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# These rules consist of the following two statements 1

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Unformatted text preview: ssed below. These rules consist of the following two statements: 1. The voltage di erence between the inputs, V+ , V, , is zero. Negative feedback will ensure that this is the case. 35 2. The inputs draw no current.  This is true in the approximation that the Zin of the op-amp is much larger than any other current path available to the inputs. When we assume ideal op-amp behavior, it means that we consider the golden rules to be exact. We now use these rules to analyze the two most common op-amp con gurations. 6.2 Inverting Ampli er The inverting ampli er con guration is shown in Fig. 30. It is inverting" because our signal input comes to the ," input, and therefore has the opposite sign to the output. The negative feedback is provided by the resistor R2 connecting output to input. R2 R1 - VIN VOUT + Figure 30: Inverting ampli er con guration. We can use our rules to analyze this circuit. Since input + is connected to ground, then by rule 1, input , is also at ground. For this reason, the input , is said to be at virtual ground. Therefore, the voltage drop across R1 is vin , v, = vin, and the voltage drop across R2 is vout , v, = vout. So, applying Kircho 's rst law to the node at input ,, we have, using golden rule 2: i, = 0 = iin + iout = vin=R1 + vout=R2 or G = vout=vin = ,R2=R1 34 The input impedance, as always, is the impedance to ground for an input signal. Since the , input is at virtual ground, then the input impedance is simply R1: Zin = R1 35 The output impedance is very small  1 , and we will discuss this again soon. 6.3 Non-inverting Ampli er This con guration is given in Fig. 31. Again, its basic properties are easy to analyze in terms of the golden rules. vin = v+ = v, = vout 36  R1  R1 + R2 where the last expression is from our voltage divider result. Therefore, rearranging gives 36 G = v =v = R1 + R2 = 1 + R2 out in R1 R1 The input impedance in this case is given by the intrinsic op-amp input impedance. As mentioned above, this is very large, and is typically in the following range: Zin  108 to 1012 VIN 37 + VOUT R2 R1 Figure 31: Non-inverting am...
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