函数信号发生器设计外文资料及翻译_毕业设计外文资料翻译

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函数信号发生器设计外文资料及翻译

英文资料原文

WAVE-FORM GENERATORS 1.The Basic Priciple of Sinusoidal Oscillators

Many different circuit configurations deliver an eentially 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 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 Xo as a consequence of the signal Xi applied directly to the amplifier input terminal.The output of the feedback network is XfFXOAFXi and the output lf the mixing circuit(which is now simply an inverter)is

X'fXfAFXi

Form Fig.1-1 the loop gain is Loop gain=X'fXiXfXiFA

Fig.1-1 An amplifier with transfer gain A and feedback network F not yet connected to form a closed loop.Suppose it should happen that matters are adjusted in such a way that the signalX'fis identically equal to the externally applied input signalXi.Since the amplifier has no means of distinguishing the source of the input signal applied to it, it 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=Ximeans that the instantaneous values of X'fandXiare exactly equal at all times.The conditionX'f=Xiis equivalent toAF1, or the loop gain must equal unity.The Barkhausen Criterion

We aume in this discuion of oscillators that the entire circuit 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 waveform the conditionXiX'fis equivalent to the condition that the amplitude, phase, and frequency ofXiandX'fbe identical.Since the phase shift introduced in a signal in being transmitted through a reactive network 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 proceed from the input terminals, through the amplifier and feedback network, and back again 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 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 poibility 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 ta all.Another condition which must clearly be met is that the magnitude of Xiand X'fmust be identical.This condition 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 le than unity.The condition of unity loop gainAF1is called the Barkhausen criterion.This condition implies, of course, both that AF1and that the phase of –A F is zero.The above principles are consistent with the feedback formula AfA.For if 1FAFA1, thenAf, 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.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 generator will make no difference.If FA is le than unity, the removal of the external generator will result in a ceation 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 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, 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 aociated with the amplifier.Such a nonlinearity becomes more marked as the amplitude of oscillation increases.This onset of nonlinearity to limit the amplitude of oscillation is an eential 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 poible to satisfy this 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 le 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 completely unrealizable in practice.It is accordingly neceary, 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, 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-plane.The poles without feedback(FA0are

0)2.Triangle/square generation s1,s2,ands3,whereas the poles after feedback is added are s1f,s2f,and s3f.Fig.2.1 shows a function generator that simultaneously produces a linear triangular wave and a square wave using two op-amps.IntegratorIC1is driven from the output ofIC2where IC2is wired as a voltage comparator that’s driven from the output of IC1via voltage divider R2--R3.The square-wave output of IC2switches alternately between positive and negative saturation levels.Suppose, initially, that the output of IC1is positive, and that the output of IC2has just switched to positive saturation.The inverting input of IC1is at virtual ground, so a current IR1equalsIR1VSAT.BecauseR1andC1are in series, IR1and R1IC1 are equal.Yet, in order to maintain a constant current through a capacitor, the voltage acro that capacitor must change linearly at a constant rate.A linear voltage ramp therefore appears acroC1,causing the output ofIC1to start to swing down luinearly at a rate of 1/C1volts per second.That output is fed via theR2--R3divider to the non-in-verting input ofIC2.Fig.2.1 Basic function generator for both triangular, and square waves.Consequently, the output ofIC1swings linearly to a negative value until theR2--R3junction voltage falls to zero volts(ground), at which point IC2enters a regenerative switching phase where its output abruptly goes to the negative saturation level.That reverses the inputs of IC1andIC2, soIC1output starts to rise linearly until it reaches a positive value that causes the R2--R3junction voltage to reach the zero-volt reference value, which initiates another switching action.The peak-to-peak amplitude of the linear triangular-waveform is controlled by the R2--R3ratio.The frequency can be altered by changing either the ratios of R2--R3, the values of R1orC1, or by feeding R1from the output of IC2through a voltage divider rather than directly from op-ampIC2output.英文资料译文

波形发生器

译者：张绪景

1.正弦振荡器基本原理

许多不同组态的电路，即使在没有输入信号激励的情况下，也能输出一个基本上是正弦形的输出波形。我们将在下文讨论所有这些振荡器的基本原理，除了确定产生振荡所需的条件之外，还研究振荡频率和振幅的稳定问题。

图1.1表示了放大器、反馈网络和输入混合电路尚未连成闭环的情况。当信号Xi直接加到放大器的书入端时，放大器提供一个输出信号Xo。反馈网络的输出为XfFXOAFXi，混合电路（现在就是一个反相器）的输出为

X'fXfAFXi

由图1-1，环路增益为

环路增益=

X'fXiXfXiFA

图1-1 尚未连成闭环的增益为A的放大器和反馈网络F

假定恰好将信号X'f调整到完全等于外加的输入信号Xi。由于放大器无法辨别加給它的输入信号的来源，于是就会出现如下情况：如果除去外加信号源，而将2端同1端接在一起，则放大器将如以前一样，继续提供一个同样的输出信号Xo。当然要注意，X'f=Xi这种说法意味着X'f和Xi的瞬时值在所有时刻都完全相等。条件X'f=Xi等价于AF1，即环路增益必须等于1。

巴克豪森判据

在以下关于振荡器的讨论中我们假定，整个电路工作在线形状态，并且放大器或反馈网络或它们两者是含有电抗元件的。在这些条件下，能保持波形形状的唯一周期性波形是正弦波。对正弦波而言，条件X'f=Xi等同于Xi和X'f的幅度、相位和频率都完全一样的条件。因为信号在通过电抗网络时引入的相移总是频率的函数，所以我们有如下重要原则：

正弦振荡器的工作频率是这样一个频率，在该频率下，信号从输入端开始，经过放大器和反馈网络后，又回到输入端时，引入的总相移正好是零（当然，或者是2的整数倍）。更简单地说，正弦振荡器的频率取决于环路增益的相移为零这一条件。

虽然还可以总结出其他可用来确定频率的原则，但可以证明，它们同上述原则是一致的。附带说明一下，满足上述条件的频率可能不止一个，这并不是不可理解的。在这种偶然情况下，有可能在几个频率处同时振荡，或在所允许的几个频率中某一频率处出现振荡。

只要电路能振荡，其频率就由上述原则来确定。显然还必须满足另一个条件，即Xi和X'f的幅度必须相等。该条件概括为下述原则：

在振荡频率处，如果放大器的转移增益和反馈网络的反馈系数的乘积（环路增益的幅值）小于1，则振荡不能维持下去。

环路增益为1，即AF1这个条件叫做巴克豪森判据。当然，这个条件意味着不仅要求AF1，而且要求—AF的相位为零。上述原则与反馈公式A是一致的。因为如果AF1，则Af，这可以解释为，即使没1FA有外加信号电压，也仍然有输出电压。Af若干实际的考虑

参考图1-2可以看出，如果FA在振荡频率处正好为1，那么将反馈信号接到输入端，再除去外部信号源将不会造成任何影响。

图1-2 三级点传递函数在S平面上的根轨迹。无反馈时（FA00）的极点是s1,s2和s3。而加

入反馈后的极点是s1f,s2f和s3f如果FA小于1，那么除去外部信号源将会导致停振。现在假定FA大于1，那么，最初出现在输入端的信号，例如是1v，再绕路一周又回到输入端时，其幅值将大于1v。然后这个较大的电压又会以更大的电压再出现于输入端，如此循环往复。于是，似乎FA在不受放大器中有源器件的非线性的限制时，振幅的增大才能继续下去。随着振幅的增大，有源器件的非线性变得更加明显。这种非线性的出现，就限制了震荡的幅度，这是所有实际振荡器工作的基本特征，正如以下讨论所表明的那样：条件AF1并不是给出AF的可取值范围，而是给出一个单一的精确值。限假设即使最初能满足这个条件，由于电路元件特性，特别是晶体管特性受老化、温度和电压等影响发生变化（漂移），于是很显然，如果整个振荡器听其自然，则在很短的时间内，AF就会变得不是小于1，就是大于1。在前一种情况下，只是振荡停止而已，而在后一种情况下，我们就有需要用非线性来限制振幅。环路增益正好为1的振荡器，实际上是一个根本不能实现的理想装置。所以，在实际振荡器的调试中，总是要调整AF多少比1大一些（比方说大50%），以保证在晶体管和电路参数发生偶然变化时，AF不致下降到1以下。上述两条原则是在纯理论基础上必须要满足的，同时，我们根据实际的考虑，在添上第三条一般原则，即：

在每个实际的振荡器中，环路增益都略大于1，并且振荡幅度由非线性特性来限制。

2.三角波/方波发生器

图2-1示出了一个用两极运放能同时产生线性三角波和方波的函数发生器。集成积分器IC1由IC2的输出驱动，IC2作为电压比较器，被IC1的输出，经R2--R3分压器分压后所驱动。IC2的方波输出于正负饱和电平间交替交换。

图2-1 具有双向三角波和方波输出的基本函数发生器

假设，开始时，IC1的输出为正，IC2的输出恰好转为正向饱和。IC1的反向输入端虚假接地，则电流IR1VSAT。因为R1和C1是串联的，所以IR1=IC1。然R1而为维持由恒定电流经过C1，加在该电容上的电压必须以恒定的速率线性变化。一个线性的斜坡电压加至C1，使IC1的输出开始以输出通过R2--R3分压器送至IC2的同相输入端。

然后，IC1的输出朝负值线性变化，直至R2和R3连接点的电压下降到0V。在该点IC2翻转动作，使输出突变到负饱和值。这样就改变了IC1和IC2的输入，使IC1的输出开始线性上升，直至升到某一正值为止，该值使R2--R3间的接点电压达到0，便引起了另一次翻转。

线性三角波的峰峰值由R2--R3的比率来控制。频率调整可以通过改变R2R3R1或C1，的比率，或通过将R1由IC2的输出端转接一个分压器，而不是直接接IC21VS的速率线性下降，这个C1的输出端来实现。

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