Page 305 - Mechatronics with Experiments

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JWST499-c05
JWST499-Cetinkunt
ELECTRONIC COMPONENTS FOR MECHATRONIC SYSTEMS 291
op-amp circuit determines whether input signal V is above or below the reference signal,
i
V . By changing the connection of V ref and V into (−) and (+) terminals, the output
ref
i
polarity of the op-amp is changed. The open loop op-amp circuit input–output relationship
as a comparator can be summarized as
V = K OL ⋅ (V − V ); (5.204)
ref
i
o
if − V sat < K OL ⋅ (V − V ) < V sat (5.205)
ref
i
= V ; if K OL ⋅ (V − V ) > V sat (5.206)
sat
ref
i
=−V ; if K OL ⋅ (V − V ) < −V sat (5.207)
ref
i
sat
Let us consider an op-amp with the following parameters,
6
K OL = 10 , V sat = 12 VDC (5.208)
Then, when the difference between the two input terminal voltages is within ±12 μV, the
output is proportional to the difference with a voltage output between ±12 V. Otherwise,
the output is either saturated at 12 V or at −12 V.
The same circuit is also used as a PWM modulator which converts the reference
V analog voltage level signal to a pulse width modulated (PWM) signal when V ref is a
i
fixed frequency periodic signal (i.e., triangular or sinusoidal signal). Similarly, compara-
tor op-amp configurations are also used as signal generator circuits. The LM311 (and
LM111/LM211) family of integrated circuit op-amps are commonly used as high-speed
comparators.
Example Consider the op-amp comparator circuits shown in Figure 5.29. Assume that
the resistances at the input terminals are
R = 4kΩ R = 6kΩ (5.209)
1 2
and the supply voltage V C1 = 10 VDC. Let the saturation output voltage be V sat = 13 VDC.
The input voltage v = 9 sin(2 t). Notice that the difference between the two circuits is the
in
connection of the reference voltage and input voltage to the op-amp terminals. Draw the
output voltage as function of time for both circuits. Notice that the reference voltage is

R 2 6
V = V = ⋅ 10 = 6 V (5.210)
ref C1
R + R 4 + 6
1 2
Notice that this is a comparator op-amp circuit. Let us neglect the raise time transient
of the output voltage response at this timescale range. Hence, we can show the change
−
+
of output state like a step function. When the (v − v ) > V ∕K ≈ 0.0, the output
sat OL
+
−
voltage is V = V and otherwise, when the (v − v ) < −V ∕K ≈ 0.0, the output
o sat sat OL
voltage is V =−V . For all practical purposes, for the first connection, when V > 6V,
o sat in
the V = V = 13 V, and when V < 6V, the V =−V =−13 V. For the second
out sat in out sat
configuration, the output polarity would be opposite to the first configuration. The input–
output voltage is shown in Figure 5.29.
Example The circuit shown in Figure 5.30 determines whether input voltage V is
in
inside the window defined by two reference voltages, V ref,l , V ref,h . The output voltage will
be V sat if the input voltage is outside the window. It will be −V sat if the input is inside the
voltage window defined by V ref,l , V ref,h . The LED will be ON when the input voltage is
outside the window.