A notch filter is a frequency selective filter that attenuates signals at a specific center frequency, creating a null or deep notch in the filter's frequency response. Notch filters work by introducing a pair of complex conjugate zeros on the unit circle at the angle of the frequency to be eliminated. They are commonly used to remove hum and interference from power lines, measure non-linearities of power amplifiers by avoiding the carrier frequency, and in applications like Raman spectroscopy and laser-based fluorescence instrumentation that require eliminating specific frequency components. Examples given include an anti-hum filter that passes all frequencies between 59-61 Hz except 60 Hz to remove mains hum, and a very narrow notch filter used in radio frequencies to avoid overloading a spectrum

1. NOTCH FILTERS
-PRAKASH KUMAR [13209]
-EED (III YEAR)

2. GENERAL
 A Filter is an electrical circuit that is designed to pass a specified band of
frequencies while attenuating all the signals outside that band.
 It is a frequency selective circuit.
 The filters are basically classified as active filters & passive filters.
 They are used in circuits which require the separation of signals according
to their frequencies.
 They are widely use in communication & signal
processing.

3. Filters
Background:
. Filters may be classified as either digital or analog.
. Digital filters are implemented using a digital computer or
special purpose digital hardware.
. Analog filters may be classified as either passive or
active and are usually implemented with R, L, and C
components and operational amplifiers.

4. COMMONLY USED FILTERS
The most commonly used filters are :-
 Low Pass Filter
 High Pass Filter
 Band Pass Filter
 Band Reject Filter
 All Pass Filter
 Notch Filter
 Comb Filter

5. NOTCH FILTER
 A notch filter is a filter that contains one or more deep notches or, ideally ,
perfect nulls in its frequency response.
 Notch filters are useful in many applications where specific frequency
components must be eliminated.

7.  To create a null in the frequency response of a filter at a frequency
ω0, introduce a pair of complex-conjugate zeros on the unit
circle at the angle ω0.
 Hence, the zeros are selected as z1,2 = e±jω0
Then, the system function for the notch filter is
H(z) = b0(1 − ejω0z−1)(1 − e−jω0z−1)
= b0(1 − (2 cos ω0)z−1 + z−2) where b0 is a gain factor.
 Figure illustrates the magnitude response of a notch filter having a null at ω = π/4.

9. APPLICATION OF NOTCH FILTER
IN OPTICS
Notch Filters are used in Raman spectroscopy, confocal or multi-photon
microscopy, laser-based fluorescence instrumentation, or other life science
applications.
IN COMMUNICATION
Notch filters are used in the for applications like elimination of 50- and 60-Hz
hum components to avoid interference of power frequency with Communication
channels.

10. EXAMPLES
In the audio domain
Anti-hum filter
For countries using 60 Hz power lines:
•Low Freq: 59 Hz
•Middle Freq 60 Hz
•High Freq: 61 Hz
This means that the filter passes all frequencies, except for the range of 59–61 Hz. This would be used
to filter out the mains hum from the 60 Hz power line, though its higher harmonics could still be
present.
For countries where power transmission is at 50Hz, the filter would have a 49–51 Hz range.
In the radio frequency (RF) domain
Non-linearities of power amplifiers
When measuring the non-linearities of power amplifiers, a very narrow notch filter can be very useful
to avoid the carrier frequency. Use of the filter may ensure that the maximum input power of a
spectrum analyser used to detect spurious content will not be exceeded.