Operational Integrators
本文虽然早在1967就发表，但它是ADI模拟对话最佳文献( The Best of Analog Dialogue )之一，很有阅读价值。特试译之，以供大家参考，并请多多批评指正。
Modern solid state operational amplifiers make remarkably good integrators. Almost any degree of accuracy can be achieved depending on the choice of the amplifier and the feedback capacitor. A great deal of literature exists which discusses integrator error in analog computers and this subject will not be covered here. But we shall review the non-ideal characteristics of operational amplifiers (and to some extent capacitors) which limit the performance of integrator in instrumentation circuits. This we hope will help the reader make a better choice of amplifiers for his for his particular application.
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An ideal operational amplifier for integrator applications would have infinite open loop gain and input impedance and zero offset voltage and current (that is, e0＝0,when es=0).For this case, Figure 1 shows the characteristics of an ideal integrator.
用于积分放大器的理想运算放大器，应当有无穷大的开环增益，输入阻抗以及0输入失调电压电流(即es=0时，e0＝0)，这样，图1显示的就是理想积分器的特性。
The gain (or characteristics time) of the circuit is given by 1/RC, which is to say the output will change by (1/RC) volts/sec for each volt of input signal. The input impedance as viewed from the source voltage, es ,is determined by the value for R.
电路的增益（或特征时间）由1/RC给出，也就是说，每伏输入电压的输出电压将为1/RC V/s。由源端es看进去的输入阻抗由R的值决定。
OFFSET AND DRIFT ERRORS偏移误差和失调误差
By far the greatest source of error in integrators is due to offset and drift of the amplifier. An equivalent circuit is given in Figure 2 from which we can predict the errors due to offset. For the moment we shall assume that open loop gain, A, and open loop input impedance, R, are infinite
积分器的误差以放大器失调和偏移引起的误差最大。图2给出了由失调引起误差的等效电路，此时，我们假定开环增益A和开环输入阻抗为Rd为无穷大。 |
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As shown the offset voltage, eos, and the offset current, Ios, can be calculated for any temperature, supply voltage and time period from the drift coefficients of the amplifier. It is usually possible to adjust the initial offset voltage and current, Eos and Ios, to zero by some biasing network.
有了失调电压eos和失调电流Ios就能通过放大器的偏移系数计算出任意温度、电源电压和time period（不知道怎么做，不然，这话好象等于说了也白说）。通过某种偏置网络，失调电流Ios和失调电压Eos通常可以调至0。
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The simplest way to analyze offset errors is to refer them to the source voltage as shown in Figure 3. IN this case offset current is multiplied by R and becomes a voltage source. When viewed at the input, the offsets cannot be distinguished from the input signal and hence introduce a basic error in the integration of the signal. The percentage error would be,% error=(e+iosR)100/e*, where e*, is the time average of the input signal over the integration period. Notice that R should be as small as possible to minimize offset errors for a given amplifier. But remember that R also sets the input impedance for the integrator.
分析失调误差的最简单方法是将它们折合成源电压，如图3所示。注意此时的由失调电流产生的源电压（误差）应当为乘上R，以化为电压源。人输入端看进去，失调不能从输入信号中加以区别，因而以引入信号积分的基本误差（概念）。其百分比误差为：% error=(e+iosR)100/e*，其中，e*为积分期间输入信号的平均值。注意，R的值应当尽可能小，以最小化给定放大器的失调误差。但要记住，R也是用来设定放大器输入阻抗的［太小了也不好，甚至造成更加大的误差］。
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