[hpsdr] Infinite precision, phased arrays,and us

[Alberto I2PHD]

Murray Lang wrote:
> 
> It's one thing to shift the phase to accurately represent a modulating 
> audio signal, but to have such fine control as to be accurate to within a 
> fraction of a wavelength of the RF carrier seems to me a lot to ask of a 
> sound card. Consider a phase modulated signal applied to such a phase 
> shifted carrier. I/Q would have both shifts encoded into it: a component 
> accurate at AF and a component accurate at RF.
> 

  Maybe this will just add to the confusion, or maybe it is plainly wrong, and if it is, I will certainly be corrected 
by someone more knowledgeable.

Picture in your mind the signal produced by the sound card as a rotating phasor, described by the two I and Q 
components. Then the instantaneous phase, phi(t), is described by

   phi(t) = atan(Q(t) / I(t))

So far, I am sure you will agree. Now, suppose you want to generate a second signal with a given phase shift wrt the 
previous one. It will have an instantaneous phase given by :

   phi(t) + delta = atan(Q'(t) / I'(t))

You just solve the above to find, given Q(t) and I(t), what Q'(t) and I'(t) should be to satisfy it.
As I and Q are described by floating point numbers, with 138 dB of dynamic range as written by Bob, the granularity of 
the solution is much more finer than needed.

Consider then that the phase shift is preserved when upconverting to the final RF frequency, and this should clear any 
residual doubts. Or not ? Sorry if I added to the confusion.

73  Alberto  I2PHD


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