I am an undergrad student of electrical enginering and I am designing a colpitts oscillator. For a starting point I used a schematic in the following link:

http://www.learnabout-electronics.org/Oscillators/osc24.php

The requirement for my design was that the circuit oscillates at the frequency 30-40 kHz(inductor L1 in my design is variable,so frequency varies).

I made the following adjustments:

values of C1 and C4 large(I used 47 uF and 10 uF, since C1 and C4 represent short circuit at the operating frequency)

value of C2 is 220 nF

value of C3 is 100 nF

value of L1 is 300 uH +- 10 uH

Other elements in the circuit stayed the same.The circuit now oscillates at the desired frequency.

Now my question:What is the theory behind choosing the values of biasing resistor R1 and R2 for the given topology?

Thank you for your help!