Author Topic: Oscilloscope as a lock-in amplifier (Rigol DS1054Z)  (Read 540 times)

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Offline RoGeorge

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Oscilloscope as a lock-in amplifier (Rigol DS1054Z)
« on: October 21, 2020, 11:14:04 pm »
A lock-in amplifier is an instrument to measure very small AC signals flooded with noise.  A lock-in amplifier is able to clean up signals many times smaller than the noise, and measure their amplitude and phase.

To achieve that, it needs a clean reference signal that is synchronous with the small one we want to measure.  The amplitude of the reference signal is irrelevant, same for the phase, just that the reference signal must be synchronous and clean.



The typical arrangement is like this:  A generator of clean signal is feeding both the device under test and the reference input, while the small signal flooded in noise (that gets out from the device under test) is fed to the measuring input of the lock-in amplifier.  At the output we will get the phase and the amplitude of the small signal.



The trick to achieve this is that the lock-in amplifier averages many periods of the signal, so the noise will average to zero.  The signal of interest will average to zero, too, except that the averaging is made synchronous with the small signal of interest (that is why it needs a clean synchronous reference signal).  As a result, the noise averages to zero, while the signal of interest averages to itself (stays the same).

Thus, all the noise is removed while the small signal of interest remains, because the small signal was synchronous with the averaging process.

Usually this functionality is implemented with analog multipliers followed by integrator circuits, sometimes by simply switching the polarity (multiply with +1/-1) followed by integrator, sometimes is made purely digital by DSP.

We will implement a lock-in amplifier with an oscilloscope, by synchronizing the oscilloscope on the clean Vref (Ch2), while feeding the small noisy signal to Channel 1, then setting the acquisition mode on Average (between consecutive traces), on DS1054Z by pressing Acquire -> Mode -> Average.

The multiplication here is made with 0/1 (by the triggering circuit) and the integration is made by the trace averaging mode (also there is no need to get the quadrature reference signal, since the multiplication and averaging happens for each and every ADC sample, including t=0, or t=pi/2, or any other point on the trace).

As a bonus, this kind of lock-in amplifier not only gives the amplitude and phase, but also shows the waveform of the small signal, which might be a big advantage, and also can work at much higher frequencies.  As a drawback, an oscilloscope might not have such a big dynamic range as a dedicated lock-in amplifier.



As an application of this technique, let's measure the contact resistance of some random banana plugs.



We set a 50 \$\Omega\$ DDS generator to output 10Vpp at 1.3kHz and measure the voltage drop on the contact resistance.  The red and black alligator clips are coming from the generator, the probe is going to channel 1 of the oscilloscope.  There is another cable not shown in the picture, cable going from the generator straight to the oscilloscope for synchronization.





The voltage drop on the banana plug is in the mV range, and the signal is very noisy.  This is the signal without averaging and synchronizing:





Same signal synchronized:





And finally, the same signal locked and averaged for 1024 traces.  Notice how all the noise has gone, and the oscilloscope can measure the Vpp without any problems:



All the noise has vanished because by synchronous averaging, the signal to noise ratio improves by \$\sqrt{N}\$ times, where \$N\$ is the number of averaged traces (here 1024).

In case you wonder what was the contact resistance for those bananas, not very good, in the ballpark of 25m\$\Omega\$:

« Last Edit: October 21, 2020, 11:46:10 pm by RoGeorge »
 
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Online jonpaul

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Re: Oscilloscope as a lock-in amplifier (Rigol DS1054Z)
« Reply #1 on: October 22, 2020, 06:55:53 am »
Scope averaging is NOT same as lock-in amp, which uses a PLL.

Suggest to study ensemble averaging definition and lock in amp app notes eg from Stanford Research Labs.

Finally the binding post R tests are not meaningful unless you first clean off all corrosion.

A 4 terminal DC or 1 kHz bridge can easily measure to resolution 1 mOhm.

Jon
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Offline RoGeorge

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Re: Oscilloscope as a lock-in amplifier (Rigol DS1054Z)
« Reply #2 on: October 22, 2020, 10:03:03 am »
Scope averaging is NOT same as lock-in amp, which uses a PLL.

Suggest to study ensemble averaging definition and lock in amp app notes eg from Stanford Research Labs.

Finally the binding post R tests are not meaningful unless you first clean off all corrosion.

A 4 terminal DC or 1 kHz bridge can easily measure to resolution 1 mOhm.

Jon

The role of the PLL here is played by the triggering circuit of the oscilloscope.

I'm aware about the classic implementations, and have been warned before about the synchronous averaging as not being the same as a lock-in amplifier, but I am still convinced they are.  Either way, by analog multiplication and PLL, by polarity switching, by DSP, or by a trace averaging oscilloscope, the basic principles to me remains the same:
- synchronous averaging is preserving the parameters of the measured signal
- noise averaging tends to zero with time
therefore I will say they are equivalent.

They are not 100% the same, I agree with that.  For example a lock-in amplifier is averaging all the consecutive alternances of a signal, while the oscilloscope might skip some of them between triggerings.  Still, the end results remains the same, because the noise is always random and the signal of interest is constant, so it doesn't matter if we skip forward.

Also the functionality remains the same, we can still use this to recover a signals from noise, or as a very narrow band pass filter (comb filter to be more precise), same as with a classic lock-in amplifier.

The advantage when using this oscilloscope technique is we can also see the waveform (which a classic lock-in amplifier doesn't show), and we can use any shape of signals, not only sinusoidal ones.

I could name it "RoGeorge averager" ;D, the amazing lock-in amplifier that shows the waveform, too!

But that would be even more offending, I guess, and most probably I'm not the only one (neither the first) using an oscilloscope this way.  And then, will need to re-explain to everybody when it is advantageous to use it.  By keeping the lock-in amplifier name, one knows in a glimpse in which situations this can be used.



Indeed, there are many ways and many instruments that can measure contact resistance.  This was just an example to show how incredibly well this technique performs in practice, with real signals and real noise, not just in theory.

Online 2N3055

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Re: Oscilloscope as a lock-in amplifier (Rigol DS1054Z)
« Reply #3 on: October 22, 2020, 10:17:58 am »
You are not synchronously band pass filtering but synchronously  low pass filtering. Low frequencies will skew your averaged signal.

DSP equivalent of lock in would be to use FFT or Goertzel algorithm to band pass filter with very narrow band and then use amplitude of that peak for measurements... And create software PLL equivalent that will lock input frequency the one measured..
 

Online jonpaul

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Re: Oscilloscope as a lock-in amplifier (Rigol DS1054Z)
« Reply #4 on: October 22, 2020, 10:37:14 am »
100% agree  with 2N3055,

the Lock In amp synthesizes a super high Q BP filter so the locking signal (int or ext) is the ONLY signal at the output.

Q 10K...1M are possible.

The ensemble averager is NOT synchronous and the trigger is NOT a lock in but for convienience in viewing a periodic signal.

Suggest to check app nots/texts/articles on Lock In Amps vs Ensemble averaging.

Jon
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Online nfmax

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Re: Oscilloscope as a lock-in amplifier (Rigol DS1054Z)
« Reply #5 on: October 22, 2020, 10:47:12 am »
You are not synchronously band pass filtering but synchronously  low pass filtering.

It is actually multiple bandpass filtering: the passbands are at the trigger frequency and its harmonics (up to the bandwidth limit of the oscilloscope). The width of each passband is set by the time record length. There is also a passband, of half this width, at DC. This may give problems in the presence of drift, but using an AC excitation as RoGeorge does, and AC coupling the input to the oscilloscope, avoids them.

It's an old book, but see T. H. Wilmshurst, Signal recovery from noise in electronic instrumentation. Bristol ; Boston: A. Hilger, 1985. ISBN 0-85274-783-7. Based on the lecture course he first gave to us unwashed students a few years previously!
 

Online 2N3055

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Re: Oscilloscope as a lock-in amplifier (Rigol DS1054Z)
« Reply #6 on: October 22, 2020, 02:13:57 pm »
You are not synchronously band pass filtering but synchronously  low pass filtering.

It is actually multiple bandpass filtering: the passbands are at the trigger frequency and its harmonics (up to the bandwidth limit of the oscilloscope). The width of each passband is set by the time record length. There is also a passband, of half this width, at DC. This may give problems in the presence of drift, but using an AC excitation as RoGeorge does, and AC coupling the input to the oscilloscope, avoids them.

It's an old book, but see T. H. Wilmshurst, Signal recovery from noise in electronic instrumentation. Bristol ; Boston: A. Hilger, 1985. ISBN 0-85274-783-7. Based on the lecture course he first gave to us unwashed students a few years previously!

Thank you for very nice comment. You actually explained what I had in mind (English is not my native language).

I was referring to DC drift, and very low frequency components. You are correct that AC coupling will help with this. But still, with all that, it is not gonna come close to Q factor of Lock-in amp. And it will be better at some frequencies etc etc..

It will still be very useful and will help in many occasions to help seeing signal. That is not questionable.

Fun fact is that a DSP code could be made that uses scope capture to mimic lock-in amp behaviour.

Thanks for the book reference.. I will try to take a look.

Regards,

Siniša

 

Offline David Hess

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Re: Oscilloscope as a lock-in amplifier (Rigol DS1054Z)
« Reply #7 on: October 22, 2020, 04:14:44 pm »
There are some significant differences:

1. A lock-in-amplifier integrates its input over time.  The DSO samples its input synchronously with the trigger.

2. Integration by the lock-in-amplifier causes harmonics to cancel out while sampling synchronously with the trigger by the DSO results in detecting harmonics just as well as the fundamental frequency.

I do not often use a lock-in-amplifier, except in the form of synchronous detection in circuits, but triggering an oscilloscope and using averaging to remove noise is a regular extersize.
« Last Edit: October 24, 2020, 06:14:50 am by David Hess »
 

Online nfmax

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Re: Oscilloscope as a lock-in amplifier (Rigol DS1054Z)
« Reply #8 on: October 22, 2020, 05:56:12 pm »
To make the oscilloscope as much like a lock-in amplifier as possible, ensure the excitation waveform fits an exact integer number of times into the time record, and use the scope's FFT function to measure the amplitude of the fundamental frequency. If available, use the flat-top window, to avoid amplitude errors from the windowing, though these should be minimal if the fit is exact.

Some lock-in amplifiers - even analogue ones - could operate as matched filters, correlating using a reference signal having multiple harmonics, for the last n'th of SNR improvement.

I forgot to mention the book Lock-in amplifiers: principles and applications now available online at https://www.sites.google.com/site/lockinamplifiers/home
 
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Online SilverSolder

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Re: Oscilloscope as a lock-in amplifier (Rigol DS1054Z)
« Reply #9 on: October 22, 2020, 07:55:56 pm »
As long as the excitation signal is a clean sine wave and the DUT doesn't distort it unduly, it seems to me that scope averaging comes pretty close to a lock-in amplifier except that it isn't as sensitive.

I have used a 40dB amplifier in front of the scope to boost sensitivity when using the scope as a pseudo lock-in amplifier in this way.


Another cool thing you can do is display two channels on the scope,  one being the original excitation wave and the other being the measured signal.  This way, you can see the phase shift between the two, so you can be sure that you are measuring pure resistance (as opposed to capacitive (or inductive) reactance).

This setup works great as a detector in a bridge measurement too, with the two-signal phase display trick.  Here, you can use a variable capacitor to balance out the stray capacitance and get the phase spot on for ultra accurate measurements.

Who knew DSOs were so much fun!  :D

 


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