【正文】 istent 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 external generator will result in a cessation of oscillations. But now suppose that |FA| is greater than unity. Then, for example, a 1V signal appearing initially at the input terminals will, after a trip around the loop and back to the input terminals, appear there with an amplitude larger than 1V. This larger voltage will then reappear as a still larger voltage, and so on, It seems j then, that if |FA| is larger than unity, the amplitude of the oscillations will continue to increase without limit, But of course, such an increase in the amplitude can continue only as long as it is not limited by the onset of nonlinearity of operation in the active devices associated with the amplifier. Such a nonlinearity bees more marked as the amplitude of oscillation increases. This onset of nonlinearity to limit the amplitude of oscillation is an essential feature of the operation of all practical oscillators, as the following considerations will show: The condition |FA|=1 does not give a range of acceptable values of |FA| , but rather a single and precise value. Now suppose that initially it were even possible to satisfy this condition. Then, because circuit ponents and, more importantly, transistors change characteristics (drift) with age, temperature, voltage, etc., it is clear that if the entire oscillator is left to itself, in a very short time |FA| will bee either less or larger than unity. In the former case the oscillation simply stops, and in the latter case we are back to the point of requiring nonlinearity to limit the amplitude. An oscillator in which the loop gain is exactly unity is an abstraction pletely unrealizable in practice. It is accordingly necessary, in the adjustment of a practical oscillator, always to arrange to have |FA| somewhat larger (say 5 percent) than unity in order to ensure that, with incidental variations in transistor and circuit parameters , |FA| shall not fall below unity. While the first two principles stated above must be satisfied on purely theoretical grounds, we may add a third general principle dictated by practical considerations, .: Fig. 12 Root locus of the threepole transfer functions in the s plane. The poles without feedback (FA0 = 0) are s1, s2, and s3, whereas the poles after feedback is added are s1f, s2f, and s3f. In every practical oscillator the loop gain is slightly larger than unity, and the amplitude of the oscillations is limited by the onset of nonlinearity. 2 Opamp Oscillators Opamps can be used to generate sine wave, triangularwave, and square wave signals. We’ll start by discussing the theory behind designing opamp oscillators. Then we’ll examine methods to stabilize oscillator circuits using thermistors, diodes, and small incandescent lamps. Finally, our discussion will round off with designing bistable opamp switching circuits. Sinewave oscillator In , an opamp can be made to oscillate by feeding a portion of the output back to the input via a frequencyselective work and controlling the overall voltage gain. For optimum sinewave generation, the frequencyselective work must feed back an overall phase shift of zero degrees while the gain work provides unity amplification at the desired oscillation frequency. The frequency work often has a negative gain, which must be pensated for by additional amplification in the gain work, so that the total gain is unity. If the overall gain is less than unity, the circuit will not oscillate。s gain of , the overall gain bees unity. If the oscillator output amplitude starts to rise, RT heats up and reduces its resistance, thereby automatically reducing the gain of the circuit, which stabilizes the amplitude of the output signal. An alternative method of thermistor stabilization is shown in Fig. 24, In that case, a lowcurrent lamp is used as a Positive Temperature Coefficient (PTC) thermistor, and is placed in the lower part of the gaindetermining feedback work. If the output amplitude increases, the lamp heats up thereby increasing its resistance, reducing the feedback gain, and providing automatic amplitude stabilization. That circuit also shows how the Wien work can be modified by using a twinganged potentiometer to make a variablefrequency oscillator over the range 150 Hz kHz. The sinewave output amplitude can be made variable using R5. A slightly annoying feature of thermistorstabilized circuits is that, in variablefrequency applications, the output amplitude of the sine wave tends to jitter or bounce as the frequency control potentiometer is swept up and down its range. Diode stabilization The jitter problem of variablefrequency circuits can be minimized by using the circuits of Figs. 25 or 26 which rely on the onset of diode or Zener conduction for automatic gain control. In essence, R3 is for a circuit gain slightly greater than unity when the output is close to zero, causing the circuit to oscillate。s driven from the output of IC1 via voltage divider R2–R3 The squarewave output of IC2 switches alternately between positive and negative saturation levels. Suppose, initially, that the output of IC1 is positive, and that the output of IC2 has just switched to positive saturation. The inverting input of IC1 is at virtual ground, so a current IR1 equals＋ VAST／ R1. Because R1 and C1 are in series, IR1 and IC1 are equal. Yet. in order to main