Page 315 - Mechatronics with Experiments

October 28, 2014 11:15 254mm×178mm
Printer: Yet to Come
JWST499-c05
JWST499-Cetinkunt
ELECTRONIC COMPONENTS FOR MECHATRONIC SYSTEMS 301
Since we want v to have a gain of 1, then
1
R 2 R + R 4
3
= 1 (5.259)
R + R R
1 2 3
R = 2 ⋅ R 2 (5.260)
1
Let R = R = 10 kΩ, then R = R = 20 kΩ.
2 3 1 4
Derivative Op-Amp The desired function is to take the derivative of the input voltage
signal and provide that as an output voltage signal,
d
V (t) = K (V (t)) (5.261)
i
o
dt
Figure 5.35 shows an op-amp circuit for differentiation. Using the ideal op-amp assump-
tions, the input–output relationship is derived as follows,
dV (t)
i = C ⋅ i (5.262)
c
dt
i = i c (5.263)
f
V = R ⋅ i f (5.264)
f
V =−V f (5.265)
o
Hence,
dV (t)
V = (−RC) ⋅ i (5.266)
o
dt
Integrating Op-Amp If we change the locations of the resistor and capacitor in
the derivative op-amp, we obtain an integrating op-amp circuit (Figure 5.35). The desired
function is

V (t) = K (V ( )d ) + V (0) (5.267)
o ∫ i o
where V (0) is the initial voltage. The derivation of the I/O relationship is straightforward,
o
i = V (t)∕R (5.268)
i
c
i = i c (5.269)
f
t
1
V (t) = i ( )d (5.270)
f C ∫ f
0
V (t) =−V (t) (5.271)
o
f
t
1
=− V ( )d (5.272)
i
RC ∫ 0
where the initial voltage values in the integrations have been neglected.
Next we present the op-amp circuits and the input–output relation for filtering oper-
ations used in signal processing and control systems. We provide op-amp circuits for the
low pass, high pass, band pass, and band reject (notch) filters. It should be noted that
digital implementations of filters in software provide more flexibility than the analog op-
amp implementations. However, op-amp implementation is simpler as it does not require a
real-time software.
Low Pass Filter Op-Amp The low pass filter passes the low frequency content of
a signal and suppresses the high frequency content (Figure 5.36). The break frequency at