The effects of up/down mixing on phase shifts at different frequencies





This is the setup we wish to analyze:



A source signal created with gr.sig_source_c() is upconverted in the hardware by M1 and applied to the DUT. The output of the DUT is to be measured in phase and amplitude after downconverting by M2. What I need to know is what effects does the downconversion have on shifts in phase in the DUT? That is, is a shift by +90 at test frequency going to still be 90 at the software frequency or is it going to be a tiny impossible to measure amount?

Using the math package, ignoring amplitude for the moment, and setting M1 and M2 phase to 0 (relative to the source signal). The source here will be 4 cycles/unit, mixed up by 1000 cycles, shifted by pi/4, then mixed back down to 4 cycles.



The source signal:



produces this plot:



Next we mix up to 1004 hz:




The above is our signal S2 applied to the DUT. Next we shift it in phase to get S3:




Then down mix back to 4 hz:




and, Voila, the final signal does indeed reflect the DUT phase shift at the lower software frequency. Lastly, collecting the exponential terms:



produces the same results as #10 above:



This shows the advantages of working with complex exponentials, all you have to do is total up the frequency conversions and phase shifts to get the final result, wOut = w0 + w1 + w2 and theta_out = theta_1 + theta_2 + theta_3. If the DUC or DDC introduced phase shifts those (theta_0 and theta_1) would be accounted for in the result.