Page 781 - Mechatronics with Experiments

LABORATORY EXPERIMENTS 767
Theory
Comparator op-amp circuits employing positive feedback are widely known as Schmitt
trigger circuits. The addition of positive feedback results in an effect called hysteresis.
Hysteresis is a phenomenon in which the transition point of the output signal as function
of the input signal is different when switching from the low state to the high state as
compared with switching from the high state to the low state. In other words, the transition
point is direction sensitive. Op-amp comparator circuits with hysteresis are used to reduce
the possibility of undesirable state changes due to spurious noise pickup. Schmitt trigger
circuits are also used in the digital I/O interfaces to remove the intended ON/OFF switching
of the digital I/O, such as the so-called switch debouncing.
The hysteresis effect is often a desirable feature in many ON/OFF control systems.
Such control systems are called relay (ON/OFF) control with hysteresis.
Consider an inverting Schmitt trigger op-amp (Figure 11.14). The voltage at the (+)
terminal is the same as the voltage across R ,
2
R 2 R 2
+
v = V R2 = ⋅ V = ⋅ V sat (11.77)
o
R + R 2 R + R 2
1
1
Let V = V . The output of the amplifier is essentially always saturated depending on the
T R2
signals on its input terminals (+) and (−). The hysteresis band between input and output,
V is
T
R 2
V = ⋅ V sat (11.78)
T
R + R 2
1
Let us trace the operation on the op-amp along the input–output relationship curve
that has the hysteresis loop. Note that the input–output relationship of the op-amp is
+
V = V sat if v > v − (11.79)
0
+
V =−V sat if v < v − (11.80)
0
V V
_ V o i _ o
v + + +
v + R
V R R 1
i i f
R R 2
R V = 2 V sat
T
i
V = V R + R
T sat 1 2
R
f
V
V o o
D +V sat C A +V
sat
–V V –V V
T T T T
V i V i
B B
A – V D – V
sat sat C

(a) (b)
FIGURE 11.14: Schmitt trigger: (a) non-inverting, and (b) inverting configuration, ON/OFF
output with hysteresis function.