#### Felix23333

I encountered a significant setback while studying the process of measuring the Equivalent Input Noise (EIN) of a microphone preamp. There are several tutorials on EIN measurement available online, but I have many areas of confusion, which has resulted in me spending over a week without fully understanding how to calculate it.

The simplest method I found is to obtain a known gain and then insert a 150-ohm plug to measure the noise. In my case, the RMS meter in Reaper shows -80.8dB, with a gain of 57.7dB. This results in an absurd value of -138.5dB, whereas the EIN (Equivalent Input Noise) should typically be around -130.X. Clearly, there seems to be some issue.

The second method I tried was from YouTube. The challenging part of this method is that my sound card has analog knobs, so I cannot precisely control the dB gain. I used the same -50dBV generator as the person in the video and tried adjusting the dBFS portion in REW to exactly increase it by 50dB. However, using their calculation method, I only obtained an EIN of around -126dB, which is a completely different value from the previous method.

The third method, I'm not entirely sure about. I used a known voltage, such as a 1mV input, to calibrate in the RTA interface within REW. Then, I disconnected the sine wave input and plugged in a 150-ohm load, switching directly to the dBu interface to view the values. This value seems to be very close to the "normal EIN value" of around -130dB, but I highly suspect it might be a coincidence because I haven't come across anyone using this method, at least not in tutorials available on the internet.

https://benchmarkmedia.com/blogs/app...c-preamp-noise
and this one completely different… I can't understand it at all.

I am soooo confused，and need some help.

#### Mark Tillotson

Firstly noise depends on bandwidth, so unless you are clear about the bandwidth and any weighting function, all bets are off.
Perhaps the best way to measure noise is measure noise-spectral-density, since this is explicitly independent of bandwidth.

Secondly you glibly talk about dB. dB is a ratio, not absolute, in electrical use. So perhaps you mean dBu or dBV? Hopefully not dBm? This matters.

Voltage noise density is measured in V/√Hz (volts per square-root hertz). Typical values are in the nanovolt range, ie nV/√Hz.
To convert such a value to dBV (which use a reference of 1Vrms), just apply the voltage to dBV formula, dBV = 20 log10(V).

So 5nV/√Hz = -166dBV/√Hz (bit of an abuse of notation there, you can't actually divide dB sensibly!)

To scale a density to a flat bandwidth, multiply by the square root of the bandwidth in hertz, for instance
5nV/√Hz over a 20kHz bandwidth = 5 x √20000 = 707nV (rms).

For something like A-weighted noise value you might have to look up the equivalent noise bandwidth of the weighting function.

The formula for voltage noise of a resistor at temperature T is √(4kTR), where T is in kelvin and k = Boltzmann's constant (1.38 x 10^-23)

Thus your 150 ohm resistor at room temperature (300K close enough) has noise √(4 x 300 x 1.38e-23 x 150) = 1.58nV/√Hz, which for a flat 20kHz bandwidth is 220nV/√Hz

This works for thin-film (metal film) resistors well, but carbon resistors are noisier (by an unpredicatable amount), so make sure that resistor is metal film.

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#### tomchr

Paid Member
The amplitude value read from an FFT plot depends on the FFT bin width too.

Tom

#### MarcelvdG

As well as the windowing function.

The noise bandwidth of A-weighting is about 12.5 kHz to 13.5 kHz; 12.5 kHz when it is combined with a sharp 20 kHz low-pass filter and 13.5 kHz when it isn't.

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#### jan.didden

Paid Member
@Mark Tillotson, not to split hairs, but should '1.58nV/√Hz, which for a flat 20kHz bandwidth is 220nV/√Hz' not be '1.58nV/√Hz, which for a flat 20kHz bandwidth is 220nV'?

Jan

1 user

Yes, you got me