Page 309 - Mechatronics with Experiments

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JWST499-c05
JWST499-Cetinkunt
ELECTRONIC COMPONENTS FOR MECHATRONIC SYSTEMS 295
+
−
+
must be met: v < v = 0.0. Then, again referring to the equation describing v , this can
happen if
R V + R V < 0.0 (5.222)
f i i o
R V + R V < 0.0 (5.223)
f i i sat
R i
V < − V sat (5.224)
i
R f
Hence, the op-amp output will switch from V = V sat state to V =−V sat state when V ≤
i
o
o
R i
− V . Similarly, the op-amp output will switch from V =−V sat state to V = V sat state
o
sat
o
R f
when V ≥ R i V .
i sat
R f
Notice that the nonlinear hysteresis function is accomplished by the feedback of the
output signal to the noninverting (positive) input of the op-amp, not the negative input.
Feedback to the negative input is used for implementing linear functions with an op-amp.
Schmitt trigger functionality is also used in digital circuits. For instance, the desired
output of a device is ON (for 5 VDC) or OFF (for 0 VDC). The input voltage might not be
exactly 0 VDC or 5 VDC but somewhere in between (Figure 5.32). Instead of defining a
single transition voltage, a hysteresis region can be defined at 3.0 VDC with a 2.0 (+1 and
−1) VDC hysteresis. This would result in an ON output state when voltage transitions from
0 VDC to 5 VDC at 4 VDC and above, and back to the OFF state when the input signal
transitions from 5 VDC region to 0 VDC region at 2 VDC and below. Schmitt triggers are
used in de-bouncing of input signals, and avoiding unintended ON/OFF state changes due
to noise. For instance, when a mechanical or electromechanical input switch is closed or
opened, the transition from ON to OFF state, or OFF to ON state, does not happen in one
single clean switching but by bouncing of the contact. This results in a noisy input signal
as shown in Figure 5.32c. Schmitt triggers can be used to “clean-out” or “de-bounce” the
switch signal. Digital IC packages typically have two, four, six or more Schmitt triggers in
one DIP package (i.e., 7413, 7414, 7418, 7419, 74310, 4093, 40106, 4024, 4040, 4022).
Example Consider the op-amp circuit shown in Figure 5.31b. Let us assume that the
saturation voltage is V sat =±13 V and that the input signal V (t) is a sinusoidal signal with
i
magnitude 10 V and frequency 10 Hz,
V (t) = 10 sin(2 t) (5.225)
i
Draw the output voltage of the op-amp for the following values of the feedback resistors,

1. R = 100 kΩ, R = 100 Ω
1 2
2. R = 100 kΩ, R = 100 kΩ
1 2
For case 1, the width of the hysteresis voltage, V is
T
R 2 100
V = ⋅ V sat = ⋅ 13 (5.226)
T
R + R 100 000 + 100
1 2
= 13∕1001 V ≈ 13 mV (5.227)
The output voltage will switch between V sat =+13 V and −V sat =−13 V when the input
signal passes the band of −13 mV and 13 mV around zero voltage. Due to the hysteresis,
the output state switching is dependent upon the previous direction of the input voltage
crossing the hysteresis band. Notice that due to the scale, the hysteresis behavior is not
visually detectable in the figure.