# How to convert noise to noise density in mic pre amps

I am trying to compare two low noise mic pres for the lowest noise, and I am looking at the

TI1012 and MAX9814

MAX9814: ♦ Low Input-Referred Noise Density of 30nV/√Hz TI1012: Output Voltage Noise (A-Weighted): −89 dBV

I thought I could get some insight from simply converting the 30nV into dBV, but ~-150dBV doesn't make sense. I would expect it to be very similar to the -89dBV. I believe my lack of understanding is in the density portion (√Hz) and how it is calculated.

• It's not 30nV, it's 30nV/√Hz. So you have to multiply by the square root of the width of the frequency band you are interested in. For human hearing, that's 20kHz, so 30nV * √(20000). Then convert to dBV. (Note this is a first order approximation. There are some details that are filter dependent that adjust this somewhat.) Commented Jan 8, 2015 at 4:21

TI is quoting a spec based on the total noise in the audio range (20 Hz-20 kHz, presumably), adjusted based on a standard A-weighting curve (see http://en.wikipedia.org/wiki/A-weighting for more, as well as figure 22 of the TI data sheet.) -89 dBv is what you'd see if you looked at the noise on a scope, after passing it through a filter with that particular response. Something on the order of 30 microvolts.

To compare that value to the MAX9814's specification, you can multiply 30 nV/root-Hz by sqrt(20 kHz-20 Hz) to get 4.3 microvolts of total noise in the audio spectrum.

This is all complicated by the fact that the volts-per-root-Hz concept assumes constant noise power per 1 Hz of bandwidth. This will not apply at offsets near DC where the noise takes on a 1/f characteristic, and neither manufacturer gives explicit information about their part's 1/f corner frequency. With these two chips in particular, you need to compare them via the one spec they both provide: the A-weighted SNR (60 dB for the TI part, 64 for Maxim.)

These 2 figures have a different meaning. The 1st one is the input-referred noise density, the last one the output noise. The reason for the √ is that thermal noise power is independent from the input resistance of the amplifier which eases comparing specs. P = U²/R so in terms of density U²/(R*f). Or U/√ f if you ignore the input resistance. Therefore V/√ Hz as a unit

In dBV: 20*log(30.10-⁹ * √20000) = -107dBV

Then there's the weighting (as mentioned in previous post) which favours certain frequencies. This weighting complicates matters considerably and therefore harder to calculate. Generally obtained automatically by the measurement instrument.

A precise calculation requires the proper 3dB BW which is lower than 20kHz.

Taking a crude stab at it, the TI (Nat Semi) LMV1012 has four fixed gain configurations. The highest gain (24dB) one is likely to be the quietest (by analogy with other low noise amp designs) : its output noise level is specced at -82 dBV.

Thus its noise referred to input level is: N(in) = N(out) / Gain = -82 dB - 24dB = -106 dBV = 5 uV.

(Re-running for the lowest gain configuration shows it to be 2dB noisier)

Converting to a noise density (voltage/rtHz) requires some assumption about the bandwidth : I'll use sqrt(20000) = 141 which is WRONG because the noise measurements are "A weighted" (which makes them look better on paper). Finding an appropriate conversion for A-weighting would improve the calculation : HOWEVER:

5 uV / 141 is about 35 nV/rtHz, which is broadly similar to the other part.

Both are a long way from the better-than-1 nV/rtHz of a good low noise mic amp, but probably adequate for a cheap electret microphone.

So I see no compelling reason here to choose one over the other : other considerations like cost or power may help.

• Here's a value for the integral of the A-weighted curve at 20kHz: 0.74 or 2.6dB. So, in your example the A-weighted noise numbers would be 0.75 times or 2.6 dB lower. Commented Apr 20, 2017 at 1:18