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 closedloop 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 openloop input impedance of the opamp, 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 openloop 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 loopgain factor 1 + AB AB . So for a typical opamp 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 opamp may typically have an openloop gain A which varies...
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 Fall '12
 Soujanu
 Cybernetics, Positive feedback, de nition Zin

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