For the purposes of this note I am using measurements I took of a Kenwood DMC-G7R minidisc machine. The recordings were digitally transferred out using a Sony RH01 HiMD recorder. You can access the WAV files if you want to replicate what is done here.
You are trying to derive two parameters from two measurements, sensitivity at full gain and system self-noise at full gain.
This is the answer to the question
"What level of signal, in dBuV, is required to give a fully modulated recording, ie a recording of 0dBFS with the recorder gain at maximum?"
Take the recording you made of the tone. Examine it with your favourite audio editor, and if necessary trim off the beginning and end, where you may have disturbances due to plugging in or moving the connectors. Usually you only need to take out a second either side. If your editor has a level meter, play a segment of the tone, which should be clear and not too noisy, though a little bit of noise may be audible. Make a note of the meter peak display, in dBFS. This was about -8dBFS in the example I am using. Remember this is the peak level, and the level of tone is usually given in r.m.s. terms, which will be 0.7 times the peak level, or 3dB lower.
Open RightMark Audio analyzer and select the Spectrum Analyzer tool
Open the tone WAV file. Rightmark will then ask you to select the FFT measurement bandwidth.
Set this to 256. Although the spectrum will be broadened, this makes it easier to read off the level of the tone.
By moving the cursor to the peak frequency you read from the display below the graph the level. The presence of the odd harmonics is normal and is not due to your recorder but due to cost reductions in the design of the tone source- they do not impair the measurement accuracy. You are looking for the largest value (least negative) which in this case was -10.98 dBFS, which we will round to -11dBFS. This is reasonably in agreement with the estimate from the level meters of Adobe Audition, which gave me -8dBFS peak, which I subtract 3dB to get rms to give -11dBFS.
The level of the tone source is indicated on the box. TS01 delivers a level of -67dBu, so the level I need for 0dBFS is -67dBu - (-11dB) = -56dBu. This is reasonably sensitive - for instance the well respected Sound Devices 702 requires a level of -50dBu for 0dBFS
Like with the tone, open the noise file and if necessary trim the beginning and end of any artefacts. Play the noise and raise the gain - the noise should sound like a hiss, and not have any significant hum. Make a note of the level metering - this is a bit harder to estimate for noise. I observed about -49dBFS
Close the spectrum analysis of the tone and run a spectrum analysis again, opening the noise this time. When the program asks you to select a FFT, repeat the selection above, but make a note of the resolution, which is 172Hz ( see spectrum analysis options above)
You will then be provided with the noise spectrum, like so
The noise spectrum of most digital recorders is fairly flat up to high frequencies, like this where it is substantially flat up to about 10k. The drop above that is an artefact of the early Minidisc ATRAC MDLP codec. I take a typical value in the flat part between 100Hz and 10k of about -76dBFS. This is measured in a narrow bandwidth of 172Hz and must be scaled up to the full 22.050 kHz bandwidth (sampling frequency ÷ 2).
We know that the noise is proportional to the square root of the system bandwidth from
So therefore the scaling factor is √(22050 ÷ 172) = 11.3 Expressed as dB this is 20 × log(11.3) = 21dB. So the scaled noise level is -76 + 21 = -55dBFS. This is in agreement with the -49dBFS peak reading from Audition's metering - the peak-to-mean ratio of noise is usually higher than that of a sinewave and depends on various unknown aspects of the metering integration time and noise character. The peak reading of Audition is 6dB higher than the rms level from RightMark, which is reasonable.
Deriving the absolute value of the recorder noise referred to the input is a matter of subtracting the measureed noise level from the sensitivity of the recorder for 0dBFS. In this case Ein is -56 -55 = -111dBu. Experimental error is of the order of ± 2dB, mainly taken up in the calibration/long term stability of the tone source.
source resistance is 150Ω so
if we perform the theoretical calculation using that value for R an Ein
of -130dBuV would be
the lowest noise possible. That is the self-noise of the 150Ω
A Sound Devices 702 is quoted at a Ein of -128dBu with a
input and gain fully up - they are one of the few manufacturers to have
the courage to cite Ein under these conditions, and show that they have
designed their mic preamps well in this respect, being only 2dB short
of the theoretical maximum performance. The MD recorder measured is
off the best performance theoretically available. This is still useful
in practice and will work with higher output mics such as the
Sennheiser ME66 with hardly any compromise to the microphones own
self-noise. It is better than some more recent Compact Flash recorders
and the high sensitivity and good level control makes this old minidisc
recorder still a good choice for a wildlife sound recordist on a budget.