The VFO has varicap control allowing a tuning range of ±3 kHz to be produced by a control voltage swing of 5 V (2.5 V = centre tuning).
Any thoughts about what varicap to use? I have an MV209, would that be ok?
MV209 has a useful range starting at about 35pF (bias 2V) through to about 6pF (bias 12V).
You can see the bias scale is logarithmic non-linear. You get more capacitance change when the bias centre voltage is low. you will see later what a big advantage feature this can be.
The next part you have to do with your calculator or spreadsheet. This is like a recipe
I can see the VFO main tuning capacitor is 20-350pF. I cannot see any additional varicap tuning, unless I misunderstand the circuit.
We need to know either the frequency ranges covered, or the value of the range inductors.
Either way, you need to use Freq ~= 1/(2*pi*SQRT(L*C)), for the the VFO tuned at C=350pF, and estimate L.
Do it again for C=20pF, estimate L. Easy enough, knowing the highest and lowest for all the ranges.
Make a spreadsheet plot using that formula, and figure how much
change in the capacitance you add across the variable C to get the 2-3kHz fine control you want. It will be a tiny amount.
Now use C_added=(1/C_series) + (1/C_varicap) OR C_added = (C_series*C_varicap)/(C_series + C_varicap).
Yes - you need some algebra to turn it into an expression fo C_series. Try (product)/(difference) I think.
Keep in mind that the shift in kHz will be much more at the high end of the ranges, because the change you add is a larger proportion of the C in the VFO circuit at that point. Notice that the MV209 non-linear characteristic works for you to very nearly counter this effect, delivering less change for a given bias as the capacitance gets small. I suggest using a small Op-Amp circuit to allow you to set the centre of the bias (offset), and the span (gain), and feed the output through a high-value (100K) to the varicap
That's about it. I don't know any more on this. There are bound to be some new situations you learn as you try to do this. The recipe is very much a "provided nothing goes wrong" scenario. It is just a starting plan.
Good luck