Filters overview
- an overview of the types of filter and the various design
considerations and parameters
Filters of all types are required in a variety of
applications from audio to RF and across the whole spectrum of frequencies. As
such filters form an important element within a variety of scenarios, enabling
the required frequencies to be passed through the circuit, while rejecting those
that are not needed.
The ideal filter, whether it is a low pass, high pass, or
band pass filter will exhibit no loss within the pass band, i.e. the frequencies
below the cut off frequency. Then above this frequency in what is termed the
stop band the filter will reject all signals.
In reality it is not possible to achieve the perfect pass
filter and there is always some loss within the pass band, and it is not
possible to achieve infinite rejection in the stop band. Also there is a
transition between the pass band and the stop band, where the response curve
falls away, with the level of rejection rises as the frequency moves from the
pass band to the stop band.
Filter types
There are four types of filter that can be defined. These are low pass, high
pass, band pass and band reject filters. As the names indicate, a low pass
filter only allows frequencies below what is termed the cut off frequency
through. This can also be thought of as a high reject filter as it rejects high
frequencies. Similarly a high pass filter only allows signals through above the
cut off frequency and rejects those below the cut off frequency. A band pass
filter allows frequencies through within a given pass band. Finally the band
reject filter rejects signals within a certain band. It can be particularly
useful for rejecting a particular unwanted signal or set of signals falling
within a given bandwidth.
Types of filter
Filter frequencies
A filter allows signals through in what is termed the pass band. This is the
band of frequencies below the cut off frequency for the filter.
The cut off frequency of the filter is defined as the point
at which the output level from the filter falls to 50% (-3 dB) of the in band
level, assuming a constant input level. The cut off frequency is sometimes
referred to as the half power or -3 dB frequency.
The stop band of the filter is essentially the band of
frequencies that is rejected by the filter. It is taken as starting at the point
where the filter reaches its required level of rejection.
Filter classifications
Filters can be designed to meet a variety of requirements. Although using the
same basic circuit configurations, the circuit values differ when the circuit is
designed to meet different criteria. In band ripple, fastest transition to the
ultimate roll off, highest out of band rejection are some of the criteria that
result in different circuit values. These different filters are given names,
each one being optimised for a different element of performance.
Butterworth: This type of filter provides
the maximum in band flatness.
Bessel: This filter provides the optimum
in-band phase response and therefore also provides the best step response.
Chebychev: This filter provides fast roll
off after the cut off frequency is reached. However this is at the expense of in
band ripple. The more in band ripple that can be tolerated, the faster the roll
off.
Elliptical: This has significant levels of
in band and out of band ripple, and as expected the higher the degree of ripple
that can be tolerated, the steeper it reaches its ultimate roll off.
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