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The difficulty here is to understand these two concepts (freq and phase). If you can control phase of two different freqs you control both. freq and phase. If you control freq only you control freq ONLY.
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This exactly what I'm doing and think I've done. Costas loop is meant to give PHASE error which happens to be very sensitive to small differences (2 times delta theta). And as you've just said, controlling phase means controlling both freq and phase.
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Your 1st design requires somebody else to control freq (apparently as we couldn't see any useful sense of error to be useful to push signal to baseband) but if given two inputs at same freq centre then it does give enough error to lock to one quadrant of cycle.
To test it keep rf and nco freqs at .1 then change the phase rf and see error.
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The later design is pretty much the first one except that I used a loop filter now, and it seemed that I tested phase offsets in a wrong way in the first design (maybe it was good and working... anyway, this is better).
I tested as you said, I set RF and NCO at 0.05, then changed the phase of NCO by pi/8, pi/7, pi/3 and it demodulated and locked in all tests.
Do I say Yuppie now? :D
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