Filters are frequency-selective circuits designed to pass some frequencies and reject others. There are five basic kinds of filter circuits: low-pass, high-pass, band-pass, band-stop (band-reject), and all-pass filters. The cutoff frequency, which determines what frequencies are passed or rejected, depends on the circuit components like resistors and capacitors or inductors and capacitors. Common filter types include passive RC and RL filters as well as twin-T notch filters used to eliminate hum.

1. FILTERS & FOURIER
THEORY

2. Filters
A filter is a frequency-
selective circuit. Filters are
designed to pass some
frequencies and reject others.
There are numerous ways to
implement filter circuits.

3. •Simple filters created by using
resistors and capacitors or inductors
and capacitors are called passive
filters because they use passive
components that do not amplify.

4. The five basic kinds of filter circuits are as
follows:

8. The cutoff frequency, also known as the
critical frequency, is determined
by the expression

10. •The RL low-pass filters are not as
widely used as RC filters because
inductors are usually larger, heavier,
and more expensive than capacitors.
Inductors also have greater loss
than capacitors because of their
inherent winding resistance.

15. • Twin-T notch filters are used primarily at
low frequencies, audio and below. A
common use is to eliminate 60-Hz power
line hum from audio circuits and low-
frequency medical equipment amplifiers.
The key to high attenuation at the notch
frequency is precise component values.
The resistor and capacitor values must
be matched to achieve high attenuation.