# Assumptions in the Calculation of Noise Vrms

I was doing some reading on noise analysis and its calculations.

The SRS lock in amplifier specifies input noise levels only at a certain frequency and not the entire spectrum itself.

For example: $$\ 6 nV \backslash \sqrt{Hz}\$$ at 1kHz,

But with such data, I can only estimate input noise using the assumption that the PSD is "flat". Are electronics usually to be assumed as "flat" when it comes to input noise?

• Most op-amps that have a reasonably good noise performance show spectral graphs so I don't know how you can say this. Worse op-amps may not but why should they? So, provide examples of what you are referring to. – Andy aka Apr 26 '20 at 8:00
• The example I was referring to was Lock in amplifiers from SRS – BlackPenguin Apr 26 '20 at 8:03
• Then link the data sheet for it. – Andy aka Apr 26 '20 at 8:08
• Thank you for the comments. I realized that my question was quite silly and rephrased it. – BlackPenguin Apr 26 '20 at 8:19
• Maybe an email to the manufacturer would clear this up. – Andy aka Apr 26 '20 at 8:30

In general analog front ends are not flat in their noise response. 1/f is a large noise contributor at low frequencies tho most decent amplifiers have this corner in the sub 100Hz range now a days. Auto-zero or chopper amplifiers are unique in that their sensing methods resulting in different noise spectrum. You can read more about them here. From the same article is also an image of generalized voltage noise repose for various architectures:

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As an example look at TI INA333 noise response which is flat at low frequencies. Chopping is done at an 8us rate (125kHz) so the graph conveniently ends at 10khz as the next decade would probably start showing anomalies in the flat response due to chopping noise.

And TI INA331 noise response (voltage on the left side of the graph). Here the 1/f characteristic actually is significant all the way up to 1-10kHz before becoming more flat. This INA uses a 2amp internal architecture:

This is just to show that even two parts that are meant for quite similar applications can have drastically different responses. The situation is further compounded by the fact that you don't know what kind of filtering is used on the input, so you cannot know for certain how the noise is shaped.

I found what claims to be the SR830 block diagram here. As you can see some power line notch filtering will affect the noise around those bands. There is also an low noise input stage and a subsequent gain stage - which each will add their own noise characteristic depending on the parts selected.

Now if we do more digging we can find the user manual here and if we do some detective work there we find the BOM for the analog board at the bottom with U101 listed as LT1793, which of all the parts in that list makes the most sense to be the input amplifier. If we open the datasheet for the part we see a noise response of exactly 6nV/sqrt(Hz) at 1kHz as per the spec of the instrument. Typically in a well designed low-signal acquisition chain the noise response will be dominated by the input amplifier and BW filters. As such, likely the entire noise response of the instrument will be similar to the noise response of the LT1793 but with some more noise due to subsequent gain stages and less noise around 50/60/100/120Hz due to notch filters. Section 3-22 also discusses how the instrument perform noise measurements and may be of interest.

Emailing the manufacturer would have been easier and more sensible but I felt like seeing how far I could get with no help :)

• Good investigative work +1 – Andy aka Apr 26 '20 at 9:54
• Extremely helpful! Thank you so much. I should have considered emailing them before I posted this.. – BlackPenguin Apr 26 '20 at 11:47

The noise of a lock-in amplifier is related to the front end noise at the modulation frequency and the bandwidth.

Usually we will pick the modulation frequency to be in the white noise portion of the front end (above the 1/f noise corner frequency) so only the bandwidth has effect. You need to look at the voltage noise and current noise of the front end as well as the Johnson-Nyquist noise of the source resistance in general.

The key feature of the lock-in is that it allows the relatively low white noise density to be used at lower frequencies.