This document contains a project report submitted by three students, Kul Vaibhav, Manish Kumar, and Munna Kumar, for their Bachelor of Technology degree. The report describes their project on RF filter design conducted under the guidance of their professor, Avishek Das. The report includes an introduction to electronic filters and RF filters. It then discusses different types of filters including Butterworth, Bessel, and Chebyshev filters. The report also covers the design of bandpass filters and their applications.

1. 1
Declaration
We declare that the project entitled “RF Filter Design” ,being submitted in partial fulfilment under
the guidance of Prof. Mr. Avishek Das for the award of Bachelor of Technology degree in
Electronics & Communication Engineering, affiliated to Maulana Abul Kalam Azad University of
Technology, is the work carried out by us.
The information provided is correct to the best of our knowledge and belief.
Submitted By :
Kul Vaibhav (13/ECE/45)
Manish Kumar (13/ECE/46)
Munna Kumar (13/ECE/54)

2. 2
Certificate of Approval
This is to be certified that Mr. Kul Vaibhav, Mr. Manish Kumar, and Mr. Munna Kumar students
of 4th
year B.Tech of Electronics & Communication Department,Haldia Institute of Technology,
have submitted their project report entitled “RF Filter Design” ,which is a bonafide work carried
out by themselves in partial fulfillment of Bachelor of Technology, Degree in Electronics &
Communication Engineering from Maulana Abul Kalam Azad University of Technology, West
Bengal.
The work has been carried out under our supervision during the academic session 2016-2017.
Head of Department
Electronics & Comm. Engg. Signature of the Guide
Date : Date :

3. 3
Acknowledgement
We express our sincere thanks to Prof. Mr. Avishek Das, Department of Electronics &
Communication Engineering, Haldia Institute of Technology, my project in-charge,who guided
me through the project also gave valuable suggestions and guidance for completing the project.He
helped us to understand the intricate issues involved in project-making besides effectively
presenting it.These intricacies would have been lost otherwise.Our project on the way of success
only because of his guidance.
Our thanks and appreciations also go to our colleague in developing the project and people who
have willingly helped us out with their abilities.
We are also thankful to the whole ECE department for providing us the technical support to carry
out the project work , to let us utilize all the necessary facilities of the institute and guidance at
each and every step during the project work. We would like to express our deepest appreciation to
all those who provided us the possibility to complete this report.
Kul Vaibhav (13/ECE/45)
Manish Kumar (13/ECE/46)
Munna Kumar (13/ECE/54)
Department of ECE
4th
Year, VII Semester

4. 4
Abstract
Electronic filters are circuits which perform signal processing functions, specifically to remove
unwanted frequency components from the signal, to enhance wanted ones, or both. Electronic
filters can be: passive or active.
An RF Filter, or radio frequency filter, is an electronic filter which is designed to operate on
signals in medium to extremely high frequencies. These ranges are used in radio, television and
wireless communications. Therefore most RF devices include some kind of filtering on the signals
transmitted or received.
The main categories of filters are defined in terms of the general response types of lowpass,
bandpass, highpass, and bandstop. The basic concepts of filters including transfer function,
insertion loss, return loss, phase delay and group delay, are described. Filter characteristics such
as maximally flat or Butterworth, equally ripple or Chebyshev, elliptic function, generalized
Chebyshev or pseudoelliptic, and maximally flat time delay are discussed in terms of the poles of
transfer function. Two-port lumped-element lowpass prototype networks and their element values
and filter transformations are given. Richards’ transformation and Kuroda's transformations (or
identities), impedance, and admittance inverters are also investigated, which are required for
transforming lumped elements to transmission-line sections, for separating physically filter
elements and changing impractical elements into more realizable elements in a filter network.
Bandpass filters are two-port devices that provide transmission at frequencies within the passband
of the filter and attenuation of other frequencies outside of the band. A band pass filter is used to
prevent interference of signals and effectively utilize a frequency. A bandpass filter is the parts
used at the mobile radio communication base station such as a cellular mobile telephone, a personal
communications service (PCS) and a wireless local loop (WLL), and a radio frequency (RF) band.
The role which a bandpass filter is to fulfill is transmitting to a few loss signals which lie in a
desired frequency band while intercepting all the frequencies outside the desired band. A bandpass
filter freely passes frequencies within specified range, while rejecting frequencies outside the
specified limits, and can be designed to provide symmetric or asymmetric characteristics. In
microwave communications, the microwave frequency spectrum has become severely crowded
and has been subdivided into a vast number of different frequency bands.
Microwave bandpass filters provide an output signal only at a precise (narrow) frequency band.
Also, the filter can be tuned to a precise frequency band with there being a separate filter for each
precise frequency band. In the field of communications, performance of a filter determines an
effective use of a frequency which is an important resource. A bandpass filter allows a narrow
range of frequencies to pass through it unattenuated, and blocks out all other frequencies. This
narrow range of frequencies is the filter's passband. In the satellite communications technology,
band pass filters in the microwave range play an important role in the preselection of individual
communication channels.

5. 5
List of Contents
Content Page no.
Introduction 7
RF filter 8-11
Butterworth filter 12-13
Bessel filter 14
Chebyshev filter 15
Basic types of RF filter 16-18
Designing of Band pass filter 19-22
Conclusion 23
References 24

6. 6
List of Figures
Figure Page no.
Miniature high performance RF filetr : µ filter 8
Design parameters of RF filter 10
Amplitude response of Butterworth filter 12
Phase response of Butterworth filter 13
Frequency response of Low pass filter 16
Frequency response of High pass filter 17
Frequency response of Band pass filter 17
Frequency response of Band reject filter 18
System level block diagram of a Band pass
filter
19
Band pass filter circuit 19
Frequency response of a 2nd
order Band pass
filter
21
Ideal characteristics of Band pass filter 22

7. 7
1. Introduction
Electrical filter is a circuit, designed to reject all unwanted frequency components of an electrical
signal and allows only desired frequencies. In other words a filter is a circuit which allows only a
certain band of frequencies.The main applications of the filters are at audio equalizers and in
sensitive electronic devices whose input signals should be conditional.These filters are mainly
categorized into 2 types. They are Active filters and passive filters.
Passive filters do not contain any amplifying elements just they are made up of Resistor, Capacitor
and inductors (passive elements). These filters will not draw any additional power from the
external battery supply.The Capacitor will allow the high frequency signals and inductor allows
low frequency signals. Similarly inductor restricts the flow of high frequency signals and capacitor
restricts the lower frequency signals. In these filters output signal amplitude is always less than the
amplitude of the applied input signal.The gain of passive filters is always less than unity.This
shows that the gain of the signals are cannot be improved by these passive filters. Due to this the
characteristics of the Filters are affected by the load impedances.These filters can work at higher
frequency ranges nearly at 500 MHz also.
Active filters contain amplifying elements such as Op-Amps, Transistors and FET’s (active
components)in addition to the passive elements (Resistors, Capacitors and Inductors). By using
these filters we can overcome the drawbacks of Passive filters. Active filters will depend on
external power supply because it will amplify the output signals. The main drawback in active
filters is the operational frequency range is less. In many applications the operational frequency
range of active filters is maximized to 500 kHz only. The active filters must require D.C power
supply. When compared with the passive filters these active filters are more sensitive. The outputs
may disturb even due to the environmental changes also.
RF filters of all types are required in a variety of applications from audio to RF and across the
whole spectrum of frequencies. As such RF 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.
The filter is a sensitive circuit and in which the output components are only frequency terms. To
analyze the filter circuit the frequency domain representation is the best one. One of the important
characteristic of the filters is cut-off frequency. It is defined as the frequency which separates both
pass band and stop band in frequency response. Pass band is the range of frequencies that are
allowed by the filter without any attenuation. Stop band is defined as the band of frequencies that
are not allowed by the filter.

8. 8
2. RF filter
An RF filter is an electrical circuit configuration (network) designed to have specific
characteristics with respect to the transmission or attenuation of various frequencies that may be
applied to it. RF filters are widely used in RF design and in all manner of RF and analogue circuits
in general. As they allow though only particular frequencies or bands of frequencies, they are an
essential tool for the RF design engineer.
Fig 1. : Miniature High Performance RF Filter;µ Filter
RF 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.
Design basics
In general terms, filters modify the amplitudes and phases of sinusoidal waveforms that pass
through them. This change varies according to the frequency of the individual sinusoids within the
overall waveform.
Most filters are what is termed linear filters. As such they have no non-linear actions in which the
response is proportional to the input. Instead the signals pass through and their amplitude and phase
is altered in a linear fashion according to their frequency.

9. 9
Real and ideal filters
When designing an RF filter it would be ideal if the filter would allow signals within the pass-band
through without any change in amplitude or phase. Filters like this could have a rectangular
response, falling straight to their stop-band and giving the required level of stop-band attenuation.
Unfortunately it is not possible to design RF filters like this, and real RF filter designs can only
approximate to the ideal response curves and parameters. These approximations can then be used
as the different types of filter that exist. These include the Butterworth, Bessel, Chebyshev,
Elliptical, Gaussian and many more.
Key filter RF design parameters
There are a number of key parameters that are of great importance for RF filter design. These are
some of the highlight requirements for any RF filter design.
 Pass-band : This is the region in which the signal passes through relatively un-attenuated.
It is the band in a low pass filter, extends up to the cut-off frequency. For high pass filters
it is designated as the band above which signal pass through, or for a band pass filter, it is
the band between the two cut-off frequencies.
 Cut-off frequency : This is normally taken to be the point at which the response of the
filter has fallen by 3 dB. With certain filters, typically equi-ripple types such as the
Chebyshev or inverse Chebyshev, the cut-off point has to be defined differently. It is often
designated fc.
 Ripple band : Within the pass-band, the filter response may show variations in its response
- ripples. The variation is known as the ripple band
 Transition band : Once the RF filter response has gone beyond the cut-off point, the
response falls away in a region known as the transition band. It is the region between the
pass-band and the stop-band. This region is also sometimes referred to as the "skirt."
 Stop-band : This is the band where the filter has reached its required out of band rejection.
The stop-band rejection may be defined as a required number of decibels.
 Number of poles : A pole is a mathematical term. There is one pole for each capacitor or
inductor in a filter.
 Roll-off : Each filter has an ultimate roll-off rate. It is governed by the number of poles in
the filter. The ultimate roll-off is 6⋅n dB where n is the number of poles. Different types of
filter may reach their ultimate roll off rate at different rates, but they all reach the same
ultimate roll-off.
 Phase shift : The phase shift is another important factor for any RF filter design. It is
accommodated into the overall response of the filter by considering the calculations for
H(s) where s = jω. The phase response can be of importance to a waveform because the
waveform shape will be distorted if the phase changes within the pass-band. A constant
time delay corresponds to the phase shift increasing linearly with frequency. This gives
rise to the term linear phase shift referred to in many RF filter designs.

10. 10
 Impedance : Filters have a characteristic impedance in the same way that as an antenna
feeder. For them to operate correctly the input and output must be properly matched.
Fig 2. : Design parameters of RF filter
RF filter design & scaling
Once the filter design has been realised in its normalised form, it is then necessary to transform
the values to the required frequency and impedance. In the normalised format the filter design has
a cut-off of 0.159 Hz, i.e. 1 radian per second and it is designed to work into a load resistance of 1
Ω.
Where:
C = real capacitor value, L = real inductor value,Cn = normalised capacitor value,
Ln=normalised inductor value,R = required load resistor value,fc = required cut-off frequency

11. 11
RF filter design process
There are a number of steps or stages in the RF filter design process. Following these in order
helps the RF filter to be designed in a logical fashion. These steps are for the low pass filter design
- further stages for transferring this to a high pass or band pass filter are given on the following
pages.
While some computer programmes may allow direct design, often design using tables, etc. is still
widely used. If a computer programme is used, the filter design process can be modified
accordingly.
 Define response needed: the first stage in the process is to actually define the response
required. Elements such as cut-off point, attenuation at a given point, etc..
 Normalise frequencies: In order to be able to use the various tables and diagrams of filter
curves, it is necessary to convert all frequencies so that the cut-off point is at 1 radio per
second and any other points are relative to this.
 Determine maximum pass-band ripple: One of the major steps in the RF filter design
is to understand how much in-band ripple can be tolerated. The more ripple, the greater the
level of selectivity that can be obtained. The greater the selectivity the faster the transition
from pass-band to ultimate roll off will be .
 Match required attenuation curves with those from filter: With a knowledge of the
characteristics, both in terms of ripple and rejection required at particular points, it is
possible to determine the filter type and also the order or number of elements required
within the filter design.
 Determine element values: Using the relevant look up tables the normalised filter
component values can be determined
 Scale normalised values: Finally the values need to be scaled for the required cut-off
frequency and resistance.
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. Three common types of filter are given below:
Butterworth filter,Bessel filter,and Chebyshev filter

12. 12
3. Butterworth Filter
This type of filter provides the maximum in band flatness, although it provides a lower stop-band
attenuation than a Chebyshev filter. However it is also able to provide better group delay
performance, and hence lower overshoot. The Butterworth filter is a form of RF filter using lumped
elements that is widely used in many radio frequency filter applications.
The key feature of the Butterworth filter when compared to other forms of filter is that it has a
nominally flat response within its pass-band and an adequate roll-off.As a result the Butterworth
filter may also be known as the maximally flat magnitude filter.The Butterworth filter is often
considered as a good all round form of filter which is adequate for many applications, although it
does not provide the sharpest cut-off.
Amplitude response : As mentioned above, the key feature of the Butterworth filter is that it has
a maximally flat response within the pass-band, i.e. it has no response ripples as in the case of
many other forms of RF filter.
There is a frequency known as the cut-off frequency. This is defined as the point on the Butterworth
filter response where the power drops to half, i.e. the voltage drops to 71%, i.e. 1/√2 of its
maximum amplitude at lower frequencies. It is also worth noting that the maximum amplitude ,
i.e. minimum loss for the Butterworth filter response occurs at 0 Hz or radians/s.
When plotted on logarithmic scales, the Butterworth filter response is flat within its pass-band and
then rolls off with an ultimate linear roll off rate of -6 dB per octave (-20 dB per decade). A second-
order filter decreases at -12 dB per octave, etc. The ultimate roll off rate is actually the same for
all low pass and high pass filters.
Fig 3. : Amplitude response of Butterworth filter

13. 13
Phase response : A further advantage of the Butterworth filter is that Butterworth filters have a
more linear phase response in the pass-band than types such as the Chebyshev or elliptic filters,
i.e. the Butterworth filter is able to provide better group delay performance, and also a lower level
of overshoot .
Fig 4. : Phase response of Butterworth filter
Impulse response : The Butterworth filter may also be judged in terms ofits time domain response
including its response to impulses. It has a response that gives an increasing level of overshoot
with increasing filter order. For a fourth order filter, i.e. n = 4, the level of overshoot exceeds 11%.
The Butterworth filter provides a maximally flat response. However this also has the advantage
that the calculations are somewhat simpler than those for other forms of filter.
This simplicity combined with a level of performance that is more than adequate for many
applications means that the Butterworth filter is widely used in many areas of electronics from RF
to audio active filters.
Using the equations for the Butterworth filter, it is relatively easy to calculate and plot the
frequency response as well as working out the values needed.
The equation can be written as below. Here H(jω) is the transfer function and it is assumed the
filter has no gain, i.e. it is not an active filter.

14. 14
4. Bessel Filter
In electronics and signal processing, a Bessel filter is a type of analog linear filter with a maximally
flat group/phase delay (maximally linear phase response), which preserves the wave shape of
filtered signals in the passband. Bessel filters are often used in audio crossover systems.This filter
provides the optimum in-band phase response and therefore also provides the best step response.
It is often used where signals incorporate square waves, etc as the shape is maintained best of all.
The Bessel filter is a linear form of filter that provides a maximally flat group delay or propagation
delay across the frequency spectrum, but offers a slower transition from pass-band to stop-band
than for other forms of filter of the same order.
The Bessel filter takes its name from a German mathematician and astronomer named Friedrich
Bessel who lived between1784 and 1846. Bessel developed the mathematical theory on which this
form of filter is based.
Occasionally the filters may also be referred to as Bessel-Thomson filters. This is because W. E.
Thomson developed the methodology of using Bessel functions within the design of this form of
filter.
However, the Bessel filter is not used as widely as the Butterworth of Chebyshev filters for RF
applications, although the fact that it has a maximally flat group delay means that Bessel filters are
often used in audio applications such as audio cross-over networks.
Some of the key features of the Bessel filter can be summarised as below:
 Maximally flat group delay : The maximally flat group delay of the Bessel filter means
that it equally exhibits a maximally linear phase response.
 Overshoot : A direct result of the maximally flat group delay of the Bessel filter it gives
an output for a square wave input with no overshoot because all the frequencies are delayed
by the same amount.
 Slow cut-off : The transition from the pass band to the stop band for the Bessel filter is
much slower or shallower than for other filters.
The Bessel filter gives a constant propagation delay across the input frequency spectrum.
Therefore applying a square wave (consisting of a fundamental and many harmonics) to the input
of a Bessel filter will yield a ‘square’ wave on the output with no overshoot (i.e. all the frequencies
will be delayed by the same amount). Any other filter will delay different frequencies by different
amounts and this will manifest itself as overshoot on the output waveform.

15. 15
5. Chebyshev Filter
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.
The Chebyshev filter is a form of filter used in RF and many other applications.
The Chebyshev filter provides a steeper roll-off than the more commonly use Butterworth filter.
However the additional roll-off of the Chebyshev filter comes at the expense of ripple, and this
makes it unsuitable for a number of applications.
Nevertheless, the Chebyshev filter is widely used in RF applications where ripple may not be such
an issue. The steep roll-off can be used to advantage to remove out of band spurious emissions
such as harmonics or intermodulation.
Some of the key features of the Chebyshev filter can be summarised as below:
 Roll-off : One of the main aspects of the Chebyshev filter is that it has a steep roll-off. It
reaches its ultimate roll-off faster than other forms of filter. Accordingly is widely used in
RF applications where a steep transition between pass-band and stop-band is required to
remove unwanted products such as intermodulation of harmonics.
 Ripple : Although the Chebyshev filter provides a steep roll-off, this is at the cost of ripple.
The in-band ripple of one type of Chebyshev filter prevents this format of filter being used
in some applications where a flat in-band response is needed.
 Cut-off frequency : The common definition of the cut-off frequency of the point at which
the response falls to -3 dB does not hold for Chebyshev filters in view of the way the filter
rolls of faster than other types like the Butterworth filter.
 Chebyshev filter name : The name of the Chebyshev filter comes from the fact that the
format and calculations for the filter are based on Chebyshev polynomials.
Chebyshev filter types
There are two types of Chebyshev filter that are available:
 Chebyshev type I filter : These are the most common Chebyshev filters. It has the steepest
roll-off but exhibits in-band ripple.
 Chebyshev type II filter : The type 2 Chebyshev filter may also be known as the inverse
Chebyshev. It is less commonly used than the Type 1 filter because it does not roll off as
fast, and also requires more components. However, its big advantage is that it has no ripple
in the pass-band, but does have what is termed equi-ripple in the stopband.
These are some of the main types of RF filter. Other types are available, although they tend to be
sued in more specialised or specific applications.

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6. Basic types of RF filter
There are four types of filter that can be defined. Each different type rejects or accepts signals in a
different way, and by using the correct type of RF filter it is possible to accept the required signals
and reject those that are not wanted. The four basic types of RF filter are:
 Low pass filter
 High pass filter
 Band pass filter
 Band reject filter
As the names of these types of RF filter 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.
Low pass filter
Low Pass Filters will pass the frequency signals less than cut-off frequency ‘fc’. Practically a small
range of frequencies will pass even after the cut-off frequency range. The gain of the filter will
depend up on the frequency. If the input signal frequency increases then, gain of the filter
decreases. At the end of the transition band the gain becomes zero. This is as shown below.
Fig 5. : Frequency response of Low pass filter
Low pass filters are used in a wide number of applications. Particularly in radio frequency
applications, low pass filters are made in their LC form using inductors and capacitors. Typically
they may be used to filter out unwanted signals that may be present in a band above the wanted
pass band. In this way, this form of filter only accepts signals below the cut-off
frequency.Applications of low pass filters are in sound system that is in various types of
loudspeakers. To block the harmonic emissions these low pass filters are used in radio transmitters.
These are also used at DSL splitters in telephone subscriber lines.

17. 17
High pass filter
They will pass the frequencies after the cut off frequency ‘fc’. In practical case a negligible
frequencies below the cut off range is allowed by the filter. This is as shown below.
Fig 6. : Frequency response of High pass filter
High pass filters are used in a wide number of applications and particularly in radio frequency
applications. For the radio frequency filter applications, the high pass filters are made from
inductors and capacitors rather than using other techniques such as active filters using operational
amplifiers where applications are normally in the audio range. Applications of the high pass filters
are at RF circuits and are also used in DSL splitters.
Band pass filter
The combination of high pass filter with low pass filter forms Band pass filter. The name of the
filter itself indicates that itallows only a certain band of frequencies and blocks all the remaining
frequencies. The upper and lower limits of the band pass filter depend on the filter design. Practical
and ideal characteristics of band pass filter are shown below.
Fig 7. : Frequency response of Band pass filter

18. 18
Applications of band pass filters are at transmitter and receiver circuits. These are mainly used to
calculate the sensitivity of the receiver circuits and to optimize the signal to noise ratio. These
filters are typically used where a small band of frequencies need to be passed through the filter and
all others rejected by the filter.
Band reject filter
These are also called as Band rejection or band elimination filters. These filters stop only a
particular band of frequencies and allow all other frequencies.The frequency limits of the filter
depend on the filter design. It has two pass bands and one stop band.
Fig 8. : Frequency response of Band reject filter
Applications of band stop filters are at instrument amplifiers.

19. 19
7. Designing of Band pass filter
There are applications where a particular band, or spread, or frequencies need to be filtered from
a wider range of mixed signals. Filter circuits can be designed to accomplish this task by combining
the properties of low-pass and high-pass into a single filter. The result is called a band-pass filter.
Creating a bandpass filter from a low-pass and high-pass filter can be illustrated using block
diagrams:
Fig 9. : System level block diagram of a Band pass filter.
Sometimes it is necessary to only pass a certain range of frequencies that do not begin at 0Hz,
(DC) or end at some upper high frequency point but are within a certain range or band of
frequencies, either narrow or wide.
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. This new type of passive filter arrangement produces a frequency selective filter known
commonly as a Band Pass Filter or BPF for short.
Fig 10. : Band Pass Filter Circuit

20. 20
A band-pass filter is a circuit which is designed to pass signals only in a certain band of frequencies
while attenuating all signals outside this band. The parameters of importance in a bandpass filter
are the high and low cut-off frequencies (fH and fl), the bandwidth (BW), the centre frequency
fc, centre-frequency gain, and the selectivity or Q.
There are 2 cut off frequencies for band pass filter.
 Upper cut off frequency (f1) - the frequency below which all the frequencies are passed
 Lower cut off frequency (f2) - all the frequencies above this frequency are passed
From this f1 and f2 we shall define following parameters which are designing parameters for band
pass filter.
Based on Q we have two types of band pass filter :
 Wide band pass filter - with Q <10 it has wide flat response over range of frequencies.
BW is more
 Narrow band pass filter - with Q>10 it has sharp bell type response. BW is very less.
Thus Q is a measure of selectivity, meaning the higher the value of Q the more selective is the
filter, or the narrower is the bandwidth (BW).
A wide bandpass filter can be formed by simply cascading high-pass and low-pass sections and is
generally the choice for simplicity of design and performance though such a circuit can be realized
by a number of possible circuits. To form a ± 20 db/ decade bandpass filter, a first-order high-pass
and a first-order low-pass sections are cascaded; for a ± 40 db/decade bandpass filter, second-order
high-pass filter and a second-order low-pass filter are connected in series, and so on. It means that,
the order of the bandpass filter is governed by the order of the high-pass and low-pass filters it
consists of.
For a wide bandpass filter the centre frequency can be defined as where fH and fL are respectively
the high and low cut-off frequencies in Hz.In a narrow bandpass filter, the output voltage peaks at
the centre frequency fc.
The “ideal” Band Pass Filter can also be used to isolate or filter out certain frequencies that lie
within a particular band of frequencies, for example, noise cancellation. Band pass filters are
known generally as second-order filters, (two-pole) because they have “two” reactive component,
the capacitors, within their circuit design. One capacitor in the low pass circuit and another
capacitor in the high pass circuit.

21. 21
Frequency Response of Band Pass Filter
Fig 11. : Frequency Response of a 2nd Order Band Pass Filter.
The Bode Plot or frequency response curve above shows the characteristics of the band pass filter.
Here the signal is attenuated at low frequencies with the output increasing at a slope of
+20dB/Decade (6dB/Octave) until the frequency reaches the “lower cut-off” point ƒL. At this
frequency the output voltage is again 1/√2 = 70.7% of the input signal value or -3dB (20 log
(Vout/Vin)) of the input.
The output continues at maximum gain until it reaches the “upper cut-off” point ƒH where the
output decreases at a rate of -20dB/Decade (6dB/Octave) attenuating any high frequency signals.
The point of maximum output gain is generally the geometric mean of the two -3dB value between

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the lower and upper cut-off points and is called the “Centre Frequency” or “Resonant Peak”
value ƒr. This geometric mean value is calculated as being ƒr 2
= ƒ(UPPER) x ƒ(LOWER).
A band pass filter is regarded as a second-order (two-pole) type filter because it has “two” reactive
components within its circuit structure, then the phase angle will be twice that of the previously
seen first-order filters, ie, 180o
. The phase angle of the output signal LEADS that of the input
by +90o
up to the centre or resonant frequency, ƒr point were it becomes “zero” degrees (0o
) or
“in-phase” and then changes to LAG the input by -90o
as the output frequency increases.
The upper and lower cut-off frequency points for a band pass filter can be found using the same
formula as that for both the low and high pass filters, For example.
Then clearly, the width of the pass band of the filter can be controlled by the positioning of the
two cut-off frequency points of the two filters.
Ideal characteristics of Band pass filter
Fig 12. : Ideal characteristics of Band pass filter
This response shows that the band pass filter will pass the frequencies between the lower cutoff
region and higher cut-off region only. It stops the frequencies which are lesser than the lower cutoff
frequency and also stops the frequencies greater than higher cut-off frequencies.
A band-pass filter works to screen out frequencies that are too low or too high, giving easy
passage only to frequencies within a certain range.
Band-pass filters can be made by stacking a low-pass filter on the end of a high-pass filter, or vice
versa.“Attenuate” means to reduce or diminish in amplitude. When you turn down the volume
control on your stereo, you are “attenuating” the signal being sent to the speakers.

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8. Conclusion
The performance of a filter, in a particular application, may be better understood from its
common-mode and differential-mode equivalent circuits. The inductors and capacitors used in a
filter are complex components with their effectiveness being dependent on material
properties,placement and means of construction.
Similar filters may not perform identically in a given application because of subtle component
differences and parasitic parameters. Many parasitic parameters exist in any filter, which are not
determined by measurements. All of these, plus the properties of the materials in the components
will likely make two apparently identical filters behave differently in any given application.Power
lines filters used in switching power supplies are exposed to over-voltages, which can cause
damages especially to the filter capacitors.
It concludes that the designed filter met the Low Freq. design requirements. On incorporating in
SMPS the problem of non-compliance was observed for high frequencies. By rearranging the
wiring and using thick wire for grounding inside the SMPS, the problem was later eliminated. It
was observed that theoretical and experimental data did match for low frequency it was also
noticed that common choke became capacitive for high frequencies due to core permeability
reduction and parasitic capacitance and hence the measured data deviated slightly from the
predicted data. To achieve the goal of compliance for low and high frequencies the filter should
be designed for Low Frequency. In case of problem for high frequency the filter should be
modified accordingly. In case of non-compliance in radiated emission, torodial /ferrite bead to be
put at the output & input to comply the requirements.

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9. References:Digital Signal Processing Signals, Systems and Filters, A. Antoniou, TMH
Publishing Co.
Digital Signal Processing, P. Rameshbabu, Scitech Publications (India).
Digital Signal Processing; Spectral Computation and Filter Design Chi-Tsong
Chen, Oxford University Press
http://www.radio-electronics.com/info/rf-technology-design/rf-filters/rf-filter-
basics-tutorial.php
http://www.circuitstoday.com/band-pass-filters
http://www.electronics-tutorials.ws/filter/filter_4.html
http://www.electronicshub.org/introduction-to-filters-and-capacitive-reactance/
http://www.allaboutcircuits.com/textbook/alternating-current/chpt-8/band-pass-
filters/
http://www.engineersgarage.com/contribution/designing-band-pass-filter

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