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Is there any study on the magnitude of local oscillator leakage as a function of oscillator frequency? If RF input is disabled and there is local oscillator at the mixer, then due to leakage, this will give rise to dc. I want to understand how the dc magnitude vary as the local oscillator frequency is varied. Let's say the range of local oscillator frequency we are interested in is 3-4 GHz. Will the dc magnitude remain fixed or will it vary? Is there any study in this direction?

Thanks.

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Leakage is not a property of the oscillator, but of the mixer fed with that oscillator's output; you'll find that mixer datasheets contain exact measurements on this. And that it depends on the mixer and the way you operate it.

So, yes, studies exist, in the sense that almost every mixer datasheet contains curves like this. I picked this figure because it doesn't only show what happens on output = LO frequency, but also at twice and three times the LO frequency – all useful operation points of a mixer (it's not inherent to using a mixer that you mix with the LO's fundamental; you might as well use one of its harmonics, very much depending on the mixer type and what you're mixing with).

LO leakage over frequency in fundamental, 2nd and 3rd harmonic from the Analog Devices LT5558 datasheet
LO leakage over frequency in fundamental, 2nd and 3rd harmonic mixer mode from the Analog Devices LT5558 datasheet

Sometimes, you don't find data on the LO leakage alone, but on "carrier feedthrough" (that is especially true for IQ mixers), which is the power of the combined LO leakage through the mixer, and the unwanted coupling of power "around" the actual mixing component. Functionally, you care about that more than about LO leakage itself, so if you find a datasheet that only specifies "carrier feedthrough", you still get the important figure:

Carrier Feedthrough of the Analog Devices ADL5375; from its datasheet
Carrier Feedthrough of the Analog Devices ADL5375; from its datasheet

Note that more modern integrated mixers sometimes sport automatic calibration, which can suppress the LO leakage by adjusting gains until branches are balanced, and the carrier "self-suppresses". Same mixer, after applying that auto-calibration:

Carrier Feedthrough of the Analog Devices ADL5375 after self-calibration; from its datasheet
Carrier Feedthrough of the Analog Devices ADL5375 after self-calibration; from its datasheet

What happened there was that offsets to the I and Q branch were added; but looking at the actual mixer component in the chip, that's just "modification of the input"; whether or not you take this as mixer device characteristic curve (as useful for application) or whether you look at the uncompensated Fig. 9 above (as useful for building and improving a mixer) is up to your needs.

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