Active and Passive Filter

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LOVELY PROFESSIONAL

UNIVERSITY

TERM PAPER

ON

ACTIVE AND PASSIVE FILTERS



TERM PAPER

ECE

ECE 131

Topic: ACTIVE AND PASSIVE FILTERS

Submitted to: Submitted by:

Mr. /Ms. AMANPREET KAUR Mr./MS.DIVYA KHUSHBOO

Deptt. Of ECE Roll. No.RG6010B56

Reg.No.11013524



ACKNOWLEDGEMENT

No work of significance can be claimed on a result of an individual Efforts and same holds true

further for this project as well, for through it carries my name the energy of many have

contributed in no small measure in completion of this project.I am extremely grateful and remainindebted to our guide Ms.Amanpreet kaur for being a source of inspiration and for her constant

support in the Design and Implementation of the term paper. I am thankful to her for her

constant constructive criticism and invaluable suggestions, which benefited a lot while

developing the term paper on “ACTIVE AND PASSIVE FILTERS”. She has been a constant

source of inspiration and motivation for hard work. She has been very co-operative throughout

this project work. Through this column, it would be my utmost pleasure to express my warm

thanks to him for his encouragement, co-operation and consent without which I mightn’t be able

to accomplish this project.No work of significance can be claimed on a result of an individual

Efforts and same holds true further for this project as well, for through it carries my name the

energy of many have contributed in no small measure in completion of this project.

I owe a deep sense of reverence to mam , my immediate instructor,

who at every step guided me with sincere efforts and enriched me with their profound knowledge

.I thank them for their inspirational guidance and frequent stimulation despite their busy

schedules.

Words elude me in expressing my profound gratitude to my whole them their pains taking

guidance, constant, encouragement, constructive suggestions, thought provoking discussion and

giving useful opportunity to practically handle the whole project



CONTENTS

1.) INTRODUCTION

2.) BASIC FILTER TYPES

3.) BANDPASS FILTERS

4.) LOW PASS FILTERS

5.) BANDREJECT FILTERS

6.) HIGHPASS FILTERS

7.) REFERENCES



INTRODUCTION

Filters of some sort are essential

to the operation of mostelectronic circuits. It is therefore

in the interest of anyone

involved in electronic circuitdesign to have the ability to

develop filter circuits capable of

meeting a given set of specifications. Unfortunately,

many in the electronics field

are uncomfortable with the

subject, whether due to a lack of familiarity with it, or a reluctance

to grapple with the mathematics

involved in a complex filter design.

This Application Note is intended

to serve as a very basic

introduction to some of thefundamental concepts and

terms associated with filters.

In circuit theory, a filter is anelectrical network that alters

the amplitude and/or phase

characteristics of a signal withrespect to frequency. Ideally, a

filter will not add new frequencies

to the input signal, nor will itchange the component

frequencies of that signal, but itwill change the relativeamplitudes of the various

frequency components and/or

their phase relationships. Filters

are often used in electronicsystems to emphasize signals in

certain frequency ranges

and reject signals in other

frequency ranges. Such a filter has a gain which is dependent on

signal frequency. As an

example, consider a situationwhere a useful signal at frequency

f1 has been contaminated with an

unwanted signalat f2. If the contaminated signal is

passed through a circuitthat has very low gain at f2

compared to f1, theundesired signal can be removed,

and the useful signal will

remain. Note that in the case of this simple example, we are

not concerned with the gain of the

filter at any frequencyother than f1 and f2. As long as f2

is sufficiently attenuated

relative to f1, the performance of this filter will be satisfactory.In general, however, a filter's gain

may be specified at

several different frequencies, or over a band of frequencies.

Since filters are defined by their

frequency-domain effectson signals, it makes sense that the

most useful analytical

and graphical descriptions of

filters also fall into the frequencydomain. Thus, curves of gain vs

frequency and

phase vs frequency are commonlyused to illustrate filter

characteristics,and the most

widely-used mathematical



tools are based in the frequency

domain.

The frequency-domain behavior

of a filter is described

mathematicallyin terms of its transfer function or

network

function. This is the ratio of the

Laplace transforms of itsoutput and input signals. The

voltage transfer function H(s)

of a filter can therefore be writtenas:

H(s) e (1)

VOUT(s)

VIN(s)where VIN(s) and VOUT(s) are

the input and output signal

voltages and s is the complexfrequency variable.

The transfer function defines the

filter's response to anyarbitrary input signal, but we are

most often concerned with

its effect on continuous sinewaves. Especially important is

the magnitude of the transfer

function as a function of frequency,

which indicates the effect of the

filter on the amplitudes

of sinusoidal signals at variousfrequencies. Knowing

the transfer function magnitude

(or gain) at each frequencyallows us to determine how well

the filter can distinguish

between signals at differentfrequencies. The transfer function

magnitude versus frequency is

called the amplitude

response or sometimes, especially

in audio applications,the frequency response.

Similarly, the phase response of

the filter gives the amountof phase shift introduced in

sinusoidal signals as a function

of frequency. Since a change in

phase of a signal also representsa change in time, the phase

characteristics of a filter

become especially importantwhen dealing with complex

signals where the time

relationships between signalcomponents

at different frequencies are

critical.By replacing the variable s in (1)

with j0, where j is equal to

0b1 , and 0 is the radian frequency(2qf), we can find the

filter's effect on the magnitude

and phase of the input signal.

The magnitude is found by takingthe absolute value of



This is a 2nd order system. Theorder of a filter is the highest

power of the variable s in its

transfer function. The order of a filter is usually equal to the

total number of capacitors

and inductors in the circuit. (A

capacitor built by combiningtwo or more individual capacitors

is still one capacitor.)Higher-order filters will obviously be more expensive to

build, since they use more

components, and they will also be more complicated to design.

However, higher-order filters

can more effectively discriminate between signals at

different frequencies.

Before actually calculating the

amplitude response of thenetwork, we can see that at very

low frequencies (small

values of s), the numerator becomes very small, as do the

first two terms of the

denominator. Thus, as sapproaches

zero, the numerator approaches

zero, the denominator approaches

one, and H(s) approaches zero.Similarly, as the

input frequency approaches

infinity, H(s) also becomes progressively

smaller, because the denominator

increases with

the square of frequency while thenumerator increases linearly

with frequency. Therefore, H(s)

will have its maximumvalue at some frequency between

zero and infinity, and will

decrease at frequencies above and

below the peak.

BASIC FILTER TYPES

BANDPASS FILTERS

There are five basic filter types

(bandpass, notch, low-pass,

high-pass, and all-pass). The filter

used in the example inthe previous section was a

bandpass. The number of possible bandpass response characteristicsis infinite, but they all

share the same basic form. Several

examples of bandpassamplitude response curves are

shown in Figure 5 . The

curve in 5(a) is what might be

called an ``ideal'' bandpassresponse, with absolutely constant

gain within the passband,

zero gain outside the passband,and an abrupt boundary

between the two. This response

characteristic is impossibleto realize in practice, but it can be

approximated to

varying degrees of accuracy byreal filters. Curves (b)



through (f) are examples of a few

bandpass amplitude response

curves that approximate the idealcurves with varying

degrees of accuracy. Note that

while some bandpassresponses are very smooth, other

have ripple (gain variations

in their passbands. Other have

ripple in their stopbandsas well. The stopband is the range

of frequencies

over which unwanted signals areattenuated. Bandpass filters

have two stopbands, one above

and one below the

passband.

Bandpass filters are used in

electronic systems to separate

a signal at one frequency or within

a band of frequencies

from signals at other frequencies.Such a filter could also reject

unwanted signals at

other frequencies outside of the passband, so it could be

useful in situations where the

signal of interest has been



contaminated by signals at a

number of different frequencies.

BAND REJECT FILTER

A filter with effectively theopposite function of thebandpassis the band-reject or notchfilter. As an example, thecomponents in the networkofFigure 3 can berearranged toform the notch filter ofFigure which has thetransfer function

Notch filters are used to remove

an unwanted frequencyfrom a signal, while affecting all

other frequencies as little as

possible. An example of the use of

a notch flter is with an

audio program that has beencontaminated by 60 Hz powerline

hum. A notch filter with a center

frequency of 60 Hz can



remove the hum while having

little effect on the audio signals.

LOW PASS FILTER

A third filter type is thelow-pass. A low-pass filter

passeslow frequency signals, andrejects signals atfrequenciesabove the filter's cutoff frequency. If thecomponents of our

example circuit are

rearranged as in Figure ,the resultanttransfer function is:

It is easy to see by inspection thatthis transfer function has

more gain at low frequencies than

at high frequencies. As 0approaches 0, HLP approaches 1;

as 0 approaches infinity,

HLP approaches 0.Amplitude and phase response

curves are shown in Figure

10 , with an assortment of

possible amplitude reponse



curves inFigure . Note that the

various approximations to

the unrealizable ideal low-passamplitude characteristics

take different forms, some being

monotonic(always having

a negative slope), and others

having ripple in the passband

and/or stopband.Low-pass filters are used

whenever high frequency

componentsmust be removed from a signal.

An example might be

in a light-sensing instrument using

a photodiode. If light levelsare low, the output of the

photodiode could be very

small, allowing it to be partiallyobscured by the noise of the

sensor and its amplifier, whose

spectrum can extend to veryhigh frequencies. If a low-pass

filter is placed at the output

of the amplifier, and if its cutoff frequency is high enough to

allow the desired signal

frequencies to pass, the overallnoise level can be reduced.

HIGH PASS FILTER

The opposite of the low-pass is the high-pass filter,whichrejects signals below itscutoff frequency. A high-

pass filtercan be made byrearranging thecomponents of ourexamplenetwork as in Figure 12 . The transfer function forthisfilter is:

and the amplitude and phase

curves are found inFigure 13 . Note that the amplitude responseof the high-pass is a ``mirror

image'' of the low-pass response.

Further examples of

high-pass filter responses areshown in Figure 14 , with the

``ideal'' response in (a) and

various approximations to theideal shown in (b) through (f).

High-pass filters are used in

applications requiring therejection



of low-frequency signals. One

such application is in

high-fidelity loudspeaker systems.

Music contains significantenergy in the frequency range

from around 100 Hz to 2 kHz,

but high-frequency drivers

(tweeters) can be damaged if low-frequency audio signals of

sufficient energy appear attheir input terminals. A high-pass

filter between the broadband

audio signal and the tweeter inputterminals will prevent

low-frequency program material

from reaching the

tweeter. In conjunction with a

low-pass filter for the low-frequency

driver (and possibly other filters

for other drivers),

the high-pass filter is part of whatis known as a ``crossover

network

.



REFERENCES

=>WWW.SWARTHMORE.EDU=>WWW.BINAVOLTA.CH

=>WWW.ELECTRONICS-

TUTORIAL.WS

=> HUGHES

http://www.swarthmore.edu/

http://www.binavolta.ch/

http://www.swarthmore.edu/

http://www.binavolta.ch/

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