Electronic – 24GHz Radar : IF amplification and strange mixer output

I've just recently started studying RF circuit design, thereby my help might be of limited use. What we can infer from your problem description is essentially that connecting the mixer alters your gain; this makes sense as the latter is given by the gm times load product of the circuit. In your case the load is modified by the introduction of the common base stage of the mixer. This part essentially behaves as current follower (linearized by R19, but let's ignore that for the analysis), thereby your new gain is to expected to be somewhere around the gm of Q1 times the load of the mixer! As for the introduction of the undesired frequencies: I have to give that some more thought, without a rigorous mathematical approach I believe pinpointing the exact reason will be difficult.

Why does the first (or only) mixer suffer from off-chip leakage, but the second mixer does not?

A hopefully simple example - say you need 80 dB of total gain in the reciever and this is split in two halves - the first 40 dB is between antenna and the first mixer and the second 40 dB of gain is before the final mixer: -

If LO1 leaks a small signal into the antenna, the output of mixer1 will contain a DC error and a frequency that is twice the LO frequency. OK so far?

Next, consider what outputs from the 1st mixer when a proper signal arrives - it will neither be DC nor twice the 1st LO frequency so those errors produced by leakage are easily filtered out leaving a desired signal that is exactly what you want.

The second stage will produce a leakage LO error of course - this cannot be avoided but, compared to a direct conversion receiver, the leakage is 40 dB down (in this simple example).

You could point out that the 2nd LO can get right back to the antenna and be amplified just as in a direct conversion receiver. However, you have to choose the 2nd LO so that any sum or difference frequencies you might get when it mixes with the first LO don't land in the desired band of frequencies due to a proper receiver input.

For instance, if your desired signal is 1000 MHz with a bandwidth of 10 MHz and your first local oscillator was 970 MHz you would get a desired mixed output of 25 MHz to 35 MHz. The 2nd LO would of course be 30 MHz and if 30 MHz fed back to the antenna it would mix to produce undesired frequencies of 970 MHz and 1030 MHz from the 1st mixer. Neither of these are anything like the desired band of frequencies so they are easily got rid of.