Another method to create active filters using opamps is to create a
voltage divider with a resistance & a reactance (from a capacitor).
This approach has some advantages over the previously mentioned filters:
they are easy to build, easy to understand, & have "programmable"
gain.
In the reactive voltage divider, the input is applied to the non
inverting input of the opamp. This is so that it can be used as a simple
non inverting amplifier, the gain being set by extra resistors that do
not interfere or need to be considered much in the filter's working;
they are just there to set the amplifier feedback's gain.
The signal is applied in series with one of the components & taken at
the input in parallel with the second. The choice of which component is
in series & which in paralel with the non inverting input has direct
consequences in the functioning of the filter.
If the series component is chosen to be a resistor, then the voltage at
the capacitor will determine the signal to be amplified. Since the
reactance of the capacitor gets lower with frequency, the higher the
frequency the lower the signal available at the opamp input (remember
the voltage divider formula: (Vin*R2)/(R1 + R2), in this case, it
becomes (Vin*Xc)/(Xc + R) where Xc is the capacitive reactance); This
configuration gives us a low pass filter.
With the capacitor being the series component, the voltage at the
resistor now determines the signal available at the opamp input. As the
frequency gets higher, the capacitor's reactance lowers, up to the point
where it acts almost as just a wire; this means that the higher the
frequency the more signal available to the opamp. This configuration
gives us a high pass filter.
These two main types of voltage divider filters can be cascaded (The
output of the first used the the input of the second) in a single stage
(one opamp, multiple voltage dividers) or multiple stages (one opamp per
voltage divider), the latter having better characteristics due to the
opamp's compensating mechanisms.
