Precision about Lock-In Amplifier

[Archer]

I was doing some works on Lock-In Amplifier of weak signal detection at
video frequency.
It is reported that some Lock-In Amplifier could do with deta frequency
about 0.0004Hz,
I think it is incredible. Could the oscillator and low pass filter can work
in such low tolerance?
How could they get it?
With Wein Bridge Oscillator and Chebyshev filter?
Help would be appreciated!

 

[Phil Hobbs]

I was doing some works on Lock-In Amplifier of weak signal detection at
video frequency.
It is reported that some Lock-In Amplifier could do with deta frequency
about 0.0004Hz,
I think it is incredible. Could the oscillator and low pass filter can work
in such low tolerance?
How could they get it?
With Wein Bridge Oscillator and Chebyshev filter?
Help would be appreciated!

A lock-in is basically an AM radio with its IF at DC. There are lots of
ways of doing it (digital and analogue), but the basic idea is to mix
the incoming AC signal with an unmodulated replica of itself, and
low-pass filter the daylights out of it. In the old days, you just used
a great big RC time constant (40 seconds for the example you give) but
nowadays it's much better to use digital filtering--you can buy a whole
DSP for the price of a Teflon capacitor, and it'll work dramatically
better. Two channel lock-ins allow measuring phase and amplitude
simultaneously.

The local oscillator signal (the replica, above) can be generated in
several ways--the most common being a phase-locked loop, whose reference
is whatever oscillator is generating the carrier.

Cheers,

Phil Hobbs

 

[Tom Bruhns]

I was doing some works on Lock-In Amplifier of weak signal detection at
video frequency.
It is reported that some Lock-In Amplifier could do with deta frequency
about 0.0004Hz,
I think it is incredible. Could the oscillator and low pass filter can work
in such low tolerance?
How could they get it?
With Wein Bridge Oscillator and Chebyshev filter?
Help would be appreciated!

Oscillators with good frequency accuracy are generally locked to a
crystal-controlled reference. With an oven-stabilized crystal
oscillator, it's possible to get stability in the part per 10^9 region
for many hours, but that's a moderately expensive oscillator. I
suppose it would take a part in 10^10 for 0.4 millihertz out of 4
Megahertz, and that could be difficult for all but the very best
crystal oscillators. Of course, atomic standards have no difficulty
reaching that level. (A GPS-stabilized oven oscillator is a way to do
this on-the-cheap at home...) But also, the lock-in amplifier can
track a user-supplied reference signal: I believe they are by far
most useful when you have such a reference. Then it's just a matter
of low-pass filtering after the desired frequency has been mixed down
to DC. Filtering to such a narrow bandwidth may be only a problem in
digital signal processing, if you wish to avoid analog filters. --
It's quite possible to do this sort of thing with an FFT-based
spectrum analyzer, too. (And expect long settling times with narrow
bandwidths!)

It's probably not easy to find many 4MHz signals that have low enough
phase noise to make looking down to 0.4mHz resolution very valuable,
though.


Cheers,
Tom

 

[Tom Bruhns]

Archer wrote: ....

and Phil Hobbs <[email protected]> replied:

....

In the old days, you just used
a great big RC time constant (40 seconds for the example you give)

Oooh, oooh, a whole lot longer than that, I think! 1/(pi*delta_f)?
About 800 seconds. (Not 2*pi cuz it's from -f to +f.) Just as you
say, MUCH nicer to do digitally; far more accurate and the filter
shape can be just about whatever you want.

Cheers,
Tom

 

[Tom Bruhns]

Archer wrote:
....
And Phil Hobbs replied:

In the old days, you just used
a great big RC time constant (40 seconds for the example you give) but
nowadays it's much better to use digital filtering ...

Um, would you believe RC = 800 seconds? I suspect a factor of 2 and a
decimal place got lost there. (RC = 1/(pi*bw) for the downconverted
BW since we're looking + and - in frequency. I'm assuming the 0.4mHz
is the bandwidth.) Certainly is a lot easier digitally, and offers
the flexibility of whatever filter shape you want, within reason. At
such frequencies, you could do it with a PIC -- darned near with an
Marchant mechanical calculator!

Cheers,
Tom

 

[Archer Xiao]

It seems that i didn't explained it clearly.The center frequency
of the object signal should be 10kHz. so that the quartz crystal seems
not very good for that.
On 12 May 2004 14:35:34 -0700

 

[Archer Xiao]

A lock-in is basically an AM radio with its IF at DC. There are lots of
ways of doing it (digital and analogue), but the basic idea is to mix
the incoming AC signal with an unmodulated replica of itself, and
low-pass filter the daylights out of it. In the old days, you just used

unmodulated replica of the AC signal? en, I am working on weak signal is it good for doing so?How to explain it theoretically?

a great big RC time constant (40 seconds for the example you give) but
nowadays it's much better to use digital filtering--you can buy a whole
DSP for the price of a Teflon capacitor, and it'll work dramatically
better. Two channel lock-ins allow measuring phase and amplitude
simultaneously.

It's a good idea! there is other work needs digital process also.
Thanks!

The local oscillator signal (the replica, above) can be generated in
several ways--the most common being a phase-locked loop, whose reference
is whatever oscillator is generating the carrier.

en, adding a PLL can take some effect on the frequency stability of the oscillator?I am confused.

 

[Winfield Hill]

Archer Xiao wrote...

It seems that i didn't explained it clearly. The center frequency
of the object signal should be 10kHz. so that the quartz crystal
seems not very good for that.

Lock-in amplifiers either generate their own frequency, or use one
that's supplied externally. In either case the frequency need not
be especially stable, because elsewhere in the measuring system the
same frequency is used to modulate the phenomenon that's generating
the signal one is measuring with the lock-in amplifier. Therefore
any drift in frequency is not apparent to the lockin, which acts as
a mixer with its output at DC. The very narrow "bandwidth" comes
from using a long-time-constant low-pass filter after the lock-in,
purely for purposes of noise-reduction - the remaining noise level
is related to the square-root of the bandwidth. [While the signal
could be measured and filtered at DC in the first place, often the
noise density (noise per root Hz) is higher at low frequencies, or
at DC (see 1/f noise, http://www.nslij-genetics.org/wli/1fnoise/ ),
so moving the signal to 10kHz, etc., by modulating it, can result
in a greatly improved signal-to-noise ratio.] Anyway, getting back
to the thread's subject, it's not necessary to have a 0.4mHz stable
frequency to use a 400-second time-constant on a lock-in amplifier.
One may simply use any old multivibrator relaxation oscillator, etc.

555, anyone?

Thanks,
- Win

(email: use hill_at_rowland-dot-org for now)

 

[Kevin Carney]

I can't add anything to the design aspect but I've seen very intelligent
people do amazing things with lock-in amps here at IBM. They are used in
finding defects in semiconductor products.

--
change .combo to .com for correct email

***************************************************
"We ought always to know precisely why a given job
is done in a particular way, and why it is done at
all, and why it can't be done more efficiently,
if it must be done at all."-- T.J.Watson

***************************************************

Archer Xiao wrote...

It seems that i didn't explained it clearly. The center frequency
of the object signal should be 10kHz. so that the quartz crystal
seems not very good for that.

Lock-in amplifiers either generate their own frequency, or use one
that's supplied externally. In either case the frequency need not
be especially stable, because elsewhere in the measuring system the
same frequency is used to modulate the phenomenon that's generating
the signal one is measuring with the lock-in amplifier. Therefore
any drift in frequency is not apparent to the lockin, which acts as
a mixer with its output at DC. The very narrow "bandwidth" comes
from using a long-time-constant low-pass filter after the lock-in,
purely for purposes of noise-reduction - the remaining noise level
is related to the square-root of the bandwidth. [While the signal
could be measured and filtered at DC in the first place, often the
noise density (noise per root Hz) is higher at low frequencies, or
at DC (see 1/f noise, http://www.nslij-genetics.org/wli/1fnoise/ ),
so moving the signal to 10kHz, etc., by modulating it, can result
in a greatly improved signal-to-noise ratio.] Anyway, getting back
to the thread's subject, it's not necessary to have a 0.4mHz stable
frequency to use a 400-second time-constant on a lock-in amplifier.
One may simply use any old multivibrator relaxation oscillator, etc.

555, anyone?

Thanks,
- Win

(email: use hill_at_rowland-dot-org for now)

 

[Phil Hobbs]

Archer wrote:
...



And Phil Hobbs replied:



Um, would you believe RC = 800 seconds? I suspect a factor of 2 and a
decimal place got lost there. (RC = 1/(pi*bw) for the downconverted
BW since we're looking + and - in frequency. I'm assuming the 0.4mHz
is the bandwidth.) Certainly is a lot easier digitally, and offers
the flexibility of whatever filter shape you want, within reason. At
such frequencies, you could do it with a PIC -- darned near with an
Marchant mechanical calculator!

Cheers,
Tom

Whoops, mea culpa on the factor of 10. We can argue about the factor of
2. If it's temporal response we're talking about, the response time is
set by the equivalent lowpass filter--a bandpass settles twice as slowly
as a lowpass of equal bandwidth. If we were discussing noise bandwidth,
the factor of 2 still isn't there, because a lock-in produces only the
in-phase component of the noise--half the total noise power in the
input, and this cancels out the doubling of the bandwidth.

Assuming we're wanting to do a SNR calculation, and not just ooh and aah
about how long it'll take to get 1024 data points, we'd need to specify
the noise bandwidth, which is a factor of pi/2 wider than the 3 dB
bandwidth for a one-pole RC lowpass. Thus that 0.0004 Hz noise
bandwidth actually comes out to

TC = (2/pi)*1/(2*pi*0.0004) = 1/(pi**2*0.0004) = 253 s.

You can probably buy a DSP *and* some nice memory for the price of that
capacitor.

Cheers,

Phil Hobbs

 

[Tom Bruhns]

It seems that i didn't explained it clearly.The center frequency
of the object signal should be 10kHz. so that the quartz crystal seems
not very good for that.

No, they are just fine for that. They are used as a reference for a
frequency synthesizer. Surely a crystal by itself is not much
interest because that locks you to a single frequency. It is just a
reference, just one part, but a critical part because then everything
else will have the same long-term stability as the crystal oscillator.

But as Win suggests, it would be rare to use a lock-in amplifier that
wasn't phase locked to the signal of interest anyway. You generally
will have SOME way to do that, or you probably should be using a
different instrument than a lock-in amplifier. If you don't have that
reference, and you know that the thing which generated the signal of
interest is very stable, you can still detect the signal very well if
your local reference is also very stable. But then it's an advantage
to use FFT or similar digital signal processing techniques to be able
to look at a range of frequencies all at once, because you won't know
the _exact_ frequency of your signal of interest. If you had to sweep
over a range of frequencies, it might take a very long time to find
the signal.

The 10kHz center frequency makes the required stability to reach
0.4mHz resolution much less of a problem. And if you are locked to
the same reference which generated the 10kHz center frequency, then
again it is just a matter of filtering the mixed-down-to-DC signal.
Surely there is no problem building a low-pass filter with 0.2mHz
bandwidth... (You can do the filtering, and even the mixing,
digitally.)

Cheers,
Tom

 

[Tom Bruhns]

unmodulated replica of the AC signal? en, I am working on weak signal is it good for doing so?How to explain it theoretically?

If you are looking for a weak signal and you only know approximately
what its frequency is (that is, you have no way of locking exactly to
it), but you know it is stable in frequency at least, I would
recommend filtering as needed to get rid of strong signals that are
very near the frequency of interest, then amplifying and digitizing
with a very linear digitizer. Then do digital mixing and an FFT on
the digitized signal. That is what a "dynamic signal analyzer" or
"FFT analyzer" or Agilent's 89410 "vector signal analyzer" can do very
well. They can display a range of frequencies with good resolution
and a low noise floor if properly used. I know that with the 89410,
it is possible to detect signals lower than 120dB below full scale, if
the spectral environment you are measuring is "clean" enough. This
will be much faster than trying to sweep something like a lock-in
amplifier across the same band.

On the other hand, if you are fortunate enough to have a reference
which is locked to the signal of interest, then you can use a lock-in
amplifier. You could also do it with an FFT analyzer locked to the
reference, but the lock-in amplifier will almost certainly be much
less expensive.

Either instrument is effectively a very narrow filter (in the case of
the lock-in) or a whole bank of very narrow filters on closely-spaced
frequencies (in the case of the FFT analyzer) which you lock to the
frequency of interest, or which you set to cover the range of
frequencies you are interested in. Those filters are effectively
followed by phase-sensitive detectors.

Cheers,
Tom

 

[Archer]

Archer Xiao wrote...

It seems that i didn't explained it clearly. The center frequency
of the object signal should be 10kHz. so that the quartz crystal
seems not very good for that.

Lock-in amplifiers either generate their own frequency, or use one
that's supplied externally. In either case the frequency need not
be especially stable, because elsewhere in the measuring system the
same frequency is used to modulate the phenomenon that's generating
the signal one is measuring with the lock-in amplifier. Therefore
any drift in frequency is not apparent to the lockin, which acts as
a mixer with its output at DC. The very narrow "bandwidth" comes
from using a long-time-constant low-pass filter after the lock-in,
purely for purposes of noise-reduction - the remaining noise level
is related to the square-root of the bandwidth. [While the signal
could be measured and filtered at DC in the first place, often the
noise density (noise per root Hz) is higher at low frequencies, or
at DC (see 1/f noise, http://www.nslij-genetics.org/wli/1fnoise/ ),
so moving the signal to 10kHz, etc., by modulating it, can result
in a greatly improved signal-to-noise ratio.] Anyway, getting back
to the thread's subject, it's not necessary to have a 0.4mHz stable
frequency to use a 400-second time-constant on a lock-in amplifier.
One may simply use any old multivibrator relaxation oscillator, etc.

555, anyone?

Thanks,
- Win

(email: use hill_at_rowland-dot-org for now)

I think generate own frequency is more important. Because if i use
externally supplied reference it would be a big problem that design a
filter which is ahead of the amplify in front of PSD. or is there any
good PSD that would deal the signal with 1.2mVpp(interested signal)
and 3Vpp(noise)? I think the interest signal is too low without filter
and amp.

 

[Archer]

Archer Xiao wrote...

It seems that i didn't explained it clearly. The center frequency
of the object signal should be 10kHz. so that the quartz crystal
seems not very good for that.

Lock-in amplifiers either generate their own frequency, or use one
that's supplied externally. In either case the frequency need not
be especially stable, because elsewhere in the measuring system the
same frequency is used to modulate the phenomenon that's generating
the signal one is measuring with the lock-in amplifier. Therefore
any drift in frequency is not apparent to the lockin, which acts as
a mixer with its output at DC. The very narrow "bandwidth" comes
from using a long-time-constant low-pass filter after the lock-in,
purely for purposes of noise-reduction - the remaining noise level
is related to the square-root of the bandwidth. [While the signal
could be measured and filtered at DC in the first place, often the
noise density (noise per root Hz) is higher at low frequencies, or
at DC (see 1/f noise, http://www.nslij-genetics.org/wli/1fnoise/ ),
so moving the signal to 10kHz, etc., by modulating it, can result
in a greatly improved signal-to-noise ratio.] Anyway, getting back
to the thread's subject, it's not necessary to have a 0.4mHz stable
frequency to use a 400-second time-constant on a lock-in amplifier.
One may simply use any old multivibrator relaxation oscillator, etc.

555, anyone?

Thanks,
- Win

(email: use hill_at_rowland-dot-org for now)

There would be another problem that the long-time-constant low-pass
filter can't be done the time constant was calculated above is 253s
and the C is several uF and the R should be very large!

 

[Rene Tschaggelar]

Archer Xiao wrote...

[snip]

I think generate own frequency is more important. Because if i use
externally supplied reference it would be a big problem that design a
filter which is ahead of the amplify in front of PSD. or is there any
good PSD that would deal the signal with 1.2mVpp(interested signal)
and 3Vpp(noise)? I think the interest signal is too low without filter
and amp.

A lock-in with your own frequency is the way to go. As switch,
I can recommend the AD630 form Analog Devices. It is made for this
purpose. We were able to recover a signal of -90dBm with it :
http://www.ibrtses.com/projects/qband_afc.html

Rene

 

[Tom Bruhns]

I think generate own frequency is more important. Because if i use
externally supplied reference it would be a big problem that design a
filter which is ahead of the amplify in front of PSD. or is there any
good PSD that would deal the signal with 1.2mVpp(interested signal)
and 3Vpp(noise)? I think the interest signal is too low without filter
and amp.

That's not really much of a problem; the signal is not quite 70dB
below the p-p noise. It is not terribly difficult to make a mixer
stage that will have over 100dB spurious-free dynamic range. But
doing that sort of job well is one of the things that you pay for in
the instrument, versus just doing it yourself with a handful of
integrated circuits. In addition, if the noise is not synchronous
with the signal, even if there are distortion products, you can
average them out with long enough integration times, if your
integration is synchronized to your signal.

You also suggested that it's difficult to make a narrow enough
bandwidth filter. I believe the time constant is much longer than you
posted: you need 0.2mHz cutoff frequency for 0.4mHz bandwidth, and
that's about 800 seconds time constant. So that would be a 10uF
capacitor and 80megohm resistor, or 100uF and 8Mohm. Those values are
NOT impossible, by any means. For example, I have several 10uF 1%
tolerance film capacitors in my "junk box." And if you can find a
high enough resistance value, you can do it with a much smaller
capacitor: modern polypropylene capacitors typically have a
self-discharge time constant of about 50 YEARS at room temperature,
and you can get operational amplifiers with input bias currents below
10fA. However, it would be silly to do it that way, instead of just
digitizing and implementing the filtering digitally.

Cheers,
Tom