WAVE-FORM GENERATORS 1 The Basic Priciple of Sinusoidal Oscillators Many different circuit configurations deliver an essentially sinusoidal output waveform even without input-signal excitation. The basic principles governing all these oscillators are investigated. In addition to determining the conditions required for oscillation to take place, the frequency and amplitude stability are also studied. Fig. 1-1 shows an amplifier, a work, and an input mixing circuit not yet connected to form a closed loop. The amplifier provides an output signal X 0 asa consequence of the signal X i applied directly to the amplifier input terminal. The output of the work is X f =FX 0 =AFX i, and the output of the mixing circuit (which is now simply an inverter) is X f ’= -X f =-AFX i From Fig. 1-1 the loop gain is Loop gain =X f ’/X i =-X f /X i =-FA Suppose it should happen that matters are adjusted in such a way that the signal X f ’ is identically equal to the externally applied input signal X i. Since the amplifier has no means of distinguishing the source of the input signal applied to it at would appear that, if the external source were removed and if terminal 2 were connected to terminal 1, the amplifier would continue to provide the same output signal Xo as before. Note, of course, that the statement X f’=X i means that the instantaneous values ofX f’ and X i are exactly equal at all times. The condition X f’=X i is equivalent to– AF=1, or the loop gain, must equal unity. Fig- 1-1 An amplifier with transfer gain A and work F not yet connected to form a closed loop. The Barkhausen Criterion We assume in this discussion of oscillators that the entire circuit operates linearly and that the amplifier or work or both contain reactive elements. Under such circumstances, the only periodic waveform which will preserve, its form is the sinusoid. For a sinusoidal waveform the condition X i=X f’ is equivalent to the condition that the amplitude, phase, and frequency ofX i and X f’ be iden
