Hi,
take a very simple LC oscillator like this:
o VCC | | |-+ +------+------->| | | |-+ N-FET | | | C =3D=3D=3D | C | C/2 | C | | C +----------+ C | | C | |=AF| C =3D=3D=3D | | | L | C/2 |_| R | | | =3D=3D=3D =3D=3D=3D =3D=3D=3D
If all components were noiseless, this would oscillate at an ideally stable frequency close to 2*pi*f0 =3D 1/(L*C)^(1/2). Some frequency offset will result from the internal capacitances and phase lag of the FET, and harmonics will be introduced by its transfer characteristic. Assume the
tank L/C to be chosen such that the FET is only mildly non-linear, i.e.
that it doesn't turn off completely during a cycle.
In reality, the resistors as well as the FET channel inject a thermal voltage noise of (4*kB*T*R)^(1/2), or alternatively a current noise of (4*kB*T/R)^(1/2). This will cause the oscillator frequency to fluctuate
around f0. If you repeately measure the average frequency over a fixed duration tau, the scatter of your results should decrease with increasing tau, however.
Now my question: is it possible to predict the average frequency offset
for a given tau from the values of the circuit components? I would naively expect the answer to depend on the tank circuit quality factor, so a coil resistance RL might have to be introduced as well. But then, R makes for tank circuit damping too.
If specific data can help, take my test circuit data of L=3D550uH, C=3D11nF, RL=3D2ohm, R=3D1kohm, BF245A (IDSS=3D4mA, VTO=3D-1.7V) for the N-FET, VCC= =3D9V, and tau=3D10sec. (The circuit is temperature-compensated to about 1ppm/deg and packed in styrofoam, where C and L are in good thermal contact.)
TIA,
Martin.