【正文】
id. For a sinusoidal waveform the conditionis equivalent to the condition that the amplitude, phase, and frequency ofandbe identical. Since the phase shift introduced in a signal in being transmitted through a reactive network is invariably a function of the frequency, we have the following important principle:The frequency at which a sinusoidal oscillator will operate is the frequency for which the total shift introduced, as a signal proceed from the input terminals, through the amplifier and feedback network, and back again to the input, is precisely zero(or, of course, an integral multiple of 2). Stated more simply, the frequency of a sinusoidal oscillator is determined by the condition that the loopgain phase shift is zero.Although other principles may be formulated which may serve equally to determine the frequency, these other principles may always be shown to be identical with that stated above. It might be noted parenthetically that it is not inconceivable that the above condition might be satisfied for more than a single frequency. In such a contingency there is the possibility of simultaneous oscillations at several frequencies or an oscillation at a single one of the allowed frequencies.The condition given above determines the frequency, provided that the circuit will oscillate ta all. Another condition which must clearly be met is that the magnitude of and must be identical. This condition is then embodied in the follwing principle:Oscillations will not be sustained if, at the oscillator frequency, the magnitude of the product of the transfer gain of the amplifier and the magnitude of the feedback factor of the feedback network (the magnitude of the loop gain) are less than unity.The condition of unity loop gainis called the Barkhausen criterion. This condition implies, of course, both that and that the phase of –A F is zero. The above principles are consistent with the feedback formula . For if , then, which may be interpreted to mean that there exists an output voltage even in the absence of an externally applied signal voltage.Practical C