measure impedance peek of a moderate Q resonant filter using DSP

You might be able to do a few selected frequencies near the expected (ie last) resonance point and use a golden ratio maximiser to track it.

Wouldn't it be easier to sweep the drive frequency around the last known resonance value and track the resonance point that way?

If you must do it DSP, do Hilbert transform followed by linear least squares.

So you can ping it, but you can't do a CW oscillator and frequency counter? (If necessary, vernier counts will give higher resolution counts at much faster update rates with far less hard/software.)

Tim

-- Seven Transistor Labs Electrical Engineering Consultation Website:

Cool; I have that identical issue now, how to measure the resonant frequency and how best to tune an LC in production.

How about making it oscillate? Connect it to a negative resistance opamp circuit and just observe the frequency?

ay 10kHz and 20KHz. I need to find the resonant frequency within 10Hz every 25mS.

If not how Long would I need to sample to get 10Hz resolution in the FFT?

the frequency of the ring down. I'm told there should be at least 4 damped cycles before if fades away. that would be ~500uS / sample so I could do some averaging over 25mS.

If the Q of the circuit is reasonably stable, the phase shift between a dri ving current at a fixed frequency near resonance - say 15kHz to start with

- and the voltage generated across the tank circuit should provide a pretty unambiguous pointer to where the resonance actually is.

You'd want to drive the current into the transducer from a current source - something like a Howland current source would work at that kind of frequen cy

and monitor the amplitude and phase of the voltage developed across the tra nsducer.

Four cycles of ringing after a ping doesn't represent a particularly high Q .

You say the transducer looks like a somewhat damped LC circuit, so presumab ly there is a certain amount of energy circulating inside it. If this is pr edictable enough for you to model it, it shouldn't be that difficult to get something pretty close to the actual resonant frequency out of the differe nce between the current you are driving into the transducer and the voltage you are getting out.

In a classical LC circuit, the way the Q would vary with resonant frequency would depends on whether the frequency was shifting because the L or the C was changing - so a simple-minded model might not work too well.

If you can hold the excitation frequency fairly close to teh actual resonan t frequency this isn't going to matter much - the tracking error would be s mall and you wouldn't have to know it very accurately, and you might be abl e to ignore it.

As Martin said it's basically 1/resolution so 0.1 seconds. If you've got control of the source you can do better than hitting it with white noise. You do better if you hit it with only sine waves that are in the center of each of your FFT bins. (Hmm I'm not explaining that very wel l.) But noise at a frequency that is between two bins is wasted signal.

How fast is the frequency going to change? It seems like you could phase l ock a signal to the center. But I don't know about a part in 10^3 resoluti on for a Q = ~4. You'd want to wiggle the sine wave at (say) 10 Hz. And that will limit the time response... and also your freque ncy resolution... though maybe you can average a faster dither??

George H.

Ohh, that's interesting. You'd need a AGC circuit (or something to limit the amplitude.) If there was a big change in the dissipation a different frequencies it might be harder. But that's probably not the case.

George H.

say 10kHz and 20KHz. I need to find the resonant frequency within 10Hz every 25mS

driven with white voltage noise will I get the frequency resolution? If not how Long would I need to sample to get 10Hz resolution in the FFT?

the frequency of the ring down. I'm told there should be at least 4 dampe d cycles before if fades away. that would be ~500uS / sample so I could do some averaging over 25mS.

ncy and how best to tune an LC in production.

circuit and just observe the frequency?

You'd want to be able to adjust the "negative resistance" to keep the volta ge swing within the rails - let it clip and you've got a much messier wavef orm to make sense of.

It's easy enough to do - high quality Wein bridges do it all the time, but there the losses are pretty predictable.

A transducer where the variation of the resonant frequency is the parameter of interest may not have a particularly stable Q across it's operating ran ge.

There are plenty of four-quadrant multipliers around which could do the job , but extracting the amplitude that you are controlling fast enough to keep it well controlled while keeping track of a rapidly changing resonant freq uency might be more interesting.

Looking at crossovers AND amplitudes between crossovers will work, but I'm always leery of 'time' waveforms and their susceptibility to noise. Really starting to lean towards frequency domain and the advanatages you get from averaging

THIS MIGHT WORK: your detection MUST be synchronous to the drive AND the packet length MUST be within integer periods for this to work. Use two tones, [or three or four] one at 10kHz and one at 20kHz. Make a 'poor man's FFT' after all, you're only looking for those two tones and it's unlikely there is energy outside those two tones. Be sure your other tones will NOT add energy to your "FFT"

Do a little math on the signal and phase and 'predict' where the resonance is. You didn't say you needed Q, right? just fres.

Between 1970-1973, I was making (Analog) active filters (thick-film hybrid modules) for the telephone industry. To precisely locate the poles of these complex filters my probe station connected the filter with some external components such that it oscillated at the pole frequency, AGC'd to prevent clipping/pulling. A laser trimmed a thick film resistor to dead-on pole location. Filter configuration was such that Fo and Q trims were orthogonal... so, after, Fo trim, the Q was trimmed. So it's quite easy to do. ...Jim Thompson

The Q is probably too high for just two tones. An impulse repeated at frequency F would give you tones spaced at F. Then you can do the FFT thing and have a rich source of phase and amplitude information to work off of.

You'd want to make sure that you knew the exact delay between your tone generator and your ADC, and then you'd probably want to check the calibration with a resistive pad in place of the sensor.

Interesting, so AGC control with a changing Q is certainly doable. Did you use a multiplier for the AGC?

George H.

Yes. No ;-) I used a current-controlled gain element in the loop. Once Fo is established, gain is a known function of Q, so Q adjust was an internal gain adjust... no longer oscillating.

Lose the google :-( ...Jim Thompson

FFT is not very precise for short samples. Probably much better to put the sensor in a free-running oscillator, filter the oscillator output a little and count the time between zero crossings.

Jon

a free running oscillator is like a long term FFT, same narrowband results. The idea is to use long packets, stick on the end a few new terms while discarding off the end the old ones. See the similarity? Envision a sudden change in tank, how long to notice? Same thing with about the same accuracy doing a 'running' FFT, right?

n say 10kHz and 20KHz. I need to find the resonant frequency within 10Hz every 25mS

en driven with white voltage noise will I get the frequency resolution?

re the frequency of the ring down. I'm told there should be at least 4 dam ped cycles before if fades away. that would be ~500uS / sample so I could do some averaging over 25mS.

uency and how best to tune an LC in production.

p circuit and just observe the frequency?

tage swing within the rails - let it clip and you've got a much messier wav eform to make sense of.

t there the losses are pretty predictable.

er of interest may not have a particularly stable Q across it's operating r ange.

ob, but extracting the amplitude that you are controlling fast enough to ke ep it well controlled while keeping track of a rapidly changing resonant fr equency might be more interesting.

The more I think about this the more I think you are going to want to sampl e the voltage appearing across the transducer, and the current that you are using to drive the transducer, and use that to determine the phase shift b etween the two.

If you've got DSP hardware, doing a least squares three parameter fit (freq uency, phase and amplitude) on two sampled sine waves would be easy. Once y ou've sampled at least one full cycle, the parameters won't interact signif icantly.

The phase shift between the voltage generated and the current driving the t ransducer is pretty sensitive to frequency at frequencies close to resonanc e, so even if you aren't driving spot-on the resonant frequency you will ha ve a pretty good idea of what it is.

The question then becomes do you use John Larkin's "negative resistance" dr iver to generate the excitation, using a slow DAC to adjust the gain to kee p the amplitude sensible, or do you synthesise a digital approximation to a sine wave to generate the excitation current.

I'd be tempted to use a direct digital synthesis chip. They offer very fine control of frequency and can be persuaded to generate a remarkably clean s ine wave in the 10kHz to 20kHz region. With DSP hardware you could probably roll your own, but it would get messy.

John Larkin's toy will start up slowly - it relies on Johnson noise to get the oscillation going, and you've got to keep the gain high for a while bef ore you've got an oscillation level you can see, but it's perfectly practic al.

Jesus, how much swing do you really think there is in a LC NR feed back circuit? I mean, we are slightly side stepping the thread here to Larkins idea, which is an old school method..

Come on, rail concerns, ha...

Jamie

On Saturday, 7 December 2013 09:27:26 UTC+11, Maynard A. Philbrook Jr. wro te:

e:

een say 10kHz and 20KHz. I need to find the resonant frequency within 10H z every 25mS

when driven with white voltage noise will I get the frequency resolution? If n ot how Long would I need to sample to get 10Hz resolution in the FFT?

sure the frequency of the ring down. I'm told there should be at least 4 d amped cycles before if fades away. that would be ~500uS / sample so I coul d do some averaging over 25mS.

equency and how best to tune an LC in production.

amp circuit and just observe the frequency?

oltage swing within the rails - let it clip and you've got a much messier w aveform to make sense of.

circuit? I mean, we are slightly side stepping the thread here to Larkins idea, which is an old school method..

Any positive-feedback oscillator driver needs to have a thought-out amplitu de-limiting scheme.

Mook Johnson is talking about using DSP hardware to extract the resonant fr equency rapidly. Getting your amplitude limiting by clipping puts an uncert ain amount of higher harmonic content into the waveform he'd be looking at and would mess up any simple accurate mathematical extraction scheme I can think of.

My choice would be generate a sine wave drive current at a level that would n't drive the transducer too close to the rails - it's Q seems to be low, a nd probably won't move around much as the resonant frequency changes - but John Larkin wants it to self-oscillate, and that really does need some kind of gain control loop.

I'd invite you to think a little harder about the issue, if I thought that you could expend the effort usefully.

Lots of great ideas guys. I appreciate the feedback!!