# Best method to measure freq of 20nV AC signal

#### nanok66

Joined Jul 14, 2016
64
Hi all,

I am trying to make a circuit that measures the frequency of a tiny 20nV AC signal (~4000Hz) generated by an inductor coil I will ultimately be bringing the signal into my PIC16F1713 (which has a Zero Crossover Detect (ZCD) module). There are many possible ways to go about this, so the ZCD may seem convenient but maybe there are better methods.

To use the ZCD at least, my method would be to chain op amps to give a combined gain of 50M to get the signal to 1Vpp. I could then reliably use the ZCD module to trigger an interrupt and count frequency. I worry though, the signal itself is from inductively picking up a resonators motion so I imagine the sine wave created will be distorted to some degree. I also imagine the large gain could make noise an issue. With these factors in consideration are there other methods that could work great with uV or mV level AC signals and therefore wouldn't require me to amplify the signal as greatly?

Just brainstorming, perhaps I could amplify to the minimum level for a comparator to work, then into the PIC? Or maybe directly into the ADC of the PIC? Any help is appreciated!

#### BR-549

Joined Sep 22, 2013
4,938
Show us your circuit and where you are measuring the nVs.

#### nanok66

Joined Jul 14, 2016
64
The nV AC signal is generated by an EMAT, which is basically an inductor coil (with maybe 0.1 - 10uH if that matters). The weak AC signal is generated in the inductor coil because of the tuning fork vibrating in the presence of the static magnetic field. Points A and B are where I am measuring the AC wave from.

#### nanok66

Joined Jul 14, 2016
64
I should also say that I've already considered that in-amps and differential amps would be choice amplifiers for amplifying this type of small signal due to lower noise and superior common mode rejection as compared to typical op-amps. Even if I use more expensive specialized amps like those there are still many ways to ultimately bring the signal into a PIC. I could still go to a comparator-->PIC or direct PIC ADC or direct PIC ZCD or who knows what might be better/simpler/more reliable.

One of my leading ideas at least for initial amplification is to chain a couple differential amps together (conveniently using one chip such as the high bandwidth dual channel THS4552), that way I can still have a decent operable bandwidth since the gain is so high.

#### BR-549

Joined Sep 22, 2013
4,938
Can you put more turns in the coil?

#### nanok66

Joined Jul 14, 2016
64
I have researched EMATs quite a bit and coil design has it's own set of physics that I can't change. There are definitely ways to optimize the generated signal but in general EMAT coils have inherently low inductive coupling efficiency. I based the 20nV level signal on my own scope measurements using a high gain op amp. It surely could end up being 10x higher for all I know but 20nV is where I'm currently hoping to start.

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#### crutschow

Joined Mar 14, 2008
24,725
How stable is the signal frequency, as you will need a narrow bandwidth filter to keep the amp noise well below the signal.
For example, the THS4552 amp has an input noise of 3.3nV per root Hertz.
Thus a bandwidth of just one Hertz would still only give a S/N of 15dB.

If the signal frequency is stable enough you may want to consider a lock-in type amplifier.
In such an amplifier you can vary an accurate reference frequency until you get an output, indicating the reference frequency is equal to the signal frequency.
The equivalent signal bandwidth of such an amp can be made to be less than 1Hz if needed.

#### nanok66

Joined Jul 14, 2016
64
The frequency will not vary over the duration of a single ring. It will only decay in amplitude during that time aka the resonator naturally stops ringing. Also to note the resonator will be immersed in liquid so the decay will occur faster than if it was ringing in air. Hopefully the decay rate won't be too high though. For now I think that if I measure for a relatively short amount of time there should still be plenty high-enough amplitude wave cycles to calculate the frequency.

The frequency will change between entirely different rings (when the resonator is immersed in a different liquid). Right now I am working at 4000Hz frequency and a change of +-200Hz but in the future may be working with freq more like 60kHz and a bigger change +-3kHz.

But I have even brainstormed of using Fast Fourier Transform once the signal is received by the PIC ADC. Perhaps that could be the most reliable?

Thank you I will definitely look up the lock-in amps!

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#### nanok66

Joined Jul 14, 2016
64
Ok you guys have definitely made me question my measurement of 20nV. I did find a detail that I do not understand and maybe it is a source of error in my measurement.

The op-amp I used for amplification was the AD8606. I used an in-amp circuit directly from the datasheet which is below. I used .1% tolerance 50kohm resistors and 1% tol .75ohm resistors to reach a calculated gain of 66666.

The thing I have realized is that the datasheet lists the unity gain bandwidth product at 10MHz. With 66k gain the bandwidth would have been reduced down to 10M/66k = 150Hz! Hopefully I am understanding this correctly.

I was looking at a ~4000Hz sine wave with the scope fully zoomed in but the bandwidth of the op-amp shouldn't cover that range. Why was I still seeing the correct freq sine wave? What exactly happens to a signal that is beyond the bandwidth of an op-amp such as this?

#### crutschow

Joined Mar 14, 2008
24,725
What exactly happens to a signal that is beyond the bandwidth of an op-amp such as this?
You are basically looking at the open loop gain at that frequency which is 10M/4k= 2500.

#### joeyd999

Joined Jun 6, 2011
4,374
The nV AC signal is generated by an EMAT, which is basically an inductor coil (with maybe 0.1 - 10uH if that matters). The weak AC signal is generated in the inductor coil because of the tuning fork vibrating in the presence of the static magnetic field. Points A and B are where I am measuring the AC wave from.

View attachment 136940
What's the output impedance of the coil? You could consider a step-up transformer to provide the initial voltage gain, followed by an amp. Just a crazy idea that popped into my head.

Alternatively, you could also consider a transimpedance amp for the initial gain stage.

#### GopherT

Joined Nov 23, 2012
8,012
The frequency will not vary over the duration of a single ring. It will only decay in amplitude during that time aka the resonator naturally stops ringing. Also to note the resonator will be immersed in liquid so the decay will occur faster than if it was ringing in air. Hopefully the decay rate won't be too high though. For now I think that if I measure for a relatively short amount of time there should still be plenty high-enough amplitude wave cycles to calculate the frequency.

The frequency will change between entirely different rings (when the resonator is immersed in a different liquid). Right now I am working at 4000Hz frequency and a change of +-200Hz but in the future may be working with freq more like 60kHz and a bigger change +-3kHz.

But I have even brainstormed of using Fast Fourier Transform once the signal is received by the PIC ADC. Perhaps that could be the most reliable?

Thank you I will definitely look up the lock-in amps!

At those frequencies, your tuning fork may be causing cavitation of your fluid like an ultrasonic bath. Operating in the cavity may appear like you are operating in a compressed gas instead of a liquid. Is that the goal or an unplanned situation?

#### Picbuster

Joined Dec 2, 2013
996
Hi all,

I am trying to make a circuit that measures the frequency of a tiny 20nV AC signal (~4000Hz) generated by an inductor coil I will ultimately be bringing the signal into my PIC16F1713 (which has a Zero Crossover Detect (ZCD) module). There are many possible ways to go about this, so the ZCD may seem convenient but maybe there are better methods.

To use the ZCD at least, my method would be to chain op amps to give a combined gain of 50M to get the signal to 1Vpp. I could then reliably use the ZCD module to trigger an interrupt and count frequency. I worry though, the signal itself is from inductively picking up a resonators motion so I imagine the sine wave created will be distorted to some degree. I also imagine the large gain could make noise an issue. With these factors in consideration are there other methods that could work great with uV or mV level AC signals and therefore wouldn't require me to amplify the signal as greatly?

Just brainstorming, perhaps I could amplify to the minimum level for a comparator to work, then into the PIC? Or maybe directly into the ADC of the PIC? Any help is appreciated!
Vibrating wire systems do have similar problems. ( pulse to a coil wire vibrate and measure the damping caused by environment.)
Some solutions might be useful to you. ( amplification and input protection)

Picbuster

#### Tesla23

Joined May 10, 2009
395
Ok you guys have definitely made me question my measurement of 20nV. I did find a detail that I do not understand and maybe it is a source of error in my measurement.

The op-amp I used for amplification was the AD8606. I used an in-amp circuit directly from the datasheet which is below. I used .1% tolerance 50kohm resistors and 1% tol .75ohm resistors to reach a calculated gain of 66666.
The AD8606 may be a poor choice as its input voltage noise is 8nV/√Hz, you can do about 20dB better using something like the LT1028. In the circuit you posted, the 1k resistors are a bit high for a low noise design (voltage noise 4nV/√Hz), if you are directly interfacing you should use a much lower impedance. Alternatively, an audio transformer like joey suggests may help your design. You really need some idea of the measurement bandwidth and S/N required before you can design the front end.

Also, I don't know how accurately you need to measure the frequency, or what noise/interference you are expecting, but FFTs are not particularly good at accurate frequency measurement. It's a well studied area, google 'frequency estimators' for more information - the maths may appear difficult, often the implementation algorithms can be relatively simple. An FFT will let you express the signal as a sum of sinusoids and find the biggest sinusoid, and you can often interpolate the FFT bins to increase the resolution. A frequency estimator tries to answer the question, if this signal consists of a sinusoid plus noise, what is the frequency of the sinusoid, and you can answer it much more accurately than with an FFT.

#### nanok66

Joined Jul 14, 2016
64
Wow glad I posted this question you guys are great. I need to go back to my scope and op-amp and redo my previous voltage measurements..

But just to make a quick estimate if my gain was actually around 2500 that would mean my calculation using 66k would have been off by a factor of 26. 26 x 20nV = 0.52uV! That would be great news for the difficulty of this circuit if true.

Also joey I'll have to look up the advantages of having a transformer in the chain for my small signal. I'll also look to see if tracking the current with a transimpedance amp could be any better than tracking the voltage, thanks.

#### nanok66

Joined Jul 14, 2016
64
Yeah Tesla I was only using the AD8606 because it was the lowest noise amp in my electronics collection. And I was using 0.75ohm resistors going in. The bandwidth I also attempted to specify, right now I am working at ~ 4000Hz and the change in frequency between the resonator ringing in different liquids will be perhaps a span of 200Hz. So lets say 3900Hz to 4100Hz. That guess is the best I can do at this point. I must design the front end first to find the true bandwidth range required, then I once I know the real bandwidth I will go back and optimize the circuit.

But thanks for the advise on the FFT solution. Frequency detection accuracy is of utmost importance. I wasn't aware that FFT is a poor frequency detector compared to other methods.

Also thank you Gopher that is a very good point but the tuning fork is not actually shaped anything like a normal tuning fork and won't create those cavitations. I just didn't want to complicate the circuit discussion.

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#### joeyd999

Joined Jun 6, 2011
4,374
Back to the transformer idea -- your transducer is nearly exactly the same as a ribbon microphone, the science of which is very mature. You can purchase transformers specifically for them. And there are lots of amplifier examples.

#### nanok66

Joined Jul 14, 2016
64
Ah I had not looked to ribbon mics for examples yet that's a great point. Nice lundahl transformer website too.