【正文】 refore, the opamp must be given a voltage gain of 3 via feedback work R3R4, which gives an overall gain of unity. That satisfies the basic requirements for sinewave oscillation. In practice, however, the ratio of R3 to R4 must be carefully adjusted to give the overall voltage gain of precisely unity, which is necessary for a lowdistortion sine wave. Opamps are sensitive to temperature variations, supplyvoltage fluctuations, and other conditions that carse the opamp’s output voltage to vary. Those voltage fluctuations across ponents R3R4 will also use the voltage gain to vary. The feedback work can be modified to give automatic gain adjustment (to increase amplifier stability) by replacing the passive R3R4 gaindetermining work with a gainstabilizing circuit. Figs. 23 through 27 show practical versions of Wienbridge oscillators having automatic amplitude stabilization. Fig. 23 Thermistorstabilized 1kHz Weinbridge oscillator. Fig. 24 Lampstabilized Wienbridge oscillator. Fig. 25 Dioderegulated Wienbndge oscillator. Fig. 26 Zenerregulated Wienbridge oscillator. Fig. 27 Three decade 15 Hz~15 kHz Wienbridge oscillator. 2. 2 Thermistor stabilization Fig. 23 shows a 1kHz fixedfrequency oscillator. The output amplitude is stabilized by a Negative Temperature Coefficient39。 at a center frequency, f0, which can be calculated using this formula: f0=1/(2πCR) Fig. 22 Basic weinbridge sinewave oscillator. The Wien work is connected between the opamp39。to ＋ 90176。WAVEFORM GENERATORS 1 The Basic Priciple of Sinusoidal Oscillators Many different circuit configurations deliver an essentially sinusoidal output waveform even without inputsignal 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. 11 shows an amplifier, a feedback work, and an input mixing circuit not yet connected to form a closed loop. The amplifier provides an output signal X0 as a consequence of the signal Xi applied directly to the amplifier input terminal. The output of the feedback work is Xf =FX0=AFXi, and the output of the mixing circuit (which is now simply an inverter) is Xf’＝ Xf =AFXi From Fig. 11 the loop gain is Loop gain=Xf’/Xi=Xf/Xi=FA Suppose it should happen that matters are adjusted in such a way that the signal Xf’ is identically equal to the externally applied input signal Xi. 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 Xf’ =Xi means that the instantaneous values of Xf’ and Xi are exactly equal at all times. The condition Xf’ =Xi is equivalent to –AF=1, or the loop gain, must equal unity. Fig 11 An amplifier with transfer gain A and feedback 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 feedback 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 Xi = Xf’ is equivalent to the condition that the amplitude, phase, and frequency of Xi and Xf’ be identical. Since the phase shift introduced in a signal in being transmitted through a reactive work 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 proceeds from the input terminals, through the amplifier and feedback work, and back again to the input, is precisely zero (or, of course, an integral multiple of 2π). 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 at all. Another condition which must clearly be met is that the magnitude of Xi and Xf’ must be identical. This condition is then embodied in the following 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 work (the magnitude of the loop gain) are less than unity. The condition of unity loop gain AF = 1 is called the Barkhausen criterion. This condition implies, of course, both that |AF| =1 and that the phase of A is zero. The above principles are consistent with the feedback formula Af=A/(1+FA). For if –FA=1, then Af → ∞ , which may be interpreted to mean that there exists an output voltage even in the absence of an externally applied signal voltage. Practical Considerations Referring to Fig. 12 , it appears that if |FA| at the oscillator frequency is precisely unity t then, with the feedback signal connected to the input terminals, the removal of the external generator will make no difference* If I FA I is less than unity, the removal of the ex