I'm at best a hack EE but I'm attempting to design a 20 meter receiver for learning reasons. I have settled on a superhet and I'm trying to avoid looking at existing designs, the struggle helps my understanding I find. I'm not attempting to build anything world class, I have commercial gear, just looking for functional.
So for the RF filter I'm looking at an RC high-pass pointed vaguely at the LO frequency, the C is (at least partially) a voltage controlled variable capacitor. For the LO I want to build a VCO colpitt using the same or similar varicaps.
So my question is, is there enough math to find a single or two voltage swings that will keep them in tune with each other? Or am I chasing something that wont work/have unobtainable values?