Is the output of a Lock In amplifier a signal with single frequency?

[ali8]

The Lock In amplifier uses Phase Sensitive Detection to "lock" to the signal using reference frequency. It is basically auto-correlation. The output of the Lock In amplifier is typically an X signal, the in-phase, and a Y signal, the out-of-phase.

My question: If the Lock In 'locks' to the reference frequency, say 200 Hz, then does this mean the output signal has only this frequency? Experimentally, I find that this is not true, as the output has lots of frequencies, only limited by measurement time and the low pass filter settings of the Lock In.

 

[jiripolivka]

The Lock In amplifier uses Phase Sensitive Detection to "lock" to the signal using reference frequency. It is basically auto-correlation. The output of the Lock In amplifier is typically an X signal, the in-phase, and a Y signal, the out-of-phase.

My question: If the Lock In 'locks' to the reference frequency, say 200 Hz, then does this mean the output signal has only this frequency? Experimentally, I find that this is not true, as the output has lots of frequencies, only limited by measurement time and the low pass filter settings of the Lock In.

The lock-in amplifier is also named synchronous detector. In fact it can have two outputs: as the lock-in amplifier, the output exactly follows the input signal frequency (and can generate also harmonics).
As a synchronous detector, it operates as a multiplier-correlator, so the output is a DC or low-frequency signal with an amplitude proportional to the input signal amplitude. This synchronous detector operation allows to narrow the noise bandwidth, so it can "detect" input signal with a level deep in noise. Often signals with a level 60 dB under noise power can be detected.

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And yes, I forgot the phase function, that between the input and reference signal. I used sync detectors in my radio-telescope radiometers, where the phase is maintained at one value peaking the output.

 

[ali8]

Let me ask the question in another way. Assume I am using the Lock In with a reference frequency f0=200 Hz. Also assume the Lock In low pass filter is adjust so as its cut off freq. fc >> f0 Hz. I bias a resistor and measure the output. Experimentally, we will see the 1/f noise in the output, which ranges from 1/t, where t is the total measurement time, to fc.

What I don't get is how you get this signal that spans all that frequency range while you're supposed to have a signal of a nearly single freq. f0.

 

[FvM]

Like jiripolivka I would describe a lock-in amplifier as synchronous demodulator. Input of frequency fc is mapped to DC, signal components around fc to low frequencies. You'll see output up to fc if you don't apply a filter. But in a usual lock-in application, only the spectral components near DC will be processed.