# [time-nuts] Phase noise with a lock-in amplifier.

David Kirkby david.kirkby at onetel.net
Sat Apr 16 10:02:14 EDT 2005

```Someone sent me this by private email, so I will not post his address,
but I hope he doe not mind me putting the information public:

> But isn't the whole idea of a lock in amplifier to "Lock" a very
noisy > signal to the strong version that you feed into the reference port?
> So using the method you describe I think the lock in amp will
> not "lock" and you'll get no output.

1) A "lock-in" amplifier does not actually *lock* a signal (such as an
ovened oscillator) to anything else (such as Cesium or GPS system). So
the name *lock-in* is perhaps not an ideal term, although they are
always called that.

The *normal* method of using one is that the signal and the reference
are at *exactly* the same frequency, since they are derived from the
same source. You can typically measure a very weak optical signal on a
photodiode by chopping the light source at the same frequency you feed
into the reference. Then signals as low as 100dB *below* the noise can
be measured.

2) A lock-in amplifier is basically a high Q tuned circuit, measuring
signals *close* to the reference frequency. It does *not* only measure
signals at exactly the reference frequency, but signals in the range
fref-bw/2 to fref+bw/2, where fref is the reference frequency and bw is
the filter bandwidth.

So if you feed in the signal in the way I described (mixer, delay line)
it would *not* measure signals at just fref. If such a lock-in could be
built, it would have an infinite Q and take an infinite time for the
measurement to settle.

In the case of the Stanford Research SR830 (which I have at work), fref
can be set in the range 0.001Hz to 102KHz and the filter time constants
from 10us to 30ks

http://www.thinksrs.com/products/SR810830.htm

The filters can be set at 6. 12, 18 or 24dB/octave, with effective noise
bandwidths of 1/4T to 5/(64T), giving effective noise bandwidths of
25kHz to 2.6uHz. (The manual actually states the effective noise
bandwidths, not the 3dB bandwidths).

So the lock-in could be set at any offset (up to 102kHz) and any filter
bandwidth from 2.6uHz to 25KHz.

I just looked in the manual on page 3-15

http://www.thinksrs.com/mult/SR810830m.htm

and see there is a discussion of noise measurements. I have not looked
at it carefully.

In fact, the front panel switches on channel 1 can show X (component of
signal in phase with reference), R (magnitude = sqrt(x^2+y^2) ), and
Xnoise.

On channel 2, there is Y (component of signal at 90 deg to reference),
theta (phase angle between signal and reference) and Ynoise.

There seems to be no Rnoise (magnitude of the noise) I must admit, which
is what would seem the most sensible unit for noise measurements. So I
have some doubts why did Stanford not provide Rnoise? You might be able
to compute it from Rnoise=sqrt(Xnoise^2+Ynoise^2), but I must admit it
seems odd it was not included. Perhaps I am wrong after all.

Better than mixing to DC (as I proposed) would be to mix to some
convenient frequency (say 1kHz). But of course the phase noise of
whatever you use to do the mixing would come into the equation then. But
then you could look at the noise either side of the signal, not just on
one side.

Should you have an oscillator in the range 0.001 Hz to 102kHz, there
would be no need for the mixer arrangement. But this would not work for
crystal oscillators, which are typically > 102kHz.

Few lockins work above 100kHz. EG&G make one to 3MHz, and Standford do
one to 200MHz, but the latter mixes down anyway.

If my method did work, what is measured would be some sort of
convolution (I use that term very loosly) between the signal you want to
measure and the noise of lock-in. But then that is I expect always the
case.

Perhaps I have it all wrong. As I say, I have never done this, but it
seems logical to me.

David Kirkby.

David Kirkby wrote:
> Does anyone know if you can use a lock-in amplifier, say something like
> the Standford SR830 dual phase unit
>
> http://www.thinksrs.com/products/SR810830.htm
>
> to measure phase noise from an oscillator?
>
> I was thinking of something like this:
>
> 1) Take an oscillator (say 10MHz)
> 2) Split the output into 2 with a power splitter.
> 3) Feed one output from the power splitter into the RF port of a mixer.
> 4) Feed the other output from the power splitter into the LO port of a
> mixer, via a cable that is a odd integer multiple of a quarter wave
>
> The outputs from the mixer, assuming the oscillator was perfect would be
>  the sum (2f) and difference (DC). But since the oscillator has noise on
> it the noise will not mix to DC since the noise will arrive a
>
> Hence the output from the mixer is the noise on the oscillator mixed
> down to DC.
>
> Use a lockin amp, set its internal reference to some figure (say 1KHz)
> and measure the magnitude on a lock-in amplifier. That gives you an rms
> noise voltage in whatever bandwidth you want - you set the bandwidth
> with the lock-in filters, which on that model can be varied from 10us to
> 30ks (i.e.  10us to 8.3 hours).
>
> That's not the usual way of using a lock-in, but it is basically a very
> high Q filter, with a centre frequency set to whatever you use as its
> internal reference. On that particular unit, the reference can be from
> 0.001Hz to 102KHz.
>
> I've built a simple lock-in using noting more than a 741 op-amp, a
> couple of FETs and a few resistors. The reference input open/closed the
> FET switches so the op-amp worked with either a gain of +1 or -1. It
> worked quite well. Not as good as the SRS830, but then it cost next to
> nothing to build.
>
> The main reason I ask about the use of a lock-in amp is that we have
> almost as many lock-in amps at work as DVM's.
>

--
Dr. David Kirkby,
G8WRB