Apologies if this has been asked before, but I couldn't find answers to my specific questions.
I built a transistor based Colpitts Oscillator and I've been confused by the difference between the standard formulas and circuit behaviour (both real and simulated). The circuit is given below:
Originally, R4 wasn't part of the simulation - I added it after I built the circuit and measured the frequency on the scope. The resonant frequency of the tank prior to R4 was approx 70kHz. This, I can calculate using the standard 1/2*pi*sqrt(LC) and spice agreed. However, the circuit on the breadboard measured 83kHz. I reasoned that the breadboard contained quite a bit of resistance and I added 10 ohms to the tank. Viola, spice now reported a frequency of 83kHz - exactly right.
So, my questions are: 1) How would I go about calculating the frequency considering the effect of the resistor? I've seen other formulas that take account of the resistance, but when I tried them the frequency was reduced. Also, intuitively, I would have thought that the damping effect of the resistor would reduce the frequency, not increase it.
2) I've noticed that the current circulating within the tank according to spice is roughly 12mA. See image below:
I tried to calculate this current myself using complex impedance calculations, but I couldn't get the right answer. The best I got was the following:
Here, I took the sum of all the complex impedances and the 9V peak reported by spice to arrive at the current. Obviously the answer is wrong, but it looked suspiciously like twice the (spice) reported current.
The problem with a lot of the books I read is that they talk about resonant circuits where the driving voltage is sinusoidal. With the Colpitts, the driving voltage is DC topping up the tank.
Any assistance would be greatly appreciated.