2-11
where QL = loaded Q
of the resonator, and df(ff) is a small
change in loop phase at
offset frequency ff away from carrier
frequency f. Systematic phase changes and phase noise within
the loop can originate in
either the resonator or the sustaining
circuits. Maximizing QL helps to reduce the effects of noise and
environmentally induced
changes in the sustaining electronics.
In a properly designed
oscillator, the short-term instabilities are
determined by the
resonator at offset frequencies smaller than
the resonator’s
half-bandwidth, and by the sustaining circuit and
the amount of power
delivered from the loop for larger offsets.
Oscillator Instabilities - General Expression