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Filters
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Filters
Electrical/Electronic filters are electronic circuits which perform
signal processing functions, specifically to remove unwanted
frequency components from the signal, to enhance wanted
ones, or both.
Audio equalizers and crossover networks are two well-known
applications of filter circuits.
Equalizers allow the amplitudes of several frequency ranges to
be adjusted to suit the listener's taste and acoustic properties
of the listening area. Crossover networks block certain ranges
of frequencies( low-frequency signals) from reaching tweeter
(high-frequency speakers).
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Types of Filters
Electronic Filters belong one of the following types:
• Digital Filters
• Sampled-data Filters
• Continuous-time Filters(Analog Filters)
Electronic filters can also be classified as
• Passive filter
• Active filter
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Types of Analog Filters
The commonly used Analog Filters belong to one of
the following types :
• Low-pass(LP)
• High-pass(HP)
• Band-pass(BP)
• Band-reject(BR)
• All-pass(AP)
• Amplitude Equalizer(AE)
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Low-pass(LP) Filter
A low-pass(LP) filter is a filter that passes lowfrequency signals but attenuates (reduces the
amplitude of) signals with frequencies higher than the
cutoff frequency.
A low-pass(LP) filter is the opposite of a high-pass(HP)
filter.
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Ideal LP response
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Continuous-time LP Filter
An ideal LP filter completely eliminates all frequencies
above the cutoff frequency while passing those below
unchanged.
Ideal LP frequency response is a rectangular function,
and is a brick-wall filter. The transition region present in
practical filters does not exist in an ideal filter.
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Frequency response of 1st order LP Filter
The gain-magnitude frequency response of a first-order (one-pole) low-pass
filter. The voltage gain is shown in decibels .At cut-off frequency there is a 3
dB decline .Angular frequency is shown in units of radians per second.
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Stop-band response of LP Filter
For a first-order LP filter ,the attenuation rate in the stop-band
is 20 dB per decade.
A second-order filter attenuates higher frequencies more
steeply. In general a second-order Butterworth filter exhibits
the 40 dB per decade attenuation rate in the stop-band. Other
all-pole second-order filters may roll off at different rates
initially depending on their Q-factor, but approach the same
final rate of 40 dB per decade.
Third- and higher-order filters are defined similarly. In general,
the final rate of power roll off for a nth order LP filter is 20n dB
per decade.
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Passive RC first order LP filter
The combination of resistance and capacitance gives
you the time constant of the filter τ = RC (represented by
the Greek letter tau)
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
An active low-pass filter
First-order
Low Pass Butterworth Filter
First-order Low-Pass(LP) Butterworth Filter
This 1st-Order low pass Butterworth type filter, consists simply of a passive RC
filter connected to the input of a non-inverting operational amplifier. The
frequency response of the circuit will be the same as that of the passive RC filter,
except that the amplitude of the output signal is increased by the pass band
voltage gain of the amplifier.
The gain in the pass band is −R2/R1
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
An active low-pass filter
First-order
Low Pass Butterworth Filter
Voltage Gain for a First-order Low-Pass(LP) Filter
Where AF = the pass band gain of the filter,
(1 + R2/R1)
ƒ = the Frequency of the Input Signal in Hertz,
(Hz)
ƒc = the Cut-off Frequency in Hertz, (Hz)
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
High-pass Filter
• A high-pass(HP) filter offers easy passage to
high-frequency signal and attenuates the lowfrequency signal.
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Passive High-pass(HP) Filter
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Frequency response of 1st order HP Filter
The cutoff frequency for a high-pass filter is that frequency at
which the output voltage equals 70.7% of the input voltage. Above
the cutoff frequency, the output voltage is greater than 70.7% of
the input, and vice versa.
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
First-order High Pass Butterworth Filter
First-order High-Pass(HP) Butterworth Filter
Voltage gain of a first-order High-Pass(HP) Filter
Where
AF = the Pass band Gain of the filter, (1 + R2/R1)
ƒ = the Frequency of the Input Signal in Hertz, (Hz)
ƒc = the Cut-off Frequency in Hertz, (Hz)
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Band-pass(BP) filter
The Band-Pass(BP) filter passes a selected range or band of
frequencies that can be either narrow or wide while attenuating all
those outside of this range.
The Band-Pass(BP) filter can be of two types:
• Broad-band Band-Pass filter
• Narrow-band Band-Pass filter
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Band-pass(BP) filter
Frequency Response of a 2nd order Band-Pass(BP) Filter
The term "bandwidth" refers to the difference between the lower
cut-off frequency(ƒcLOWER) and the upper cut-off frequency
(ƒcUPPER) points.
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Active Band Pass Filter Circuit
Band-pass(BP) filter
A band-pass(BP) filter arrangement commonly consists of
combination of a Low-pass (LP) and a High-pass(HP) filter.
2nd order Band-Pass(BP) Filter
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
a
:
Wide-band and narrow-band BP Filter
:
The "Q" of a BP filter is the ratio of the
Resonant Frequency, (ƒr) to the
Bandwidth(BW) and is given as:
In BP Filter, the width of the pass-band between the upper and lower-3dB
corner points determine the Quality Factor(Q-point) of the circuit. This Q Factor
is a measure of how "Selective" or "Un-selective" the band pass filter is
towards a given spread of frequencies.
The lower the value of the Q factor the wider is the bandwidth of the filter and
consequently the higher the Q factor the narrower and more "selective" is the
filter.
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Band-Reject(BR) Filter
A band-stop filter or band-rejection filter passes most
frequencies unaltered, but attenuates those in a specific range to
very low levels. It is the opposite of a band-pass filter.
A notch filter is a band-stop filter with a very narrow stop
band.(high Q factor).Notch filters are used in live sound
reproduction(Public Address systems, also known as PA systems)
and in instrument amplifier(especially amplifiers or preamplifiers
for acoustic instruments such as acoustic guitar, mandolin etc.) to
reduce the noise and unwanted frequencies.
e.g., Anti-hum filter is used to filter out the mains hum from a 50
Hz power line, though its higher harmonics could still be present.
The filter passes all frequencies, except for the range of 49–51
Hz.
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Frequency response of BS filter
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
All-pass Filter
The all-pass filter is an important building block in audio
signal processing systems. It is called all-pass because
all frequencies are passed equally.
In other words, the amplitude response of an all-pass
filter is any nonzero constant at each frequency, but filter
changes the phase relationship between various
frequencies.
Generally, the first-order all-pass filter is described by
the frequency at which the phase shift crosses 90°
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Phase response of 1st order All-pass Filter
For 1st order all-pass filter ,the amplitude response is flat (within
the bandwidth limitation of the amplifier), and there is a 90 degree
phase shift at the "corner" frequency.
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
Applications of All-pass Filters
All pass filters are most often used for following:
• for matching phase in systems where phase is
important
• for producing delays in circuits that need to
delay a signal
• for creating 90o shifts for quadrature modulators
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA
END
Department of Electronics and Communication Engineering,
Manipal Institute of Technology, Manipal, INDIA

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