Another variation of the opamp filter is the band stop or notch filter,
called like that because it is as if you cut a notch in the frequencies
that pass through the filter, allowing all frequencies outside the notch
to pass & blocking the frequencies in that range.
Just as the high pass filter is a variation of the low pass filter,
changing the reactive element from input to feedback, so is the band
stop filter a variation of the band pass filter, but instead of changing
components we are going to change the configuration of the components.
For this circuit, the input impedance consists of a resistor & capacitor in parallel (it was in series for the band pass), & the
feedback impedance will be a capacitor & resistor in series (was
parallel in bandpass). As you can see, only the connections change, the
components stay the same.
At low frequencies, the input impedance is dominated by the resistor,
since the reactance is much higher than the resistance (the connection
is in parallel, the equivalent is always lower than the lowest value).
At the same low frequencies, the feedback impedance is dominated by the
capacitor's reactance, since it is also high compared to the resistor
(the connection is in series, the equivalent is always higher than the
highest value).
The gain of the opamp, connected in an inverting amplifier
configuration, is given by -Zf/Zin. The input impedance Zin is very low,
near by the input resistance, & the feedback impedance is very high,
driven by the capacitors reactance; this makes the ratio very high,
tending towards infinity by the increasing Zf at lower & lower
frequencies (it is theoretically infinite at DC, or 0hz frequency).
One way to limit the gain, similar to what was done for the low pass
filter is to use a resistor in series with either the whole feedback
series connection or just across the capacitor. This makes the extremely
high reactance of the capacitor not dominate at very low frequencies,
instead the parallel connection is closer to the lower value, in this
case the resistor. This is done to ensure that the opamp does not go
into saturation, because if it does it clips the signal & distorts it.
At very high frequencies, the input impedance tends towards, since the
capacitor acts as a very low value. With the feedback connection, the
capacitor is also a very low value, but since there's the series
resistor, the impedance will be limited to that value.
Looking at the gain equation (-Zf/Zin), you can see that the gain tends
towards infinity, since the input impedance goes very low at high
frequencies. To limit this, you can put resistor in series with the
original parallel combination.
At intermediate frequencies, where the input impedance & feedback impedance are very close, the gain will be close to 1.
With all this, you can see that the notch filter is the opposite of the
band pass filter: the band stop filter highly amplifies signals above & below the "notch" or middle frequencies, & doesn't amplify
(instead of blocking) the intermediate frequencies. This is in contrast
with the band pass that attenuated signals above & below, & also
didn't amplify intermediate frequencies (gain of 1).
For all the filters discussed so far there are other far more efficient & that also block undesired signals & amplify the frequencies of
interest
