波形发生器WAVE-FORM-GENERATORS翻译及原文.doc

WAVE-FORM GENERATORS1.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 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 as a consequence of the signal applied directly to the amplifier input terminal. The output of the feedback network is and the output lf the mixing circuit (which is now simply an inverter) is Form Fig.1-1 the loop gain is Loop gain=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 signalis identically equal to the externally applied input signal. 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 as before. Note, of course, that the statement =means that the instantaneous values of andare exactly equal at all times. The condition=is equivalent to, or the loop gain must equal unity. The Barkhausen Criterion We assume in this discussion 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 conditionis equivalent to the condition that the amplitude, phase, and frequency ofandbe 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 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 ta all. Another condition which must clearly be met is that the magnitude of and must 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 less than unity.The condition of unity loop gainis called the Barkhausen criterion. This condition implies, of course, both that and that the phase of A F is zero. The above principles are consistent with the feedback formula . For if , then, 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 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 is less than unity, the removal of the external generator will result in a cessation of oscillations. But now suppose that 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 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 becomes 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 does not give a range of acceptable values of , but rather a single and precise value. Now suppose that initially it were even possible 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 will become 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 completely unrealizable in practice. It is accordingly necessary, in the adjustment of a practical oscillator, always to arrange to have somewhat larger (say 5 percent) than unity in order to ensure that, with incidental variations in transistor and circuit parameters, 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 () are ,and,whereas the poles after feedback is added are ,and .2. Triangle/square generationFig.2.1 shows a function generator that simultaneously produces a linear triangular wave and a square wave using two op-amps. Integratoris driven from the output ofwhere is wired as a voltage comparator thats driven from the output of via voltage divider -. The square-wave output of switches alternately between positive and negative saturation levels.Suppose, initially, that the output of is positive, and that the output of has just switched to positive saturation. The inverting input of is at virtual ground, so a current equals. Becauseandare in series, and are equal. Yet, in order to maintain a constant current through a capacitor, the voltage across that capacitor must change linearly at a constant rate. A linear voltage ramp therefore appears across,causing the output ofto start to swing down luinearly at a rate of 1/volts per second. That output is fed via the-divider to the non-in-verting input of.Fig.2.1 Basic function generator for both triangular, and square waves.Consequently, the output ofswings linearly to a negative value until the-junction voltage falls to zero volts (ground), at which point enters a regenerative switching phase where its output abruptly goes to the negative saturation level. That reverses the inputs of and, sooutput starts to rise linearly until it reaches a positive value that causes the -junction 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 -ratio. The frequency can be altered by changing either the ratios of -, the values of or, or by feeding from the output of through a voltage divider rather than directly from op-ampoutput.英文资料译文 波形发生器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。当信号直接加到放大器的书入端时，放大器提供一个输出信号。反馈网络的输出为，混合电路（现在就是一个反相器）的输出为由图1-1，环路增益为环路增益=图1-1 尚未连成闭环的增益为A的放大器和反馈网络F假定恰好将信号调整到完全等于外加的输入信号。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。当然要注意，=这种说法意味着和的瞬时值在所有时刻都完全相等。条件=等价于，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=等同于和的幅度、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，即和的幅度必须相等。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，而且要求AF的相位为零。上述原则与反馈公式是一致的。因为如果，则，这可以解释为，即使没有外加信号电压，也仍然有输出电压。若干实际的考虑 参考图1-2可以看出，如果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（）的极点是,和。而加入反馈后的极点是,和如果小于1，那么除去外部信号源将会导致停振。现在假定大于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：条件并不是给出的可取值范围，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，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，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。集成积分器由的输出驱动，作为电压比较器，被的输出，经-分压器分压后所驱动。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，的输出为正，的输出恰好转为正向饱和。的反向输入端虚假接地，则电流。因为和是串联的，所以=。然而为维持由恒定电流经过，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，使的输出开始以的速率线性下降，这个输出通过-分压器送至的同相输入端。然后，的输出朝负值线性变化，直至和连接点的电压下降到0V。在该点翻转动作，使输出突变到负饱和值。这样就改变了和的输入，使的输出开始线性上升，直至升到某一正值为止，该值使-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-的比率来控制。频率调整可以通过改变的比率，或，或通过将由的输出端转接一个分压器，而不是直接接的输出端来实现。8