6.1 Principles of Active Filtering

Filters are electronic circuits designed to pass signals with specific frequency components while rejecting or attenuating others. Passive filters are constructed solely from passive components (resistors, capacitors, and inductors). In contrast, active filters incorporate an active element, such as an Op-Amp, along with passive components. This allows for gain, buffering, and the elimination of bulky inductors.

Active filters are classified into four main types based on their frequency response:

1. Active Low Pass Filter: Passes low-frequency components and rejects high-frequency components.
2. Active High Pass Filter: Passes high-frequency components and rejects low-frequency components.
3. Active Band Pass Filter: Passes a specific band of frequencies, rejecting frequencies both below and above this band.
4. Active Band Stop Filter: Rejects a specific band of frequencies, passing frequencies both below and above this band.

Active Low Pass Filter

An active low pass filter is typically constructed by connecting a passive RC low pass filter to the input of a non-inverting amplifier. The passive filter stage determines the frequency cutoff characteristic, while the Op-Amp stage provides signal gain and buffering. The gain of the filter is determined by the amplifier’s feedback resistors and is given by \left(1+\frac{R_f}{R_1}\right).

Active High Pass Filter

Similarly, an active high pass filter is constructed by connecting a passive CR high pass filter to the input of a non-inverting amplifier. The passive stage allows high frequencies to pass to the amplifier, which then provides gain and buffering. The overall gain is again determined by the amplifier stage.

Active Band Pass Filter

An active band pass filter can be created by cascading an active high pass filter with an active low pass filter. The high pass filter sets the lower cutoff frequency, and the low pass filter sets the upper cutoff frequency. Only the frequencies that fall between these two cutoff points are passed by the combined circuit.

Active Band Stop Filter

An active band stop filter is constructed by connecting an active low pass filter and an active high pass filter in parallel. The outputs of both filters are then fed into a summing amplifier. By setting the cutoff frequency of the low pass filter to be lower than the cutoff frequency of the high pass filter, the circuit passes both very low and very high frequencies, while the summing amplifier effectively creates a “notch” or stop-band for the frequencies in between.

These Op-Amp-based circuits represent general-purpose building blocks. We now turn to specialized integrated circuits designed for distinct functions.