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40 voutvin g 1 a ab 42 662 input and output impedance

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Unformatted text preview: n which precludes having B or A be a function of frequency. 40 6.6.2 Input and Output Impedance We can now also calculate the e ect that the closed-loop con guration has on the input and output impedance. The gure below is meant to clearly show the relationship between the de nitions of input and output impedances and the other quantities of the circuit. The quantity Ri represents the open-loop input impedance of the op-amp, that is, the impedance the hardware had in the absence of any negative feedback loop. Similarly, Ro represents the Thevenin source output impedance of the open-loop device. v in Ro Ri v out b B Figure 36: Schematic to illustrate the input and output impedance of a negative feedback con guration. We start the calculation of Zin with the de nition Zin = vin=iin. Let us calculate the current passing through Ri: , iin = vinR vb = vin , Bvout R i i Substituting the result of Eqn. 42 gives 1 v , Bv A  iin = R in in 1 + AB i Rearanging allows one to obtain Zin = vin=iin = Ri 1 + AB 43 A similar procedure allows the calculation of Zout vopen=ishort. We have vopen = vout and the shorted current is what gets when the load has zero input impedance. This means that all of the current from the ampli er goes into the load, leaving none for the feedback loop. Hence, B = 0 and Avout = Avout 1 + AB = vout 1 + AB  i = A v , Bv  =R = Av =R = short in This gives our result out o in o Ro G Ro Ro Zout = vopen=ishort = 1 + AB 41 A Ro 44 Therefore, the efect of the closed loop circuit is to improve both input and output impedances by the identical loop-gain factor 1 + AB  AB . So for a typical op-amp like a 741 with A = 103, Ri = 1 M , and Ro = 100 , then if we have a loop with B = 0:1 we get Zin = 100 M and Zout = 1 . 6.6.3 Examples of Negative Feedback Bene ts We just demonstrated that the input and output impedance of a device employing negative feedback are both improved by a factor 1 + AB  AB , the device loop gain. Now we give a simple example of the gain equation Eqn. 42 in action. An op-amp may typically have an open-loop gain A which varies...
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