# What is wrong with my PSD computation?

I'm trying to calibrate the RX of my SDR Board to become a measuring receiver. I.e, by connecting it to a known source of power (in my case, a frequency generator), at a fixed frequency, I'm trying to create a LUT that would establish a relation between external power applied to RX and the IQ samples received, at that frequency.

This is my process:

1) I acquire the signal with a known power and frequency, from the frequency generator, during an acquisition time t;

2) I perform the DFT of the signal;

3) I then proceed by squaring the DFT and divide it by N² (N being the number of points in my acquisition). This way, I am obtaining a power spectrum in adimensional digital units;

4) From this, I store both the values of the Power spectrum at the bin of interest (corresponding to the frequency of the frequency generator, demodulated), and the sum over the whole power spectrum, i.e., the power of the whole signal.

These are the problems:

I would expect that the bin of interest of the power spectrum, when properly normalized to Watts/Hz, i.e., divided by the width of the bin, would yield a constant value (with acceptable noise nuances) independently of N (i.e, of the acquisition time, t). But this is not the case. As I increase N, the power will get smaller (not the total power thought, that remains constant). But I can't understand why is this happening.

Furthermore, based on this paper, https://holometer.fnal.gov/GH_FFT.pdf, I tried to calculate the PSD instead. Therefore, on step 3, instead of dividing the |FFT|² by N², I divide it by sample_rate*N. Again, the value will get smaller as N increases. And I really can't understand why.

I want to find the right coefficient that would allow me calibrate RX into a measuring receiver. I expect this coefficient to remain somewhat constant (apart from noise influence) if the same power is applied to RX, independently of how much time the power was applied. Is this wrong to assume? Otherwise, how can I calibrate an unknown source of power with the calibrated RX? The unknown source of power would only yield correct values if the signal it transmits would be acquired at the same acquisition time that the reference signals used in the RX calibration were. Does this makes any sense?

I'm very lost and all the help is appreciated. Thanks