Digital Signal Processing Reference
In-Depth Information
i
(
t
)
C
i
(
t
)
R
v
i
(
t
)
v
o
(
t
)
Figure 1.7
Integrating amplifier.
Substitution of (1.7) into (1.9) yields
t
1
RC
L
v
i
(t) - v
i
(t) -
v
i
(t)dt - v
o
(t) = 0.
(1.10)
-
q
Thus, the equation describing this circuit is given by
t
1
RC
L
v
0
(t) =-
v
i
(t)dt.
(1.11)
-
q
This circuit is called an
integrator
or an
integrating amplifier;
the output voltage is
the integral of the input voltage multiplied by a negative constant This in-
tegrator is a commonly used circuit in analog signal processing and is used in sever-
al examples in this topic.
If the positions of the resistance and the capacitance in Figure 1.7 are inter-
changed, the op-amp circuit of Figure 1.8 results. We state without proof that the
equation of this circuit is given by
(-1
>
RC).
v
o
(t) =-RC
dv
i
(t)
dt
.
(1.12)
(The reader can show this by using the previous procedure.) This circuit is called a
differentiator,
or a
differentiating amplifier;
the output voltage is the derivative of the
input voltage multiplied by a negative constant The differentiator has limited
use in analog signal processing, because the derivative of a signal that changes
(-RC).
R
i
(
t
)
i
(
t
)
C
v
i
(
t
)
v
o
(
t
)
Figure 1.8
Differentiating amplifier.
