Page 849 - Mechanical Engineers' Handbook (Volume 2)

840 Mechatronics

V (s) R 1 (35)
out
I (s) (L/R ) s (1 R /R )
1
L
L
in
2 OPERATIONAL AMPLIFIERS
Operational amplifiers, or op amps, are extremely useful in mechatronics. They are primarily
used to modify an analog signal, such as increasing the voltage output of a strain gauge
circuit or removing noise from a signal. They are often used to amplify, sum, subtract,
integrate, or differentiate analog signals. They are also used to create active filters. They are
active devices in that they add energy to the circuit.
Consider the ideal op amp model in Fig. 26. All voltages shown in the figure are
referenced to the same ground. As active elements, the op amp adds energy to the circuit
through the power supplied by V , V (V is often but does not have to be 15 V). The
s
s
s
supply voltages are often left off Fig. 26 for convenience.
Circuit analysis of op amps requires only two additional observations. For ideal op amp
behavior it must be remembered that
V (V V ) 0 (36)

or
V V (37)

and
i i 0 (38)

It should also be noted that, in general,
0 (39)
i out
Op amps produce an output voltage (V ) that is related to an input voltage (V , not
out in
necessarily V or V ). The relationship can frequently be viewed as a gain defined by

A V out (40)
v
V in
The op amp generally has a very high input impedance (ideally infinite) defined by

Z V in (41)
in
i in

Inverting
input terminal
+V s

i –
V – – I out
i +
V out
V + +

Noninverting –V s
input terminal Figure 26 Ideal operational amplifier.