波形发生器外文资料及翻译

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1、 1 中文 2040 字 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 determi

2、ning the conditions required for oscillation to take place, the frequency and amplitude stability are also studied. Fig.1-1 show an amplifier, a feedback network, and an input mixing circuit not yet connected to form a closed loop. The amplifier provides an output signal oX as a consequence of the s

3、ignal iX applied directly to the amplifier input terminal. The output of the feedback network is iOf AFXFXX and the output lf the mixing circuit (which is now simply an inverter) is iff AFXXX Form Fig.1-1 the loop gain is Loop gain= FAXXXXifif Fig.1-1 An amplifier with transfer gain A and feedback n

4、etwork F not yet connected to form a closed loop. Suppose it should happen that matters are adjusted in such a way that the signal fXis identically equal to the externally applied input signaliX. Since the amplifier has no means of distinguishing the source of the input signal applied to it, it woul

5、d 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 oX as before. Note, of course, that the statement fX=iXmeans that the instantaneous values of fXandiXare exactly equal at all times. The c

6、ondition fX=iXis equivalent to 1AF , or the loop gain must equal unity. The Barkhausen Criterion We assume in this discussion of oscillators 2 that the entire circuit operates linearly and that the amplifier or feedback network or both contain reactive elements. Under such circumstances, the only pe

7、riodic waveform which will preserve, its form is the sinusoid. For a sinusoidal waveform the condition fi XX is equivalent to the condition that the amplitude, phase, and frequency ofiXand fXbe identical. Since the phase shift introduced in a signal in being transmitted through a reactive network is

8、 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 ag

9、ain 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 loop-gain phase shift is zero. Although other principles may be formulated which may serve equally to determine the fre

10、quency, 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 oscil

11、lations 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 iXand fXmust be identical. This condi

12、tion 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 unit

13、y. The condition of unity loop gain 1AF is called the Barkhausen criterion. This condition implies, of course, both that 1AF and that the phase of A F is zero. The above principles are consistent with the feedback formula FAAA f 1. For if 1FA , then fA , which may be interpreted to mean that there e

14、xists an output voltage even in the absence of an externally applied signal voltage. Practical Considerations Referring to Fig.1-2, it appears that if FA at the oscillator frequency is precisely unity, then, with the feedback signal connected to the input terminals, the removal of the external gener

15、ator will make no difference. If FA 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 1-V signal appearing initially at the input terminals will, after a trip around the loop and b

16、ack 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, then, that if FA is larger than unity, the amplitude of the oscillations will continue to increase without limit. But of course, such an i

17、ncrease in the amplitude can continue only as long as it is not limited by the onset of nonlinearity of operation in the active devices 3 associated with the amplifier. Such a nonlinearity becomes more marked as the amplitude of oscillation increases. This onset of nonlinearity to limit the amplitud

18、e of oscillation is an essential feature of the operation of all practical oscillators, as the following considerations will show: The condition 1FA 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 t

19、his condition. Then, because circuit components and, more importantly, transistors change characteristics (drift) with ahe, temperature, voltage, etc., it is clear that if the entire oscillator is left to itself, in a very short time FA will become either less or larger than unity. In the former cas

20、e 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 completely unrealizable in practice. It is accordingly necessary, in the adjustment of a practical

21、 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, w

22、e may add a third general principle dictated by practical considerations, i.e.: In every practical oscillator the loop gain is slightly larger than unity, and the amplitude of the oscillations is limited by the onset lf nonlinearity. Fig.1-2 Root locus of the three-pole transfer function in the s-pl

23、ane. The poles without feedback ( 00 FA) are 1s , 2s ,and3s,whereas the poles after feedback is added are fs1,fs2,and fs3. 2. Triangle/square generation Fig.2.1 shows a function generator that simultaneously produces a linear triangular wave and a square wave using two op-amps. Integrator 1IC is dri

24、ven from the output of 2IC where 2IC is wired as a voltage comparator thats driven from the output of 1IC via voltage divider 2R -3R. The square-wave output of 2IC switches alternately between positive and negative saturation levels. Suppose, initially, that the output of 1IC is positive, and that the output of 2IC has just switched to positive saturation. The inverting input of 1IC is at virtual