NOTCH FILTERS-PRAKASH KUMAR [13209]

-EED (III YEAR)

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.

FiltersBackground:

. 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.

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

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.

To create a null in the frequency response of a filter at a frequencyω0, introduce a pair of complex-conjugate zeros on the unitcircle 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.

APPLICATION OF NOTCH FILTER

IN OPTICSNotch 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.

EXAMPLESIn the audio domain

Anti-hum filterFor countries using 60 Hz power lines:•Low Freq: 59 Hz•Middle Freq 60 Hz•High Freq: 61 HzThis 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 amplifiersWhen 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.