Colpitts Oscillator

[Nigella]

Good day, everyone!
I'm working on a design that starts with a standard Colpitts oscillator. As an example, consider the following:
It works, but I'm not sure how to determine the values of the individual components. I've run several simulations and have a paper with numbers and results, but I'm still stumped about which two Cs to use for the LC tank. If the values are not properly matched to those of the coil, the oscillation does not start or is distorted (even if the relationship between Cs is roughly 10). I've been looking for a direct solution to this question, but despite a few discussions on the issue, there aren't any conclusive responses in the forum.
I know F=1/(2pi sqrt(LC)), but I can't see making a 5 Mhz oscillator with an mH coil and pF coils, or a 5Khz with a 1uH coil and 1000uF capacitors (approximate values).
I'm not sure, but I believe it all has to do with the components' impedances. In any manner possible, the impedance should be matched to the amplifiers in and out resistances. It could be an issue with common-base amplifiers.

 

[nomadradio]

Years ago I got into the habit of just finding an oscillator circuit from the schematic of a commercial radio, built for a frequency near my target. Might find that component values would work better if they're tweaked from what I copied. But starting with someone else's working circuit got to be a habit.

There are two capacitor-value issues with a Colpitts. First, there are two capacitors in series that become a RF voltage divider and control the level of positive feedback.

Second issue is a parallel-resonant tuned circuit that will set the frequency.

The feedback-capacitor pair has one of them across the base and emitter of a bipolar transistor. The second one goes from the emitter to ground.

The capacitance values of these two series caps will typically be too large to resonate above a couple of MHz, so a smaller-value cap will connect the base of the transistor to the actual resonant tuned circuit. Typically a parallel circuit of a coil and capacitor with the other end of each grounded. The equivalent capacitance of that blocking capacitor simply appears to be in parallel with the coil, when it's time to calculate values for a desired resonant frequency. This capacitor, between the transistor base and the tank coil also serves to block DC voltages on the transistor base from being shorted to ground through the coil. The value of this blocking cap also has some bearing on the magnitude of positive feedback you get. The bigger the capacitance, the more feedback. Too much capacitance will limit how high the frequency can get.

Maybe Andy will chime in from here with some cool graphics. Next step should be a diagram that spells out the Colpitts circuit.

But it's past my bed time. I'm bound to have more stuff to continue this with at work, but I'm at home right now. Haven't put my whole digital life in the cloud just yet.

Bit off a bit too much to chew for now.

73