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 opamp is much larger than any
other current path available to the inputs.
When we assume ideal opamp behavior, it means that we consider the golden rules to be
exact. We now use these rules to analyze the two most common opamp 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 Noninverting 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 opamp 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: Noninverting am...
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 Fall '12
 Soujanu
 Cybernetics, Positive feedback, de nition Zin

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