Can A Band Pass Filter Speed Up Lock In Amplification?

I think you may be conflating "lock-in amplifier" with "phase locked loop". Lock-in amps typically use PLLs to acquire their own internal copy of an external reference signal. Modern lock-ins then multiply sine and cosine versions of this reference by the input signal to be measured.

In many applications, where the reference is under your control (you are generating it), the PLL is totally superfluous and is actually detrimental, due to the long lock time. If you generate sine and cosine versions of the reference and feed them to the multipliers directly, there is no "lock" time. Then the only time lag is due to the low-pass output filter that follows each multipler... the narrower the ultimate bandwidth, the longer the lag.

In that respect, it's just the same as if you had (somehow) built up a super-duper narrowband bandpass filter from conventional circuitry instead of going the multiplier/low-pass route: The ultimate bandwidth determines the lag.

Typically, lock-ins are used to get ultra-narrow bandwidths (1 Hz or less, often *way* less), which you couldn't approach with a conventional analog bandpass filter due to impossible Q (and hence stability) requirements.

Preceding the signal input with a filter will only add the delay of that filter to the lock-in process. It won't improve the response of the overall output. (Not to mention that in most situations the external pre-filter will be orders of magnitude wider than the ultimate lock-in bandwidth anyway.)

However, the "acquisition time" that lock-in specs mention has to do with the PLL lock time. Nothing you put on the signal input will help that, and anything you put on the reference input will most likely degrade it.

Best regards,

Bob Masta DAQARTA v5.10 Data AcQuisition And Real-Time Analysis

Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, FREE Signal Generator Pitch Track, Pitch-to-MIDI DaqMusic - FREE MUSIC, Forever! (Some assembly required) Science (and fun!) with your sound card!

I have no idea what you mean by 'speed up'.

The old EG&G 124A

had a band pass filter on the front end. This was to increase the dynamic range. (Filter and then amplify some more!)

Why do you say your signal frequency is in a narrow band? Typically the lockin has a single frequency. (The modulation frequency.) If you are changing the modulation frequency then the phase shift of the band pass filter might cause some problems.

George H.

The original intent was for the reference to be generated externally.

That still takes time.

Which could be years . .

The low pass filtering operation of band pass should always take more time than the high pass step. It doesn't take any time to eliminate dc.

It depends on the how much time you have to eliminate how much noise.

If you have a good in-phase reference then adding on more "blind" forms of filtering, even adaptive filtering using a reference of unknown phase angle filtering, isn't going to save any time.

Bret Cahill

It takes a certain amount of time for the ac signal + ac noise, after it is converted to a dc signal + ac noise, to integrate and overwhelm the ac noise.

This was originally about the multiplication of a noisy signal by a good clean reference. Both the signal and reference always have the same phase angle, 0, but the frequency of both change [together] over a narrow frequency range.

Supposing you cannot get a good clean reference, just another noisy signal where the second signal is in phase with the first? The product of two noisy signals is a rectified signal plus ac noise -- just like in conventional phase sensitive detection except the magnitude of the rectified signal has no use. If the product of the two signals isn't desired the only thing the product could be used for is the frequency which would need to be picked out by tuning another circuit to that frequency.

Bret Cahill

If the two signals are in phase (implying that they have the same frequency) then when you multiply them together you will get terms at 0 Hz and twice the frequency. Sure, you could tune another circuit to 2f, but then what was the point of the multiplication in the first place? How are you any farther ahead than if you had just tuned your circuit to the original frequency?

Best regards,

Bob Masta DAQARTA v5.10 Data AcQuisition And Real-Time Analysis

Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, FREE Signal Generator Pitch Track, Pitch-to-MIDI DaqMusic - FREE MUSIC, Forever! (Some assembly required) Science (and fun!) with your sound card!

Wouldn't the multiplication increase the [product signal] SNR?

The SNR of the original is somewhere between 0.3 - 3.

The goal was to use the product signal to somehow get a clean reference for the original noisy signals, but if it's just as easy to glean the phase and frequency from the original signals, that step is unnecessary at best.

Bret Cahill

Instead of prefiltering the signal for the signal input, prefilter the signal to get something that would trigger a clean reference signal.

Bret Cahill

It might... I'll have to think about this (and maybe run some experiments with Daqarta).

I think the best you could hope for would be a 3 dB improvement. That's what you'd get if you just added them together and divided by 2 (synchronous averaging), assuming that the noise in each signal is uncorrelated with the other's noise, while the underlying desired waves are identical.

But synchronous averaging assumes that the desired portions of each signal are identical in shape, frequency, and amplitude. I don't think you intended to assume identical amplitudes, just shapes and frequencies. So if the multiplier idea can deal with different amplitudes, it might be useful.

I'll report back tomorrow...

Best regards,

Bob Masta DAQARTA v5.10 Data AcQuisition And Real-Time Analysis

Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, FREE Signal Generator Pitch Track, Pitch-to-MIDI DaqMusic - FREE MUSIC, Forever! (Some assembly required) Science (and fun!) with your sound card!

That's what the PLL is there for... it "filters" the signal you provide to extract the reference. The question is whether there are conditions where a pre-filter on the PLL would improve overall lock time, as opposed to changes in the PLL itself.

Dunno about that, but note that since this implies that you know the desired frequency pretty well, you might instead choose to apply that knowledge to the PLL oscillator control. such that in the absence of a signal it runs at the desired center frequency, and has an overall frequency range that matches the known signal range. That might speed up lock time.

Just a thought.

Best regards,

Bob Masta DAQARTA v5.10 Data AcQuisition And Real-Time Analysis

Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, FREE Signal Generator Pitch Track, Pitch-to-MIDI DaqMusic - FREE MUSIC, Forever! (Some assembly required) Science (and fun!) with your sound card!

That isn't necessarily the cleanest extraction.

Is there a boot strap or iterative approach?

+/- 10% or less.

Thanks again.

Bret Cahill

Report on multiplication as possible noise reduction strategy:

Test signal was a 468.75 Hz sine. (This frequency was set using Daqarta's Line Step option so it is an exact submultiple of the 48000 Hz sample rate and thus produces a perfect single vertical line spectrum, with no "skirts" that would require windowing to reduce.)

The sine was at 50% of full-scale (on Daqarta Stream 0), mixed with 50% white noise (on Daqarta Stream 1). This produces a spectrum with the sine spike at -6 dB (relative to full scale) and the noise floor at each frequency at about -36 dB. Across the whole 24 kHz spectrum, the integrated noise (using Daqarta's Sigma cursor option) is -9 dB. So the signal is 3 dB above the noise.

(Measurements were made in Daqarta's Spectrum mode using

32-frame Exponential averaging. This better shows the average noise level, at the cost of making the spectrum respond a bit more slowly to transients... which weren't present here.)

If two *waveform* frames (1024 samples each) of this signal are synchronously averaged (equivalent to 2 copies of the signal with independent noise sources, since the noise is different for each frame), the tone spike is of course still at -6 dB, but the noise across the band is at -12 dB, a 3 dB improvement, just as predicted by theory.

Note: The above measurement was made by setting the waveform averager (Spectrum off) to 2 frames Exponential and starting the average, then toggling to Spectrum. This shows the spectrum of the waveform average, rather than the spectrum average of the waveform.

Finally, Daqarta Streams 2 and 3 were created identical to Streams 0 and 1, respectively, except that the Stream 3 noise source was independent from that of Stream 1. To multiply 0+1 times 2+3, Streams 2 and 3 each used AM modulation set to 200% (Daqarta's way of specifying pure multiplication), and each used as its modulation source the sum of Streams 0+1. (When a stream is used as a modulator, it is no longer summed directly to the output.) The overall output was thus:

Sine 2 * (Sine 0 + Noise 1) + Noise 3 * (Sine 0 + Noise 1)

which is identical to:

(Sine 0 + Noise 1) * (Sine 2 + Noise 3)

The result was a spectrum with a noise floor at about -40 dB, with spectral lines at 0 and 2f at -18 dB. The noise across the band was -13.5 dB... 4.5 dB *above* the 2f signal spike.

So the upshot is that multiplication makes things worse, not better. If you don't have equal-amplitude sines to use for waveform averaging, then one very effective way to distinguish signal from noise is to take an FFT. With a 1024-sample FFT, the signal spike was 30 dB above the noise floor, even though it was only 3 dB above the overall integrated noise. FFTs with more samples reduce the noise floor even further (since the overall noise will be the same, but made up of more small contributions from each frequency).

Best regards,

Bob Masta DAQARTA v5.10 Data AcQuisition And Real-Time Analysis

Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, FREE Signal Generator Pitch Track, Pitch-to-MIDI DaqMusic - FREE MUSIC, Forever! (Some assembly required) Science (and fun!) with your sound card!

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The higher the frequency of the noise in each signal the more independent it is of the noise in the other signal. The lower the frequency of the noise the more the same noise appears in both signals.

It's probably an inverse relationship between sq rt of frequency and noise correlation, certainly something well known as well behaved.

For very low frequency noise the magnitudes as well a phase and frequency are pretty much the same so a clean reference, at least clean of low frequency noise, can be generated simply by subtracting one signal from the other and the PSD multiplication would be:

s1(s1 - s2) and

s2(s1 - s2)

The really high frequency noise, of course, can be filtered with a conventional filter and the really low frequency noise disappears in the subtraction.

The problem is near the signal frequency.

If the ratio of the magnitude of the noise in one signal that correlates to the other signal's noise was known, then that could appear as a correction factor in the subtractions above.

It may require breaking the problem into a lot of bandwidths each with its own ratio.

Another solution would be to try to use a frequency higher than most of the noise.

This would decrease the SNR so it may not change much.

The clean signal amplitudes are different.

Determining the frequency would be just as good, however, and may be the way to go.

Thanks again.

Bret Cahill

This sounds like a very unusual situation, not the behavior of ordinary noise sources. I assume you have some particular case in mind... perhaps if you gave more details the group could give better advice.

Best regards,

Bob Masta DAQARTA v5.10 Data AcQuisition And Real-Time Analysis

Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, FREE Signal Generator Pitch Track, Pitch-to-MIDI DaqMusic - FREE MUSIC, Forever! (Some assembly required) Science (and fun!) with your sound card!

The information is in there just like other situations where PSD works. The question is if it can be teased out somehow.

Bret Cahill