Page 850 - Mechanical Engineers' Handbook (Volume 2)

2 Operational Amplifiers 841

For real op amps the input impedance is usually 100 k . Op amps also have a very low
output impedance (ideally zero) defined by
V
Z out (42)
out
i out
For real op amps this is usually less than a few ohms.
Circuits for two of the most common op amps, the inverting op amp and the noninverting
op amp, are analyzed in Figs. 27 and 28.

2.1 Inverting Amplifier
Apply op amp rules:

V 0 (43)
or
V V (44)

i i 0 (45)

Kirchhoff’s current law gives
i i Rƒ i (46)
R
Kirchhoff’s voltage law gives
V iR 0 (47)
in
in
V in i (48)
R in

V out iR 0 (49)
out
ƒ
V
out i out (50)
R ƒ
Setting i i gives
in out
V in V (51)
R R ƒ
or

R f i Rf

R i R
–
+ +
+
V in V out
C
– –
Figure 27 Inverting operational amplifier.