#### Richarrd

##### Member
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.

#### Blumlein 88

##### Grand Contributor
Forum Donor
Are you keeping dbV and dbu straight. They are not the same. Also dbFS will vary in how it relates to voltage levels from one piece of gear to another. Reaper is showing dbFS I would think.

The third method you used should be correct. It is normal to use 60 db of gain for this measurement or the highest gain you have if it is less than 60 db. EIN will vary somewhat with different gain levels.

#### AnalogSteph

##### Major Contributor
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.
I see nothing wrong with this one though. You do definitely need an absolute level calibration under these circumstances. For the last bit of precision you'd want the same ratio of source and input impedance for calibration, but that shouldn't make much of a difference (150 ohms into 2-3 kOhms would deviate from an unloaded measurement by 0.63 dB at worst).

I guess you are already arriving at your 1 mV level by calibrating the output to, say, 1 V and then reducing generator level by 60 dB, right?

You do still have to set your measurement bandwidth to 20 kHz and enable A-weighting if desired (though on white noise, I can tell you right away it should be about 2.3 dB less than 20k unwtd).

The only method that is clearly incorrect is #1, because - I think - your system gain calculation is wrong. You are basically assuming that 0 dBFS at minimum preamp gain is = 0 dBu, which generally is not the case. You have to know the actual system gain or its inverse, input sensitivity. You should be able to determine that by seeing where your 1 mV signal ends up in dBFS. Once you know your 0 dBFS level in terms of input dBu, your EIN should be 80.8 dB below that (full-bandwidth unwtd, I guess).

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#### Rja4000

##### Major Contributor
Forum Donor
Your confusion seems to come from the Unit of Measurement, indeed.
20 × Log10(1Vrms) = 0dBV = 2.22dBu
As EIN is usually measured in dBu, you'd probably want to use this unit.
But you may as well measure everything in Vrms and convert at the end.

dBFS is another kind of beast, and you need, indeed, to use an external (True RMS) volt meter to link it to dBu.
After that, it should be linear.

All PC softwares work with dBFS.

To make things more confusing dBFS don't always refer to the same: if that's referring to noise level, your Sine at maximum amplitude will have a -3.01dBFS level.
As this is confusing, most systems, including REW, align 0dBFS to the Sine max RMS level.
So a square wave at max level will reach a level 0f +3.01dBFS.
(Actually, in REW, you may choose with a setting in "Preferences")

Your 3rd method is perfectly valid.
The calibration in REW is indeed what you'd need to do manually with the other methods,
(Just make sure to measure RMS voltage with the generator plugged to the input, though.)

Also, you've set bandwidth to 20Hz-20kHz, which is the usual. So it's good.

To optimize it a bit, I'd advise to use Rectangle (no window) FFT function instead of Blackman Harris 7, and to use 8 averages or so, to stabilize the figures.
And to record room temperature and the exact resistance you're using.

Out of curiosity: What's your setup ?

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#### Rja4000

##### Major Contributor
Forum Donor
What really puzzles me is the "N" value in your REW

I guess you're not using the same version I'm using.

Here is an example I'm getting:
(Important to use the High pass and Low pass settings in REW)

Zooming a bit on the values:

which is identical to N+D (A weighted) and N

And here is what I get with my usual method

As you see, we get identical results.

But your method with REW is faster and gives you A-weighted value as well.

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#### Richarrd

##### Member
I see nothing wrong with this one though. You do definitely need an absolute level calibration under these circumstances. For the last bit of precision you'd want the same ratio of source and input impedance for calibration, but that shouldn't make much of a difference (150 ohms into 2-3 kOhms would deviate from an unloaded measurement by 0.63 dB at worst).
I did notice a difference in the data compared to others. Mine is consistently at -129.8dBu Awt, while others are around -130.5dBu. I'm not sure if this is related to what you mentioned. Could you please provide more detailed instructions on how to calibrate this?
The only method that is clearly incorrect is #1, because - I think - your system gain calculation is wrong. You are basically assuming that 0 dBFS at minimum preamp gain is = 0 dBu, which generally is not the case. You have to know the actual system gain or its inverse, input sensitivity. You should be able to determine that by seeing where your 1 mV signal ends up in dBFS. Once you know your 0 dBFS level in terms of input dBu, your EIN should be 80.8 dB below that (full-bandwidth unwtd, I guess).
So, if I input a -50dBV signal and increase the gain to 50dB, will I get 0dBu on the analog side? The dBFS headroom above the waveform is the value I need to add to the measured noise and then subtract the gain, right? However, my sound card uses an analog potentiometer to control the gain, making it difficult to achieve a perfect 50dB gain in the digital domain. This is a challenge.

Perhaps I will use the method in REW, which is more intuitive. However, as mentioned earlier, my data still differs by 0.X, and I cannot be certain that my multimeter readings are 100% accurate. This may also be a factor causing the deviation.

#### Rja4000

##### Major Contributor
Forum Donor
my data still differs by 0.X, and I cannot be certain that my multimeter readings are 100% accurate.
This is obviously a factor.

First your multimeter has to be True RMS and calibrated.
Second, it's best to use it just below range limit:
As an example, if you have a range up to 100mV, measure at 90mV

Also, it's possible that your resistor is not exactly 150 Ohm. Measure it and, if required, correct the value accordingly. If it's 140 Ohm, you'll get a 0.3dB lower thermal noise, so may have to add that.
Same for your room temperature. Measures should be done around 20°C
Do it at 40°C and thermal noise for your resistor will increase by 0.3dB, so you'll have to substract that.
(You may use this calculator to estimate resistor thermal noise)

All in all, getting accuracy below 0.5dB is all but trivial.

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#### Richarrd

##### Member
What really puzzles me is the "N" value in your REW

View attachment 310198

I guess you're not using the same version I'm using.

Here is an example I'm getting:
(Important to use the High pass and Low pass settings in REW)

View attachment 310199

Zooming a bit on the values:

View attachment 310201
which is identical to N+D (A weighted) and N

View attachment 310202

And here is what I get with my usual method

View attachment 310200

As you see, we get identical results.

But your method with REW is faster and gives you A-weighted value as well.
Thank you for the detailed explanation! I am trying different versions of REW to see if this part changes. and all the suggestions you mentioned. It will take some time, and I will get back to you later with an update.

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#### Richarrd

##### Member

Rja,although i decide to use rew,I still have some questions about this method. I actually tried to increase my preamp gain to 50dB and record a sine wave signal in reaper, then watch the rms above it,which is about around-12 as i remember. so-80.8+12-57.7=-126.5, far away from the true data. so i cant think out which part this way i got wrong.

#### AnalogSteph

##### Major Contributor
I'd think you're within 2 dB of the actual value at this point, probably better. Keep in mind that the absolute physical limit, the 150 ohm resistor's voltage noise itself, is -130.8 dBu (20 kHz flat) or -130.4 dBu (22 kHz flat) at 300 K. The best audio interfaces according to @Julian Krause's measurements make it just below -131 dBu(A), so somewhere around 129 dBu flat. At the very least you're no worse off than a Focusrite Scarlett 3rd gen.

I suggest taking some more data points for better accuracy.
Using your preferred method, please record the noise level (at full preamp gain) for the following source resistance values R:
1. 0 ohms (a dead short)
2. 150 ohms
3. ...and a few values in between that you might have floating around (maybe 22 - 47 - 100 ohms or 15 - 33 - 68 ohms).
Then try to match the following function to the values obtained in a spreadsheet:
N[dB] = 10 log(1 + R/R_eq) + C
Vary C and R_eq.

C is just some constant we're not overly interested in, it should roughly be N[dB] for the shorted input so start with that. You could also just look at N[dB](R) - N[dB](short) and ignore C altogether, with a slight loss of accuracy.
R_eq is the preamp's equivalent input noise resistance, the resistor value which would result in the same amount of voltage noise if in series with an ideal noiseless input. This is what we want. Once you have a good approximation for its value, adding that to 150 ohms and calculating unweighted noise voltage is trivial, the old √(4kTRB), you can use my RMS summing calculator for that. (Adjust T according to actual ambient temperature, which I suspect may be closer to 300 K where you are.)

This model assumes that input current noise is negligible, which at 150 ohms and below it should generally be. The good thing about it is that it eliminates a lot of variables, leaving only resistor noise and input noise.

I can try to explain the math later if so desired, just wanted to get this one out quickly.

You could also just post a list of the corresponding resistor and noise floor values you get and I'd have a go in LibreOffice Calc. I can't say my last attempt at regressions was overly successful though...

As a further simplification, you can even calculate R_eq directly from the "150 ohm" and "short" data points (though I would assume that accuracy improves with more of them).
N[dB](150Ω) - N[dB](0Ω) = 10 log(1 + 150Ω/R_eq) - 0
10^((N[dB](150Ω) - N[dB](0Ω))/10) = (R_eq + 150Ω)/R_eq
Let's call the left-hand side "dB2linpwr(ΔN)". Then
(dB2linpwr(ΔN) - 1) R_eq = 150Ω
or
R_eq = 150Ω / (dB2linpwr(ΔN) - 1)

Let's say we're seeing a 6 dB difference in noise level. Then
R_eq = 150Ω / (10^0.6 - 1) ~= 50.3Ω.
Then the thermal noise of 150Ω + 50.3Ω over a 20 kHz bandwidth (unweighted) at 300 K would come out as -129.6 dBu - there's your EIN figure. Still unweighted, but hey. Consult REW for the delta between 20 kHz flat and A-weighted in the 150 ohm measurement (e.g. 1.7 dB as shown above), then you should get a pretty good estimate for A-weighted.

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#### Richarrd

##### Member

1. 0 欧姆（完全短路）
2. 150欧姆
3. ...以及您可能会浮动的一些介于两者之间的值（可能是 22 - 47 - 100 欧姆或 15 - 33 - 68 欧姆）。

N[dB] = 10 log(1 + R/R_eq) + C

C 只是我们不太感兴趣的一些常数，对于短路输入来说它应该大致为 N[dB]，所以从这个开始。您也可以只查看 N[dB](R) - N[dB](short) 并完全忽略 C，但精度会略有损失。
R_eq 是前置放大器的等效输入噪声电阻，如果与理想的无噪声输入串联，该电阻值将导致相同量的电压噪声。这就是我们想要的。一旦您对其值有了很好的近似值，将其添加到 150 欧姆并计算未加权噪声电压就很简单了，即旧的 √(4kTRB)，您可以使用我的 RMS 求和计算器来计算。（根据实际环境温度调整T，我怀疑你所在的地方可能更接近300K。）

N[dB](150Ω) - N[dB](0Ω) = 10 log(1 + 150Ω/R_eq) - 0
10^((N[dB](150Ω) - N[dB](0Ω))/10) = (R_eq + 150Ω)/R_eq

(dB2linpwr(ΔN) - 1) R_eq = 150Ω

R_eq = 150Ω / (dB2linpwr(ΔN) - 1)

R_eq = 150Ω / (10^0.6 - 1) ~= 50.3Ω。

thank you! I have to spend sometime to figure it out

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