ABSTRACT
While the coefficient multiplier, integrator, and summer are fundamental to solving differential equations, op-amp circuits have many other uses. Figure 3-30 shows an arrangement which allows easy design of many devices useful in the electronic portions of dynamic measurement, control, and signal processing systems. These include high-pass filters, low-pass filters, band-pass filters, band-reject filters, lead controllers, lag controllers, lead-lag controllers, approximate integrators and differentiators. In the figure, the impedances Z; and Zlb represent arbitrary impedances, that is, any combination of R, C, and L exhibiting two terminals, such as Fig. 3-13a. (Actually, L is rarely used, for reasons explained earlier.) From the definition of impedance,
Rtb ( 1 Rtb) e = --e1 1 +-+- " R; A AR;
The open-loop gain A may be in the range of 104 to 108, while Rfb! R; rarely exceeds I 03 ; thus, the error upper limit is from about 10-5 (0.00 1%) to 0.1 ( 10% ). The meaning of this error is that if one selects precision resistors for R; and Rfb so as to get a precise e0 je 1 ratio, and if the gain A is too low, the ratio will be inaccurate. Of course, if A is known and .fixed, we could select the resistors to compensate for the error due to low A. However, as we noted earlier, A may drift in random fashion due to temperature, age, etc., reducing the effectiveness of the compensation.
