波形發(fā)生器外文翻譯

1、<p>　　WAVE-FORM GENERATORS</p><p>　　1 The Basic Priciple of Sinusoidal Oscillators</p><p>　　Many different circuit configurations deliver an essentially sinusoidal output waveform even w

2、ithout 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 stabili

3、ty are also studied.</p><p>　　Fig. 1-1 shows an amplifier, a feedback network, and an input mixing circuit not yet connected to form a closed loop. The amplifier provides an output signal X0 as a consequence

4、 of the signal Xi applied directly to the amplifier input terminal. The output of the feedback network is Xf =FX0=AFXi, and the output of the mixing circuit (which is now simply an inverter) is</p><p>　　Xf’＝

5、-Xf =-AFXi</p><p>　　From Fig. 1-1 the loop gain is </p><p>　　Loop gain=Xf’/Xi=-Xf/Xi=-FA </p><p>　　Suppose it should happen that matters are adjusted in such a way that the signal

6、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 remove

7、d 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</p><p>

8、　　Fig- 1-1 An amplifier with transfer gain A and feedback network F not yet connected to form a closed loop.</p><p>　　The Barkhausen Criterion We assume in this discussion of oscillators that the entire circ

9、uit operates linearly and that the amplifier or feedback network or both contain reactive elements. Under such circumstances, the only periodic waveform which will preserve, its form is the sinusoid. For a sinusoidal wav

10、eform 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 transmi</p><p>　　The fr

11、equency 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 network, and back again to th

12、e 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 loop-gain phase shift is zero.</p><p

13、>　　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 t

14、hat 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 oscillati

15、on at a single one of the allowed frequencies.</p><p>　　The condition given above determines the frequency, provided that the circuit will oscillate at all. Another condition which must clearly be met is tha

16、t the magnitude of Xi and Xf’ must be identical. This condition is then embodied in the following principle:</p><p>　　Oscillations will not be sustained if, at the oscillator frequency, the magnitude of the

17、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.</p><p>　　The condition of unity loop gain

18、-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,

19、then Af → ∞, which may be interpreted to mean that there exists an output voltage even in the absence of an externally applied signal voltage.</p><p>　　Practical Considerations Referring to Fig. 1-2 , it app

20、ears 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 un

21、ity, 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, aft

22、er a </p><p>　　Fig. 1-2 Root locus of the three-pole 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 s3

23、f.</p><p>　　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.</p><p>　　2 Op-amp Oscilla

24、tors</p><p>　　Op-amps can be used to generate sine wave, triangular-wave, and square wave signals. We’ll start by discussing the theory behind designing op-amp oscillators. Then we’ll examine methods to stab

25、ilize oscillator circuits using thermistors, diodes, and small incandescent lamps. Finally, our discussion will round off with designing bi-stable op-amp switching circuits.</p><p>　　11.2.1 Sine-wave osci

26、llator</p><p>　　In Fig.2-1, an op-amp can be made to oscillate by feeding a portion of the output back to the input via a frequency-selective network and controlling the overall voltage gain.</p><

27、p>　　For optimum sine-wave generation, the frequency-selective network must feed back an overall phase shift of zero degrees while the gain network provides unity amplification at the desired oscillation frequency. The

28、 frequency network often has a negative gain, which must be compensated for by additional amplification in the gain network, so that the total gain is unity. If the overall gain is less than unity, the circuit will not o

29、scillate; if the overall gain is greater than unity, the output wav</p><p>　　Fig- 2-1 Stable sine-wave oscillation requires a zero phase shift between the input and output and an orerall gain of 1.</p&

30、gt;<p>　　As Fig. 2-2 shows, a Wien-bridge network is a practical way of implementing a sine-wave oscillator. The frequency-selective Wien-bridge is coostructed from the R1-C1 and R2-C2 networks. Normally, the Wien

31、 bridge is symmetrical, so that C1=C2=C and R1 =R2=R. When that condition is met, the phase relationship between the output and input signals varies from-90°to ＋90°, and is precisely 0° at a center frequen

32、cy, f0, which can be calculated using this formula:</p><p>　　f0=1/(2πCR)</p><p>　　Fig. 2-2 Basic wein-bridge sine-wave oscillator.</p><p>　　The Wien network is connected between

33、the op-amp's output and the non-inverting input, so that the I circuit gives zero overall phase shift at f0, where the voltage gain is 0.33; therefore, the op-amp must be given a voltage gain of 3 via feedback networ

34、k R3-R4, which gives an overall gain of unity. That satisfies the basic requirements for sine-wave oscillation. In practice, however, the ratio of R3 to R4 must be carefully adjusted to give the overall voltage gain of p

35、recisely unity, which is n</p><p>　　Op-amps are sensitive to temperature variations, supply-voltage fluctuations, and other conditions that carse the op-amp’s output voltage to vary. Those voltage fluctuatio

36、ns across components R3-R4 will also use the voltage gain to vary. The feedback network can be modified to give automatic gain adjustment (to increase amplifier stability) by replacing the passive R3-R4 gain-determining

37、network with a gain-stabilizing circuit. Figs. 2-3 through 2-7 show practical versions of Wien-bridge oscilla</p><p>　　Fig. 2-3 Thermistor-stabilized 1kHz Wein-bridge oscillator.</p><p>　　F

38、ig. 2-4 Lamp-stabilized Wien-bridge oscillator.</p><p>　　Fig. 2-5 Diode-regulated Wien-bndge oscillator.</p><p>　　Fig. 2-6 Zener-regulated Wien-bridge oscillator.</p><p>　　Fig. 2

39、-7 Three decade 15 Hz~15 kHz Wien-bridge oscillator.</p><p>　　2. 2 Thermistor stabilization</p><p>　　Fig. 2-3 shows a 1-kHz fixed-frequency oscillator. The output amplitude is stabilized by a

40、 Negative Temperature Coefficient' (NTC) thermistor Rt which, together with R3 forms a gain-determining feedback network. The thermistor is heated by the mean power output of the op-amp The desired feedback thermisto

41、r resistance value is triple that of R3, so the feed-back gain is X3. When the feedback gain is multiplied by the frequency network's gain of 0.33, the overall gain becomes unity. If the oscilla</p><p>　

42、　An alternative method of thermistor stabilization is shown in Fig. 2-4, In that case, a low-current lamp is used as a Positive Temperature Coefficient (PTC) thermistor, and is placed in the lower part of the gain-determ

43、ining feedback network. 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

44、 Wien network can be modified by using a twin-ganged potentio</p><p>　　A slightly annoying feature of thermistor-stabilized circuits is that, in variable-frequency applications, the output amplitude of the

45、 sine wave tends to "jitter" or "bounce" as the frequency control potentiometer is swept up and down its range. </p><p>　　2.3 Diode stabilization</p><p>　　The jitter probl

46、em of variable-frequency circuits can be minimized by using the circuits of Figs. 2-5 or 2-6 which rely on the onset of diode or Zener conduction for automatic gain control. In essence, R3 is for a circuit gain slightly

47、greater than unity when the output is close to zero, causing the circuit to oscillate; as each half-cycle nears the desired peak value, one of the diodes starts to conduct, which reduces the circuit gain, automatically s

48、tabilizing the peak amplitude of the output </p><p>　　In Fig- 2-5, the diodes start to conduct at 500 mV, so the circuit gives an output of about 1-volt peak-to-peak. In Fig, 2-6, the Zener diodes D1 and D2

49、are connected back-to-back, and may have values as high as 5 to 6 volts, giving a p-p (peak-to-peak) output of about 12 volts. Each circuit is set up by adjusting R3 for the maximum value (minimum distortion) at which os

50、cillation can be maintained across the frequency band.</p><p>　　The frequency range of Wein-bridge oscillators can be altered by changing the C1 and C2 values; increasing C1 and C2 by a decade reduces the ou

51、tput frequency by a decade. Fig. 2-7 shows the circuit of a variable-frequency Wien oscillator that covers the range 15 Hz to 15 kHz in three switched-decade ranges. The circuit uses Zener-diode amplitude regulation,

52、and its output is adjustable by both switched and fully-variable attenuators. Notice that the maximum useful operating frequency is restr</p><p>　　2. 4 Tvuin-T oscillators</p><p>　　Another way o

53、f designing a sine-wave oscillator is to wire a twin-T network between the output and input of an inverting op-amp, as shown in Fig, 2-8. The twin-T network comprises R1-R2-R3-R4 and C1-C2-C3. In a "balanced" c

54、ircuit, those components are in the ratios R1=R2=2(R3＋R4), and C1=C2=C3/2. When the network is perfectly balanced, it acts as a notch filter that gives zero output at a center frequency (f0), a finite output at all other

55、 frequencies, and the phase of the output is 180" inverte</p><p>　　Fig. 2-8 1kHz twin-T oscillator.</p><p>　　By critically adjusting R4 to slightly unbalance the network, the twin-T giv

56、es a 180º inverted phase shift with a small-signal f0. Because the inverting op-amp also causes a 180º input-to-output phase shift, there is zero overall phase inversion as seen at the inverting op-amp input, a

57、nd the circuit oscillates at a center frequency of 1 kHz, In practice R4 is adjusted so that oscillation is barely sustained, and under that condition the sine wave has less than 1% distortion.</p><p>　　F

58、ig. 2-9 shows an alternative method of amplitude control, which results in slightly less distortion. Here, DY provides a feedback signal via potentiometer R5. That diode reduces the circuit gain when its forward voltage

59、exceeds 500 mV. To set up the circuit, first set R5 for maximum resistance to ground, then adjust R4, so that oscillation is just sustained. Under those conditions, the output signal has an amplitude of about 500 mV p-p.

60、 Further R5 adjustment enables the output signal to be vari</p><p>　　Note that twin-T circuits make good fixed-frequency oscillators t but are not suitable for variable-frequency operation due to the difficu

61、lties of varying three or four network components simultaneously.</p><p>　　Fig. 2-9 Diode-regulated 1kHz twin-T oscillator.</p><p>　　Fig. 2-10 Relaxation square wave oscillator.</p>

62、;<p>　　2.5 Square-wave generator</p><p>　　An op-amp can be used to generate square-waves by using the relaxation oscillator configuration of Fig. 2-10. The circuit uses dual power supplies, and the op

63、-amp output switches alternately between positive and negative saturation levels. When the output is high, C1 charges via R1 until the stored voltage becomes more positive than the value set by R2-R3 at the non-inverting

64、 input. The output then regeneratively switches negative, which causes C1 to start discharging via R1 until C1 voltage fal</p><p>　　A symmetrical square wave is developed at the output, and a non-linear tria

65、ngular waveform is developed across C1; those waveforms swing symmetrically on both sides of ground. Notice that the operating frequency can be varied by altering either the R1 or C1 values, or by altering the R2-R3 rati

66、os, which makes that circuit quite versatile.</p><p>　　Fig. 2-11 shows how to design a practical 500 Hz to 5kHz squarewave generator, with frequency variations obtained by altering the attenuation ratio of R

67、2-R3-R4. Fig-11-2-12 shows how to improve Fig. 2-11 by using R2 to preset the range of frequency control R4, and by using R6 as an output amplitude control.</p><p>　　Fig. 2-11 500Hz-5kHz squarewave oscilla

68、tor.</p><p>　　Fig. 2-12 Improved 500Hz - 5k Hz squarewave oscillator.</p><p>　　Fig. 2-13 shows how to design a general purpose square-wave generator that covers the 2Hz to 20kHz range in fou

69、r switched-decade ranges. Potentiometers R1 to R4 are used to vary the frequency within each range; 2Hz-20Hz, 20Hz-200Hz, 200Hz-2kHz, and 2 kHz-20 kHz, respectively.</p><p>　　Fig. 2-13 Four decade 2 Hz~20

70、 kHz square wave generator. </p><p>　　2.6 Variable duty-cycle</p><p>　　In Fig. 2-10, C1 alternately charges and discharges via R1, and the circuit generates a symmetrical square-wave output. Th

71、at circuit can be modified to give a variable duty-cycle output by providing d with alternate charge and discharge paths.</p><p>　　In Fig. 2-14, the duty cycle of the output waveform is fully variable from 1

72、1:1 to 1: 11 via R2, and the frequency is variable from 650 Hz to 6.5 kHz via R4, The circuit action is such that C1 alternately charges through R1-D1 and the bottom of R2, and discharges through R1 –D2 and the top of R

73、2. Notice that any variation of R2 has negligible effect on the operating frequency of the circuit.</p><p>　　In Fig. 2-15, the duty cycle is determined by C1-D1-R1 (mark), and by C1-D2-R2 (space). The pulse

74、frequency is variable between 300 Hz to 3 kHz via R4.</p><p>　　Fig. 2-14 Square-wave generator with variable duty-cycle, and frequency.</p><p>　　Fig. 2-15 Variable frequency narrow-pulse genera

75、tor.</p><p>　　2.7 Resistance activation</p><p>　　Notice from the description of the oscillator in Fig. 2-10 that the output changes state at each half cycle when the C1 voltage reaches the thres

76、hold value set by the R2 –R3 voltage divider. Obviously, if C1 is unable to attain that value, the circuit will not oscillate. Fig. 2-14 shows a resistance activated oscillator that will oscillate only when R4, which is

77、 in parallel with C1, has a value greater than R1. The ratio of R2:R3 must be 1:1. The fact that R4 is a potentiometer is only for illu</p><p>　　Fig. 2-16 Resistance-activated relaxation oscillator.</p&g

78、t;<p>　　Fig. 2-17 is a precision "light-activated" oscillator (or alarm), and uses a LDR as the resistance activating element. The circuit can be converted to a “dark -activated" oscillator by trans

79、posing the position of LDR and R1. Fig, 2-18 uses a NTC thermistor, RT, as the resistance-activating element y and is a precision over-temperature oscillator/alarm. The circuit can be converted to an under temperature os

80、cillator by transposing RT and R1.</p><p>　　The LDR or RT can have any resistance in the range from 2000 ohms to 2 megohms at the required trigger level, and R1 must have the same value as the activating ele

81、ment at the desired trigger level. R1 sets the trigger level the C1 value can be altered to change the oscillation frequency.</p><p>　　Fig 2-17 Precision light-activated oscillator</p><p>　　Fig.

82、 2-18 Precision over-temperature oscillator/alarm,</p><p>　　2.8 Triangle/square generation</p><p>　　Fig 2-19 shows a function generator that simultaneously produces a linear triangular wave an

83、d a square wave using two op-amps- Integrator IC1 is driven from the output of IC2, where IC2 is wired as a voltage comparator that's driven from the output of IC1 via voltage divider R2–R3 The square-wave output of

84、IC2 switches alternately between positive and negative saturation levels.</p><p>　　Suppose, initially, that the output of IC1 is positive, and that the output of IC2 has just switched to positive saturation.

85、 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 maintain a constant current through a capacitor, the voltage acr

86、oss that capacitor must change linearly at a constant rate, A linear voltage ramp therefore appears across C1, causing the output of IC1 to start to swing d</p><p>　　Consequently, the output of IC1 swings li

87、nearly to a negative value until the R2 –R3 junction voltage falls to zero volts (ground), at which point IC2 enters a regenerative switching phase where its output abruptly goes to the negative saturation level. That re

88、verses the in puts of IC1 and IC2 so IC1 output starts to rise linearly until it reaches a positive value that causes the R2-R3 junction voltage to reach the zero-volt reference value, which initiates another switching a

89、ction.</p><p>　　The peak-to-peak amplitude of the linear triangular-waveform is controlled by the R2 –R3 ratio. The frequency can be altered by changing either the ratios of R2R3 the values of R1 or C1 or by

90、 feeding R1 from the output of IC2 through a voltage divider rather than directly from op-amp IC2 output.</p><p>　　In Fig. 2-10, the current input to C1 (obtained from R3-R4) can be varied, over a 10: 1 rang

91、e via R1, enabling the frequency to be varied from 100 Hz to 1kHz; resistor R3 enables the full-scale frequency to be set to precisely 1 kHz, The amplitude of the triangular waveform is fully variable via R5 and the squa

92、re wave via R8. The output generates symmetric waveforms, since C1 alternately charges and discharges at equal current values determined by R3-R4.</p><p>　　Fig.2-19 Basic function generator for both triangul

93、ar and square waves.</p><p>　　Fig. 2-20 100 Hz 1 kHz function generator for both triangular and square waves.</p><p>　　Fig. 2-21 shows how to modify Fig.2-20 to make a variable symmetry ramp/rec

94、tangular generator T where the slope of the ramp and duty cycle is variable via R4. C1 alternately charges through R3-D1 and the upper half of R4, and discharges through R3-D2 the lower half of R4.</p><p>　　

95、Fig.2-21 400 Hz~1kHz function generator with variable slope and duty cycle. </p><p>　　2. 9 Switching circuits</p><p>　　Fig- 2-22 shows the connections for making a manually triggered bitable

96、circuit. Notice that the inverting terminal of the op-amp is tied to ground via R1, and the n on-inverting terminal is tied directly to the output. Switches S1 and S1 are normally open. If switch S1 is briefly closed the

97、 op-amp inverting terminal is momentarily pulled high, and the output is driven to negative saturation j consequently , when S1 is released again T the inverting terminal returns to zero volts ,but the output</p>

98、<p>　　Figure 2-23 shows how Fig- 2-22 can be modified for operation from a singleended power supply.</p><p>　　Fig. 2-22 Bi-stable with simple manual triggering,</p><p>　　Fig. 2-23 Single su

99、pply bi-stable.</p><p>　　Finally, Fig, 2-24 shows how to connect an op-amp as a Schmitt trigger, which can be used to convert a sine wave into a square wave. Suppose, initially, that the op-amp's output

100、is at a positive saturation value of 8 volts. Under that condition the R^R? divider feeds a positive reference voltage about 80 mV to the non-inverting input* Consequently, the output remains in that state until the inpu