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# absolute phase shift through a frequency converter

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#### biff44

I thought I understood this, but maybe I don't.

Lets say I have a 1 GHz tone. Then I upconvert it to say 5 GHz with a 4 GHz LO. Then I phase shift it while at 5 GHz, from say 0 to 100 degrees. If I then down convert it with the same 4 GHz LO back to 1 GHz, and observe the received phase vs the initial transmitted phase, does the received 1 GHz tone also go through a 0 to 100 degree phase shift?

Is there a way to simulate this accurately with some math equations? I tried doing some simple trigonometry identities to figure it out, like Sin a * Cos b stuff, but it does not seem to be the complete answer.

For instance, what happens if I instead downconvert with a 6 GHz LO to get a 1 GHz received tone. Is it a "negative frequency" tone (5-6=-1), and does the phase shift go backwards, so it goes 0 to -100 degrees? In the lab it looks like it does just that.

My brain is hurting on this one!

In all these, assume balanced LO phase paths, both LOs phase locked to the same frequency reference, etc.

According to the mixer definition given by Stephen Maas (one of the most qualified mixer guru) a mixer is not only a nonlinear device, actually is a linear device which is shifting a signal from one frequency to another and keeping (faithfully) the properties of the initial signal (phase and amplitude).

So, after up and down conversion theoretically the phase properties of the signal should remain unchanged.

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