The Barkhausen conditions require the signal fed back to the non- inverting input of an amplifier to have the same frequency, amplitude and phase as the output for the system to oscillate. For high frequency oscillators, the main requirement is usually frequency stability. This is normally achieved by obtaining an abrupt change of phase at the operational frequency. Amplitude variation with frequency, on the other hand, is not steep enough to produce a sharp resonance. As the amplification is not constant for any amount of time, it is common practice to provide more gain than necessary (unity), and then limit its value by use of a non- linear mechanism. One (or two) of the transistors in the amplifier enter cutoff or saturation, and provide compensation thereby stabilizing the amplitude of the oscillations.
The Colpitts oscillator is shown in figure 16: At the oscillator frequency, the left limb of the resonance tank is predominantly inductive, so the current in it lags the amplifier output current by 90o. The voltage across an inductor leads its current by 90o, so, at resonance, the amplifier input and output currents are in phase. Since an inductor and a capacitor have impedances of opposite signs, the potential 'divider' formed by L and C2 actually provides voltage gain; this, then, is not required of the amplifier. The frequency of resonance is given by:
f = (LC)-1/2/(2 pi)
where C is the series combination of C1 and C2.
A high input and low output impedance is a reasonable simplification for any buffer or voltage- controlled amplifier providing voltage. Using components of a suitable grade, design variations exist which function well into the UHF band.
Substituting inductors for capacitors and vice- versa yields a Hartley oscillator: This time, L is the series combination of L1 and L2 (their sum, in this case.) Any significant degree of coupling between the inductors will render the above equation useless.
In figure 16, an AC- coupling capacitor must be present at the amplifier input if the input stage is not depletion MosFet/ JFet, to prevent the inductor from upsetting the input DC conditions. The restriction for the amplifier to be non- inverting is hardly a serious one, and is most easy to obviate by interchanging the positions of C2 and L.
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