C,
R2
R,
Input Rout
Output
R3
Figure 3-26. Schematic of an example active integrator.
In practice, active integrators never have an ideal response. Figure 3-26 shows an
example active integrator. An ideal active integrator would only have a capacitor in the
feedback loop of the op-amp, however the resistor is required to have a DC feedback
path. If this were not present, the active integrator would integrate the small DC offset
voltage present at the input of the op-amp until the output saturated.
This feedback resistor has the effect of limiting the low-frequency response of the
active integrator, which can be viewed in the time domain as introducing a decay time
constant into the system. The reader can easily verify, using simple circuit analysis,
that the decay time constant of the example active integrator is given by
S= R2C1 (3-119)
In addition, the output of an active integrator is not just the integral of the input,
but the integral of the input multiplied by a constant. This constant is referred to as the
integration constant, kit, and is expressed in units of s-1. For the example integrator,