# Amplitude Modulation - Paper

**Topics:**Amplitude modulation, Modulation, Carrier wave

**Pages:**15 (4568 words)

**Published:**February 16, 2013

Amplitude Modulation

Date: 4th February 2013

Submitted By ADARSH V R AKHIL KRISHNA R ANANTHU R KRISHNAN ARUN KOSHY T B100291EC B100125EC B100256EC B100091EC S6 ECE Batch: A

Contents

1 Introduction 2 Theory 3 Principles and Circuits Used 4 Design 5 Observations and Results 6 Conclusion 3 5 8 15 21 23

2

Chapter 1

Introduction

Today,communication has entered into our daily lives in so many diﬀerent ways that it is very easy to overlook the multitude of its facets.From the radios and televisions to the mobile phone in our hand,all are capable of providing us with rapid communication from every nook and corner of the world.In the most fundamental sense,communication deals with transmitting and receiving information from one point to another through a channel. But we can’t transmit information as such from one place to another.The message signal is needed to undergo a process called modulation before being transmitted due the following reasons: 1. To send a signal over long distance, it requires more energy.Energy and frequency are related by the Planck’s formula E = hν (1.1)

where E = energy of the signal h = Planck’s Constant ν = frequency of the signal So when the frequency is low,energy will be obviously low.To increase the energy of the signal, we have to use a high frequency signal,which is done by modulation. 2. To decrease the antenna height.We know that for transmitting a signal of wavelength λ ,the antenna height must be λ/4.So if we want to send 1 Hz ( λ = 3 × 108 m)signal using an antenna, its height must be 3

75,000 km. It is impossible to build such a huge antenna.Suppose ,if the same signal is modulated to some high frequency say 88 MHz (λ = 3.4m), antenna height needed is 0.8522 m only which is quite easy to construct. Thus, we can see that the message signal which we have to send must be modulated before its transmission.In the process called modulation, we use a high frequency signal called carrier whose parameters may be varied in accordance with the message signal. We may classify the modulation schemes into continuous-wave modulation and pulse modulation.In continuous-wave modulation,we have three types of modulation schemes, namely, amplitude ,frequency and phase modulation.In amplitude modulation,the amplitude of the carrier wave is varied in accordance with the message signal.AM is the scheme which are used in broadcasting radio programs. In this project, we would be trying to implement an analog medium wave modem,which uses a super heterodyne receiver and would try to generate,transmit,receive and demodulate the AM signal and retrieve the message signal.

Chapter 2

Theory

Before designing the AM modem, the ﬁrst step we have to do is to make a mathematical model of the system so that we can analyse it easily.In Amplitude modulation,we would be varying the amplitude of the carrier signal in accordance with the message signal.So, let m(t) denote the message signal and M (f ) its Fourier transform.Let us denote the carrier frequency to be ωc and the carrier amplitude to be Ac .Then the carrier signal is given by c(t) = Ac cos(ωc t) (2.1) Now we are modulating the amplitude of the carrier signal c(t) with the message signal m(t). So, A(t) = Ac + m(t) where A(t) is the amplitude of the modulating signal. Now, we can write the equation of the modulated signal as x(t) = A(t)cos(ωc t) Substituting A(t), x(t) = (Ac + m(t))cos(ωc t) ie, x(t) = Ac (1 + m(t) Ac )cos(ωc t)

(2.2)

(2.3)

Now, we deﬁne mn (t) as the normalised message signal and Am as max(m(t)). So,the above equation can be modiﬁed as 5

x(t) = Ac (1 +

Am mn (t) )cos(ωc t) Ac

Now, we can deﬁne another term k such that, k= Am Ac (2.4)

This k is called the modulation index which is a measure of the modulation done.It is a quantity which gives a measure of how much the modulated parameter (the amplitude in this case) of the carrier signal varies around its unmodulated level....

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