SRS Labs manual SR850 Basics, Narrow band detection, Where does Lock-in reference come from?

SR850 Basics

This is a very nice signal - it is a DC signal propor- tional to the signal amplitude.

Narrow band detection

Now suppose the input is made up of signal plus noise. The PSD and low pass filter only detect sig- nals whose frequencies are very close to the lock- in reference frequency. Noise signals at frequen- cies far from the reference are attenuated at the

PSD output by the low pass filter (neither ωnoise- ωref nor ωnoise+ωref are close to DC). Noise at fre- quencies very close to the reference frequency will

result in very low frequency AC outputs from the

PSD (ωnoise-ωref is small). Their attenuation depends upon the low pass filter bandwidth and

roll-off. A narrower bandwidth will remove noise sources very close to the reference frequency, a wider bandwidth allows these signals to pass. The low pass filter bandwidth determines the band- width of detection. Only the signal at the reference frequency will result in a true DC output and be unaffected by the low pass filter. This is the signal we want to measure.

Where does the

lock-in reference come from?

We need to make the lock-in reference the same as the signal frequency, i.e. ωr = ωL. Not only do the frequencies have to be the same, the phase between the signals can not change with time, oth-

erwise cos(θsig - θref) will change and Vpsd will not be a DC signal. In other words, the lock-in refer-

ence needs to be phase-locked to the signal reference.

Lock-in amplifiers use a phase-locked-loop (PLL) to generate the reference signal. An external refer- ence signal (in this case, the reference square wave) is provided to the lock-in. The PLL in the lock-in locks the internal reference oscillator to this external reference, resulting in a reference sine wave at ωr with a fixed phase shift of θref. Since the PLL actively tracks the external reference, changes in the external reference frequency do not affect the measurement.

All lock-in measurements require a reference signal.

In this case, the reference is provided by the exci- tation source (the function generator). This is called an external reference source. In many situa- tions, the SR850's internal oscillator may be used instead. The internal oscillator is just like a func- tion generator (with variable sine output and a TTL

sync) which is always phase-locked to the refer- ence oscillator.

Magnitude and phase

Remember that the PSD output is proportional

to Vsigcosθ where θ = (θsig - θref). θ is the phase difference between the signal and the lock-in refer-

ence oscillator. By adjusting θref we can make θ equal to zero, in which case we can measure Vsig (cosθ=1). Conversely, if θ is 90°, there will be no output at all. A lock-in with a single PSD is called a single-phase lock-in and its output is Vsigcosθ.

This phase dependency can be eliminated by adding a second PSD. If the second PSD multi- plies the signal with the reference oscillator shifted

by 90°, i.e. VLsin(ωLt + θref + 90°), its low pass fil- tered output will be

Vpsd2 = 1/2 VsigVLsin(θsig - θref)

Vpsd2 ~ Vsigsinθ

Now we have two outputs, one proportional to cosθ and the other proportional to sinθ. If we call the first output X and the second Y,

X = Vsigcosθ Y = Vsigsinθ

these two quantities represent the signal as a vector relative to the lock-in reference oscillator. X is called the 'in-phase' component and Y the 'quadrature' component. This is because when θ=0, X measures the signal while Y is zero.

By computing the magnitude (R) of the signal vector, the phase dependency is removed.

R = (X2 + Y2)1/2 = Vsig

R measures the signal amplitude and does not depend upon the phase between the signal and lock-in reference.

A dual-phase lock-in, such as the SR850, has two PSD's, with reference oscillators 90° apart, and can measure X, Y and R directly. In addition, the phase θ between the signal and lock-in reference, can be measured according to

θ= tan-1(Y/X)

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