374CHAPTER 8. OPERATIONAL AMPLIFIERSto R1. Also note that the output voltage is always the opposite polarity of the input voltage.A positive input voltage results in a negative output voltage, and vice versa (with respect toground). For this reason, this circuit is referred to as an inverting ampliﬁer. Sometimes, thegain formula contains a negative sign (before the R2/R1 fraction) to reﬂect this reversal ofpolarities.These two ampliﬁer circuits we’ve just investigated serve the purpose of multiplying ordividing the magnitude of the input voltage signal. This is exactly how the mathematicaloperations of multiplication and division are typically handled in analog computer circuitry.• REVIEW:• By connecting the inverting (-) input of an op-amp directly to the output, we get negativefeedback, which gives us a voltage followercircuit. By connecting that negative feedbackthrough a resistive voltage divider (feeding back a fractionof the output voltage to theinverting input), the output voltage becomes a multipleof the input voltage.• A negative-feedback op-amp circuit with the input signal going to the noninverting (+)input is called a noninverting ampliﬁer. The output voltage will be the same polarity asthe input. Voltage gain is given by the following equation: AV = (R2/R1) + 1• A negative-feedback op-amp circuit with the input signal going to the ”bottom” of theresistive voltage divider, with the noninverting (+) input grounded, is called an invertingampliﬁer. Its output voltage will be the opposite polarity of the input. Voltage gain isgiven by the following equation: AV = -R2/R18.6An analogy for divided feedbackA helpful analogy for understanding divided feedback ampliﬁer circuits is that of a mechanicallever, with relative motion of the lever’s ends representing change in input and output voltages,and the fulcrum (pivot point) representing the location of the ground point, real or virtual.Take for example the following noninverting op-amp circuit. We know from the prior sectionthat the voltage gain of a noninverting ampliﬁer conﬁguration can never be less than unity (1).If we draw a lever diagram next to the ampliﬁer schematic, with the distance between fulcrumand lever ends representative of resistor values, the motion of the lever will signify changes involtage at the input and output terminals of the ampliﬁer: