Page 313 - Mechatronics with Experiments

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JWST499-c05
JWST499-Cetinkunt
ELECTRONIC COMPONENTS FOR MECHATRONIC SYSTEMS 299
As a result, the input voltage range is limited to the ±6.5 V range. Beyond that, the output
voltage saturates at 13 V.
Notice that a typical op-amp can handle input voltages up to the supply voltage values
or a few volts less. However, the feedback resistor values can be such that the output of
the linear amplifier saturates much earlier than the maximum input voltage the op-amp can
accept. For further discussion, consider the same example with R = 1kΩ and R = 99 kΩ.
f
i
Then, the nominal gain of the noninverting op-amp is 100.0. The output voltage would
saturate when the input voltage is outside the range of ±0.13 V.
Differential Input Op-Amp The desired function is to determine the difference
between two signals and possibly multiply the difference with a gain,
V = K ⋅ (V − V ) (5.247)
o 1 2
which is used in closed loop control circuits as the summing junction that is find the
difference between a command signal and sensor signal. (Figure 5.35a) shows a differential
input op-amp circuit. In its general form, the input–output relationship can be obtained
using the superposition principle. The output is the sum of the outputs due to the inverting
input and the noninverting input. The superposition principle can be used in the derivation:
′
(i) connect V to ground and solve for v = K ⋅ V , and (ii) connect V to ground and solve
2 o 1 1 1
′′
′
′′
for v = K ⋅ V . Then, add them together to get V = v + v . The output due to input at
o 2 2 o o o
its noninverting terminal is (Figure 5.34b)
R
+ 2
v = V 1 (5.248)
R + R 2
1
R + R
3
′
v
v = 4 + (5.249)
o
R 3
R + R 4 R 2
3
= ⋅ V 1 (5.250)
R 3 R + R 2
1
And the output due to input at its inverting terminal is (Figure 5.34a)
R 4
′′
v =− ⋅ V (5.251)
o 2
R 3
The total output is
′
V = v + v ′′ (5.252)
o
o
o
( )( ) ( )
R 2 R + R 4 R 4
3
V = ⋅ V − ⋅ V (5.253)
o 1 2
R + R R R
1 2 3 3
Note that when R = R = R = R , the input–output relationship is
2
1
4
3
V = V − V (5.254)
o 1 2
Similarly, when R = R = R and R = R = K ⋅ R,
2
3
4
1
V = K ⋅ (V − V ) (5.255)
1
2
o
One of the main usages of differential op-amps is in amplifying noise sensitive signals.
As discussed in Figure 5.25, single-ended signals are referenced with respect to ground.
Any noise induced on the signal wire coming into the op-amp would be amplified. This is
particularly problematic when the noise signal is comparable to the actual signal magnitude.
In such cases, it is best to transmit the signal voltage in differential-ended format. That is
using two wires and the signal information is the voltage difference between the two wires.
If any noise is induced during the transmission, it would be induced on both lines and the