oscillator circuit's small signal input impedance is when not oscillating and into the amplifier with a test voltage isn't the same as its large-signal input impedance when it is oscillating, its large-signal input impedance will be a non-linear function of time

what does it matter measuring various parameters of circuits under conditions they never experience when they're operating