This design used the return ratio method.The approximate value of the return ratio is: T=-gmRLC1/C2. C1 (the 470 pf) was chosen by setting the parallel Q factor with RL (the 470R resistor) at 10 with fo being 7 Mhz, where Q=RL/XC1. Once you know C1 and you choose T (must be at least 1, I chose 2), you can rearrange the formula to find C2.
If it does not oscillate make C2 smaller. If the sinewave is distorted make C2 bigger. Change by small increments. Since C2 is much greater than C1 the inductors value can be found from L=1/((2xpixfo)^2xC1).
Surprisingly the approximate equation for the value of the return ratio "T" is almost the same for both common emitter and common collector configurations. In the common collector equation replace Rl with Rpi.
These equations have been developed by using a method put forward by Professor Ali Hajimiri. He has a full breakdown of the return ratio method used for a Colpitts oscillator on Youtube.
