Elements Of
Telecommunication
CHAPTER 3
FILTERS
Aim
To provide participants with the fundamental knowledge of filter
networks so that they can design and implement the networks
in telecommunication circuit to enable frequency selection.
Objectives
At the end of the chapter participants should be able to:
• Define filters and give practical applications of filters in
telecommunication.
• List types of filters and circuit symbols.
• Sketch frequency response characteristics of any filter network
• Use RC, LC and RLC to illustrate different types of filters
• Define resonance
• Find resonance frequencies, cut off frequencies, bandwidth,
circuit impedance and quality factor for the above filters
• Identify differentiating and integrating circuits using passive
components and determine their time constant.
Introduction
• “A filter” is a circuit which has the ability to discriminate
between signals at different frequencies
• It has an attenuation that varies with frequency in a particular
manner.
• If a signal with a number of different frequencies is applied to
its input some of those components will appear at its output
terminals, whilst others are greatly attenuated hence
suppressed.
Types of filters
• Four basic types of filter are available for use in telecommunication systems:
• the low-pass,
• the high-pass
• the band-pass and
• the band-stop.
• Filters can be designed using one of the following different techniques:
• resistor –capacitor RC
• resistor- inductor RL
• inductor-capacitor filters, LC
• crystal filters
• Filters can either be passive or be active
• Passive filters are made of passive components (inductance, capacitance, and resistance).
The term passive merely means that the filter circuit is constructed without an amplifying element.
• Active filters are the electronic circuits, which consist of active element like op-amp(s)
along with passive elements like resistor(s) and capacitor(s).
SYMBOLS
Low pass filter High pass filter
Band pass filter Band stop filter
Filter Design
• The transmission of an unwanted frequency through a
network can be prevented either by
• connecting a high impedance (at that frequency) in series
• and/or by connecting a low impedance in shunt, with the signal
path.
• The high series impedance will oppose the flow of currents, at
the unwanted frequencies through the network.
• The shunt impedance will bypass unwanted currents to earth.
Components used to design
filters
Capacitive Reactance
• Capacitive Reactance is the complex impedance of a capacitor
who’s value changes with respect to the applied frequency
• Capacitive Reactance has the electrical symbol “XC” and has
units measured in Ohms the same as resistance. It is
calculated using the following formula:
• Where:
• Xc = Capacitive Reactance in Ohms, (Ω)
• π (pi) = 3.142
• F = Frequency in Hertz, (Hz)
• C = Capacitance in Farads, (F)
Capacitive Reactance vs Frequency
• Capacitive reactance decreases with increase in frequency
Inductive Reactance
• Inductive Reactance is the complex impedance of a Inductor
who’s value changes with respect to the applied frequency
• Inductive Reactance has the electrical symbol “XL” and has
units measured in Ohms the same as resistance. It is
calculated using the following formula:
• Where:
• XL = Inductive Reactance in Ohms, (Ω)
• π (pi) = 3.142
• F = Frequency in Hertz, (Hz)
• L = Inductance in henrys, H
Inductive Reactance vs Frequency
• Inductive reactance increases with increase in frequency
Resistance vs frequency
• Resistance R has no dependency on frequency and, V=IR
Low pass filters
Low-Pass
• Low pass filter allows low frequencies to pass whilst blocking
high frequencies.
• Lo frequencies Should be able to pass, with zero attenuation,
all frequencies from zero up to a certain frequency which is
known as the CUT-OFF FREQUENCY (Fc).
• At frequencies greater than the cut-off frequency the
attenuation of the filter will increase with increase in
frequency.
• Low frequency signals are propagated through the filter
without loss.
RC Low-Pass Filter
• A Low pass RC filter, again, is a filter
circuit composed of a resistor and
capacitor.
• It passes through low-frequency signals
• While blocking high frequency signals.
• The resistor is placed in series to the
input signal.
• The capacitor is placed in parallel to the
input signal.
• we can create a RC circuit that allows a
range of frequencies below a certain
value to pass through the circuit
unaffected while any frequencies applied
to the circuit above this cut-off point to
be attenuated.
• Cut off frequency is given by :
LR low pass filter
• If a coil is used instead of
the capacitor, low-pass
filter can also be built.
• however, the output
voltage must be tapped
parallel to the resistor.
• The mode of operation is
exactly the opposite
• The cutoff frequency is
calculated with the
following formula for LR
low pass:
LC Low-Pass
• Inductance L is connected in series
with the signal and capacitance C
is connected in shunt
• L will allow the low frequencies to
pass whilst C will shunt high
frequencies to the ground
• The inductive resistance XL
increases with frequency while the
capacitive reactance XC is inversely
proportional to it
• The cutoff frequency is the
frequency at which XC=XL.
• Thus, at a frequency greater than
the cutoff frequency, XC is less
than XL. At a lower frequency, XC
is greater than XL.
• Cut off frequency is given by :
Low-Pass frequency response
• Any high frequency signals • Bandwidth is given
applied to the low pass filter
circuit above this cut-off
by:
frequency point will become
greatly attenuated, that is
they rapidly decrease.
• This happens because at very
high frequencies the
reactance of the capacitor
becomes so low that it gives
the effect of a short circuit
condition on the output
terminals resulting in zero
output.
High pass filters
High-Pass
• Transmits all frequencies which are higher than its out- off
frequency and to prevent the passage of all lower frequencies.
• At low frequencies the series capacitance C has a high
reactance and the shunt inductive reactance is low, so low-
frequency signals are attenuated as they travel through the
filter.
• At high frequencies, on, the other hand, the series reactance is
low and the shunt reactance is high and the filter offers zero
attenuation.
RC high-Pass Filter
• A high pass filter prevents frequencies
below its cut-off frequency from passing
and lets through signals above it.
• A high pass is used where low
frequencies are undesirable and
therefore should be filtered out.
• The capacitive reactance XC decreases
as the frequency increases, while the
ohmic resistance R remains constant.
• The cutoff frequency fc is the
frequency at which the resistances are
equal.
• Consequently, at a frequency above fc,
R>XC and at a lower frequency XC>R.
• Cut off frequency is given by :
LR high pass filter
• If a coil is used instead of
the capacitor, high -pass
filter can also be built.
• however, the output
voltage must be tapped
parallel to the coil.
• The mode of operation is
exactly the opposite
• The cutoff frequency is
calculated with the
following formula for LR
low pass:
LC high –Pass filter
• Inductance L is connected in shunt
with the signal and capacitance C
is connected in series
• C will allow the high frequencies
to pass whilst L will shunt low
frequencies to the ground
• The inductive resistance XL
increases with frequency while
the capacitive reactance XC is
inversely proportional to it
• The cutoff frequency is the
frequency at which XC=XL.
• Thus, at a frequency greater than
the cutoff frequency, XC is less
than XL. At a lower frequency, XC
is greater than XL.
• Cut off frequency is given by :
high-Pass frequency response
• The high pass filter is in • Bandwidth is given
many ways the inverse of
the low pass filter.
by:
• It only allows signals
through that are higher
than the cut-off frequency.
• Above this point it is
nominally flat,
• and below the RF filter cut-
off frequency the response
falls away at a rate
determined by the order of
the filter.
Bandpass filters
Band-Pass
• Ideally the filter passes with zero attenuation, a particular band of
frequencies and offers considerable attenuation to all frequencies
outside of this pass band.
• By connecting or “cascading” together a single Low Pass Filter circuit
with a High Pass Filter circuit, we can produce another type of passive RC
filter that passes a selected range or “band” of frequencies that can be
either narrow or wide while attenuating all those outside of this range
• At frequencies either side of the required pass band the tuned circuit
impedance have varied to such an extent that considerable attenuation is
offered.
Bandpass filter designs
RC Bandpass RL bandpass
LC Bandpass
Band-Pass frequency response
curve
• Bandwidth is given by:
• In addition to the two cutoff frequencies, the calculation of the center
frequency fc is also interesting.
• It forms the geometric mean of the upper limit frequency fH and the lower limit
frequency fL. The formula is:
Bandstop filters
Band-stop filters
• Ideally the filter attenuates a particular band of frequencies
and passes to all frequencies outside of this pass band.
• The terms “band reject filter” or “notch filter” are common
too.
• The name band stop has a circuit to attenuate a frequency
band or blocks.
• Frequencies outside of this band should pass with as little loss
as possible.
• A passive band stop filter basically consists of the parallel
connection of a high pass and a low pass.
Bandstop filter designs
RC LC
LC
Band-stop frequency response
curve
• Stop Bandwidth is given by:
• Pass band is given by:
• In addition to the two cutoff frequencies, the calculation of the center frequency fc is
also interesting.
• It forms the geometric mean of the upper limit frequency fH and the lower limit
frequency fL. The formula is:
RLC Filters
RLC low pass RLC high pass
RLC band pass RLC bandstop
Active filters
Active filters
• The term passive merely means that the filter circuit is
constructed with an amplifying element.
• are the electronic circuits, which consist of active element like op-
amp(s) along with passive elements like resistor(s) and
capacitor(s).
Active Filters
high pass
low pass
band pass bandstop
Any questions?
Thank you!
