IQ magnitude vs Spectrum magnitude

Question

Trying to sort something out.....Consider the following experiment where I transmit a single CW tone, which is caputred with an A/D that does a complex demodulation.  The IQ samples that result have been decimated to some BW.
Now...I can do two things.  I can take those IQ samples and compute the magnitude for each IQ pair (i.e. - sqrt(I^2 + Q^2)).  OR, I can send those IQ samples into some of the Spectral Measurements Toolkit vi's, and observe the magnitude *spectrum* over the acquisition BW.  In this case, the spectrum consists only of a single impulse at the CW tone.  My feeling was that the magnitude I measure from each IQ pair should be approximately the same as the peak of the computed spectrum, since even though my measurement has some bandwidth, all of my energy is located in a single place.
Unfortunately, this is not the case.  For example, if I put a known power level of x-dBm into say, my NI-5660, then I expected that the magnitude I calculated (i.e. sqrt(I^2+Q^2)), should be traceable back to that known input power.  However, whether I interpret that result in Volts, Vrms, Vpk, Vpk-pk....I can never quite get an "output" power that matches my "input".    
Furthermore, if I take those same IQ samples and put them through the Basic Power Spectrum.vi and then the Scale Power Spectrum.vi.....the peak magnitude of my CW tone is yet another different answer from the previous method, or the actual input.  To make things worse, the Scale Power Spectrum.vi is terribly difficult to follow, making it hard to figure out exactly how the code is scaling everything and what each of the options really does.
I suppose I have three short questions....
1. If I calculate the sqrt(sum of squares)....what units is that in?  Are I and Q scaled somehow such that I shouldn't expect to exactly trace back the input power?
2. Why, for a single CW tone and relatively narrow BW, would the sqrt(sum of squares) method be different than finding the peak of a power spectrum?
3. Is there a decent explanation anywhere regarding how the SMT vi's do scaling?
Brandon

Answer 1

Hi Brandon,
It looks like you're pretty much on the right track with the computations, but as you seemed to allude to the units can get a little confusing. The I and Q values that come out of the niRFSA Fetch IQ (Complex Cluster) VI will be in Volts. If you look in the help for that VI it lays out the equation for conversion to power:
Y returns the complex-value time domain data array.
The real and imaginary parts of this complex data array correspond to the in-phase (I) and quadrature-phase (Q) data, respectively. To calculate the instantaneous power of a sampled I/Q point, use the equation (I2 + Q2)/2R, where R is the input impedance in ohms (Ω). For NI RF vector signal analyzers, R = 50 Ω.
From there you should be able to compare to the peak of the spectrum, but the value won't necessarily match up for a given IQ pair since the FFT for the spectrum is calculated over a full record, generally with some averaging involved. In the case of the SMT IQ Spectrum for niRFSA shipping example it is set up for RMS averaging. You could also change the Fetch IQ VI to return an unscaled 1D array of I16 which will give you the raw data that is acquired by the card.
Your second question may be answered by the inclusion of scaling for the input impedance in the excerpt from the help above. You would also need to bridge the gap between the power in Watts from calculation and the, presumably, dB(m) of the spectrum.
For your third question the answer is sort of yes and no. The "spectral info" output from VIs such as the SMT Zoom Power Spectrum VI will give you some scaling information, and if you are using the SMT Spectrum Unit Conversion VI as well (as in the IQ Spectrum example I've been referencing) then there is a user controlled conversion to a wide range of of units. Did you have specific SMT VIs in mind other than those?
Regards,
Peter Williams