Can A Band Pass Filter Speed Up Lock In Amplification?

[Bret Cahill]

Is prefiltering or filtering before the phase sensitive detection step
of lock in a common practice?

If the signal frequency is in a fairly narrow band, say one octave,
can a band pass filter speed up the aquistion time of a lock in?


Bret Cahill

 

[Bob Masta]

On Thu, 1 Jul 2010 17:45:07 -0700 (PDT), Bret
Cahill <BretCahill@peoplepc.com> wrote:

Is prefiltering or filtering before the phase sensitive detection step
of lock in a common practice?

If the signal frequency is in a fairly narrow band, say one octave,
can a band pass filter speed up the aquistion time of a lock in?

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
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[George Herold]

On Jul 1, 8:45 pm, Bret Cahill <BretCah...@peoplepc.com> wrote:

Is prefiltering or filtering before the phase sensitive detection step
of lock in a common practice?

If the signal frequency is in a fairly narrow band, say one octave,
can a band pass filter speed up the aquistion time of a lock in?

Bret Cahill

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

The old EG&G 124A

http://www.kandelelectronics.com/products/6980/

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.

 

[Bret Cahill]

Is prefiltering or filtering before the phase sensitive detection step
of lock in a common practice?

If the signal frequency is in a fairly narrow band, say one octave,
can a band pass filter speed up the aquistion time of a lock in?

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.  

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

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...

That still takes time.

the narrower the ultimate bandwidth,
the longer the lag.  

Which could be years . .

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.

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.

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.

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

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.  

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

Best regards,

Bob Masta

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[Bret Cahill]

Is prefiltering or filtering before the phase sensitive detection step
of lock in a common practice?

If the signal frequency is in a fairly narrow band, say one octave,
can a band pass filter speed up the aquistion time of a lock in?

Bret Cahill

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

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.

The old EG&G 124A

http://www.kandelelectronics.com/products/6980/

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.

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

 

[Bob Masta]

On Fri, 2 Jul 2010 17:25:23 -0700 (PDT), Bret
Cahill <Bret_E_Cahill@yahoo.com> wrote:

<snip>

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.

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
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[Bret Cahill]

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.

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?

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

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

How are
you any farther ahead than if you had just tuned
your circuit to the original frequency?

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

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[Bret Cahill]

Is prefiltering or filtering before the phase sensitive detection step
of lock in a common practice?

If the signal frequency is in a fairly narrow band, say one octave,
can a band pass filter speed up the aquistion time of a lock in?

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


Bret Cahill

 

[Bob Masta]

On Sat, 3 Jul 2010 09:28:23 -0700 (PDT), Bret
Cahill <Bret_E_Cahill@yahoo.com> wrote:

Supposing you cannot get a good clean reference, just another noisy
signal where the second signal is in phase with the first? =A0The
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. =A0If 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.

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?

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

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
www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
Frequency Counter, FREE Signal Generator
Pitch Track, Pitch-to-MIDI
DaqMusic - FREE MUSIC, Forever!
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[Bob Masta]

On Sat, 3 Jul 2010 12:04:12 -0700 (PDT), Bret
Cahill <Bret_E_Cahill@yahoo.com> wrote:

Is prefiltering or filtering before the phase sensitive detection step
of lock in a common practice?

If the signal frequency is in a fairly narrow band, say one octave,
can a band pass filter speed up the aquistion time of a lock in?

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

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
www.daqarta.com
Scope, Spectrum, Spectrogram, Sound Level Meter
Frequency Counter, FREE Signal Generator
Pitch Track, Pitch-to-MIDI
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[Bob Masta]

On Sun, 04 Jul 2010 12:59:50 GMT, N0Spam@daqarta.com (Bob
Masta) wrote:

On Sat, 3 Jul 2010 09:28:23 -0700 (PDT), Bret
Cahill <Bret_E_Cahill@yahoo.com> wrote:

Supposing you cannot get a good clean reference, just another noisy
signal where the second signal is in phase with the first? =A0The
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. =A0If 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.

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?

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

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...

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
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[Bret Cahill]

Is prefiltering or filtering before the phase sensitive detection step
of lock in a common practice?

If the signal frequency is in a fairly narrow band, say one octave,
can a band pass filter speed up the aquistion time of a lock in?

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

That's what the PLL is there for...  it "filters"
the signal you provide to extract the reference.

That isn't necessarily the cleanest extraction.

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.  

Is there a boot strap or iterative approach?

Dunno about that, but note that since this implies
that you know the desired frequency pretty well,

+/- 10% or less.

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.

Thanks again.


Bret Cahill

Best regards,

Bob Masta

              DAQARTA  v5.10
   Data AcQuisition And Real-Time Analysis
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[Bret Cahill]

Supposing you cannot get a good clean reference, just another noisy
signal where the second signal is in phase with the first? =A0The
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. =A0If 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.

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?

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

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.

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.

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.  

The clean signal amplitudes are different.

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

So if the multiplier idea
can deal with different amplitudes, it might be
useful.  

I'll report back tomorrow...

Thanks again.


Bret Cahill

Best regards,

Bob Masta

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- Show quoted text -

 

[Bob Masta]

On Sun, 4 Jul 2010 10:27:18 -0700 (PDT), Bret Cahill
<BretCahill@peoplepc.com> wrote:

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.

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
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[Bret Cahill]

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.

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.

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


Bret Cahill

Best regards,

Bob Masta

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