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88 Hands-on electronics R2 R1 Vin ~ I2 − op amp I1 + Vout Fig. 7.2. Op amp inverting-amplifier circuit. Note the negative feedback resulting from the resistor that connects the output to the inverting input. Op amps are almost always used with negative feedback. We shall see next that these approximations lead to a very simple way of analyzing op amp circuits. 7.1.3 Gain of inverting and noninverting amplifiers Fig. 7.2 shows an op amp configured as an inverting amplifier. The key principle at work in this circuit is negative feedback. The idea is that a fraction of the output signal is applied at the inverting input. Since the gain of the op amp is large and the noninverting input is grounded, any nonzero voltage at the inverting input will cause a large output voltage of the opposite sign. If you think about it, you will see that the only stable situation that can result is that the voltage difference between the inverting and noninverting inputs is zero. In other words, the op amp will do whatever is necessary to zero the voltage difference at its inputs. Once this principle is grasped, it is easy to compute the gain of the op amp inverting amplifier. Assuming the input currents of the op amp are zero, all the current flowing in through R1 must flow out through R2 , i.e. I2 = I1 . Assuming that the open-loop voltage gain (i.e. that without any feedback) of the op amp is infinite, the voltage difference at the op amp’s inputs must be zero. Applying Ohm’s law to R1 and R2 , and designating the voltage at the inverting input as V− , V− = Vin − I1 R1 = 0 ⇒ I1 = − Vin R1 (7.1) (7.2)
