# high frequency vs low frequency lock-in regarding signal to noise ratio

I understand that the lock-in technique came about in an effort to improve signal to noise ratio.

There are lock-in amplifiers operating in high and low frequency regimes.

In the context of signal to noise ratio, it seems what determines the noise portion is the bandwidth of your lock-in signal (since rms noise voltage at the output is proportional to the square root of the band width).

So, what are the benefits and downsides of running it at high frequencies vs low frequencies?

• HF has higher lock-in speed than LF. – Andy aka Jul 31 '18 at 14:30

## 2 Answers

Noise is only proportional to the square root of the bandwidth in the white noise region. Below the corner frequency (and in virtually all real situations there is a corner frequency) there is 1/f noise.

The lock-in moves you up into the white noise region. • Are you sure the effect is not the opposite? One problem of the Weaver and other homodyne/direct conversion receivers, is that the zero IF is in the 1/f range. Is the difference between Hf and LF, using a high IF vs a zero IF? (in which case HF lockin is why you said, and LF is what I said. [I may be talking b.s as I am not very familiar with lockin amplifiers] – Henry Crun Jul 31 '18 at 14:53
• OK, so the analog block diagrams show a direct conversion to DC, so my original comment seems to me to be right: The signal is being down converted into the 1/f range then amplified. What am I missing? If it was a commutating filter, then the bandwidth filtering would be passive and lacking 1/f noise. The amplification would be at the signal frequency after the down/filter/up conversion. – Henry Crun Jul 31 '18 at 15:23
• @HenryCrun Usually you find some way to make the signal high frequency like energizing a low resistance sensor with a few uA at AC then the amplification is at the high frequency and you don't get the 1/f noise you would get with a DC amplifier. – Spehro Pefhany Jul 31 '18 at 15:28

Besides moving away from 1/f noise as explained by Spehro, the other advantage of moving to higher frequency, is that you are averaging more samples of the signal. (For a fixed output low pass time constant, which determines the bandwidth.) You can think of a lockin as making a measurement of the signal once every period. For N measurements your signal to noise decreases as 1/sqrt(N). This is most important when there is a lot of noise. (ie. for a 1 sec time constant, 100 Hz modulation would give you N=100, for 10 kHz, N=10k.)