Analog Communication - AMPLITUDE MODULATION

Analog Communication: 

Analog Communication Suresh P. Nair [AIE, ME, (PhD)] MIEEE Professor & Head Department of Electronics and Communication Engineering Royal College of Engineering and Technology Chiramanangad PO, Akkikkavu, Thrissur, Kerala, India

Module 2: 

Module 2 MODULATION

Introduction: 

Introduction

Topics to be covered: 

Topics to be covered Need for Modulation What is Modulation? Types of Modulation Amplitude Modulation (AM) Angle Modulation Frequency Modulation (FM) Phase Modulation (PM)

Baseband vs Passband Transmission: 

Baseband vs Passband Transmission Baseband Signal :- Information bearing Signal or Message Signal. The term Baseband refers to the band of frequencies representing the original signal obtained from the source (or Base ). Voice (0-4kHz) TV (0-6 MHz) A signal may be sent in its baseband format when a dedicated wired channel is available. Otherwise, it must be converted to passband .

Need for Modulation: 

Need for Modulation Size of the antenna For efficient radiation, the size of the antenna should be λ/10 or more (preferably around λ/4 ), where λ is the wavelength of the signal to be radiated. Easy to Multiplex Several message signals can be transmitted on a given channel, by assigning to each message signal an appropriate slot in the channel. Channel Selectivity Each station can be assigned a suitable carrier so that the corresponding program material can be received by tuning to the station desired.

Need for Modulation: 

Need for Modulation Improved Signal to Noise Ratio Will be dealt in future lectures Less Fading of transmitted signal As the energy of a signal is proportional to its frequency , fading by the atmospheric particle is less

What is Modulation?: 

What is Modulation? So for better transmission, we need to send a high frequency signal. But message signal is of low frequency. If we alter the frequency of message signal, the information will be lost. We can send a high frequency signal which reflects the characteristics of message signal. This high frequency signal is called CARRIER SIGNAL

What is Modulation?: 

What is Modulation? The message signal is called MODULATING SIGNAL or BASEBAND SIGNAL. The word modulation means the systematic alteration of one waveform, called the carrier , according to the characteristic of another waveform, the modulating signal or the message . We use c(t ) and m(t ) , to denote the carrier and the message waveforms respectively.

What is Modulation?: 

What is Modulation? The resultant signal after modulation is called MODULATED SIGNAL. For study purpose, the commonly used carrier and message signal is SINUSOIDAL WAVE. Transmitter Side - Modulation Receiver Side - Demodulation

Definition for Modulation: 

Definition for Modulation Modulation is defined as the process by which some characteristic of a carrier wave is varied in accordance with the message signal .

Modulation and Demodulation: 

Modulation and Demodulation

Types of Modulation: 

Types of Modulation Modulation - Characteristics of Carrier Wave is varied in accordance with the characteristics of message signal. Consider a Carrier wave: c(t) = Ac Cos ( θ ) Instantaneous Value Maximum Amplitude Angle ( 2 π fc t + φ ) Frequency Phase

Types of Modulation: 

Types of Modulation MODULATION Angle Modulation Amplitude Modulation (AM) Phase Modulation (PM) Frequency Modulation (FM) AM DSB FC AM DSB SC SSB VSB NBFM WBFM NBPM WBPM

Amplitude & Angle Modulation - Definition: 

Amplitude & Angle Modulation - Definition

AM, FM & PM: 

AM, FM & PM A M – The amplitude of the carrier signal is varied in accordance with the instantaneous amplitude of the message signal . F M – The frequency of the carrier signal is varied in accordance with the instantaneous amplitude of the message signal . P M – The phase of the carrier signal is varied in accordance with the instantaneous amplitude of the message signal .

AM & FM Waveforms: 

AM & FM Waveforms AM FM MESSAGE CARRIER

FM & PM Waveforms: 

FM & PM Waveforms FM PM MESSAGE CARRIER

TDM: 

TDM

FDM: 

FDM

FDM: 

FDM

AMPLITUDE MODULATION: 

AMPLITUDE MODULATION

Definition of Amplitude Modulation (AM): 

Definition of Amplitude Modulation (AM) Amplitude Modulation (AM) is defined as the process in which the amplitude of the Carrier Signal, c(t) is varied about a mean value , linearly with the Base band Signal, m(t).

Types of Amplitude Modulation: 

Types of Amplitude Modulation Amplitude Modulation Non Linear AM Linear AM AM DSB FC AM DSB SC SSB VSB

Topics to be Covered: 

Topics to be Covered AM DSB FC (or simply AM) AM DSB SC SSB VSB Signal to Noise Ratio of AM

AM DSB FC (or simply AM): 

AM DSB FC (or simply AM) Introduction Signal & Spectrum representation of AM Power Relation Modulators Switching Modulator Square Law Modulator Demodulators Square Law Demodulator Envelope Detector

Introduction: 

Introduction

Introduction: 

Introduction

AM DSB FC or simply AM: 

AM DSB FC or simply AM Consider a Carrier Signal: Message signal m(t) and Carrier signal c(t) are independent. AM is defined as the process in which the amplitude of the Carrier Signal, c(t) is varied about a mean value , linearly with the Base band Signal, m(t). where K a = 1/A c , is the Amplitude Sensitivity Factor or Modulation Sensitivity measured in volt -1

Non Linearity in AM DSB FC: 

Non Linearity in AM DSB FC Does Full-Amplitude Modulation Satisfy the Linearity Property ? Amplitude modulation, as defined in Eq. (2.2), fails the linearity test (i.e. Super Position Theorem )in a strict sense. 1) Suppose that m ( t ) = m 1 (t) + m 2 ( t ). Let s 1 ( t ) and s 2 ( t ) denote the AM waves produced by these two components acting separately . 2) Let the operator H denote the amplitude modulation process, therefore we have: and The superposition principle is violated!

Conditions for AM: 

Conditions for AM

Modulation Index of AM: 

Modulation Index of AM K a = 1 / A c K a *m(t) = (1/A c ) * A m Cos (2 π f m t ) = (1/A c ) * A m (1) = A m / A c = k a *A m This “ Ka * Am ” is called as Modulation Index. It is denoted using m a or μ

Modulation Index of AM: 

Modulation Index of AM Two cases arise, depending on the magnitude of k a m ( t ), when comparing with unity: 1) Undermodulation , which is governed by the condition 1 + k a m ( t ) > 0 2) Overmodulation , which is governed by the weaker condition Percentage of modulation   k a m ( t )  100%

Modulation Index: 

Modulation Index Important conclusion: The envelope of the AM wave has a waveform that bears a one-to-one correspondence with that of the message signal if the percentage modulation is less than or equal to 100%. If percentage modulation > 100%, the modulated wave is said to suffer from envelope distortion .

Modulation Index: 

Modulation Index

Modulation Index: 

Modulation Index

Modulation Index: 

Modulation Index

Modulation Index: 

Modulation Index

Signal Representation of AM: 

Signal Representation of AM An unmodulated RF carrier wave A carrier wave amplitude modulated (AM) with a simple audio tone

Signal Representation of AM: 

Signal Representation of AM 1 st Condition Envelope Distortion

Spectrum Representation of AM: 

Spectrum Representation of AM To draw the spectrum of any wave, we need to find out the Fourier Transform of that signal. Cos (x) = (1/2)*(e jx + e -jx ) F [m(t) Cos (x)] = M(f – x)/2 + M(f + x)/2

Slide 42: 

Frequency shifting (Modulation) Therefore multiplying a time function by causes its spectral density to be translated in frequency by ω 0 . Example Some properties of the Fourier transform  

Spectrum Representation of AM: 

Spectrum Representation of AM

Spectrum Representation of AM: 

Spectrum Representation of AM

Spectrum Representation of AM: 

Spectrum Representation of AM From Eqn. (2.5), we can draw the spectrum as:

Bandwidth: 

Bandwidth

Bandwidth of AM: 

Bandwidth of AM

Spectral Overlap (2nd Condition): 

Spectral Overlap (2 nd Condition) Spectral overlap phenomenon in amplitude modulation. The phenomenon arises when the carrier frequency  c is less than the highest frequency component  m of the modulating signal. 2 nd Condition Spectral Overlap

Time domain & Frequency domain: 

Time domain & Frequency domain

Phasor Representation of AM: 

Phasor Representation of AM Ac/2 Ac/2 AcKaAm/4 AcKaAm/4 AcKaAm/4 AcKaAm/4 Ac/2 + AcKaAm/4 Ac/2 + AcKaAm/4

Power relation in AM: 

Power relation in AM

Power relation in AM: 

Power relation in AM

Transmission Efficiency of AM: 

Transmission Efficiency of AM

Carrier Power Vs Sideband Power: 

Carrier Power Vs Sideband Power

AM Modulators: 

AM Modulators Switching Modulator Utilizing the Switching characteristic or time varying characteristic of a diode. Square Law Modulator Utilizing the non linear characteristic of any square law device ( like Diode, Transistor etc.)

Switching Modulator: 

Switching Modulator

Switching Modulator: 

Switching Modulator Assume that Let The diode will turn on if and will turn off if The output across the load resistor is Since g(t ) is a periodic rectangular function, the Fourier series is

Switching Modulator: 

Switching Modulator

Switching Modulator: 

Switching Modulator

Switching Modulator: 

Switching Modulator

Square Law Modulator: 

Square Law Modulator

AM Demodulators: 

AM Demodulators Square Law Demodulator Envelope Detector

Square Law Demodulator: 

Square Law Demodulator

Envelope Detector: 

Envelope Detector

Envelope Detector: 

Envelope Detector

Envelope Detector: 

Envelope Detector The operations of the circuit requires careful selection of t = RC If RC is too large, discharging will be slow and the circuit cannot follow a decreasing envelope. When RC is too small the ripples will be high. The ripples are finally removed by LPF. The DC value is blocked by a capacitor.

Envelope Detector: 

Envelope Detector

Features of AM: 

Features of AM AM system is very cheap to build and maintain. AM is wasteful of power - max efficiency is 33% AM is wasteful of bandwidth - twice the message bandwidth is required

Demerits of AM DSB FC: 

Demerits of AM DSB FC An unmodulated RF carrier requires narrow bandwidth Modulation results in creation of a carrier and 2 Sidebands. This requires more power. Moreover carrier contains no information.

Why DSB SC?: 

Why DSB SC? The carrier contains no information. So we can think of avoiding or suppressing carrier.

Linear Modulation: 

Linear Modulation In its most general form, linear modulation is defined by: where s I ( t ) is the in-phase component and s Q ( t ) the quadrature component of the modulated wave s(t) . In linear modulation, both s I ( t ) and s Q ( t ) are low-pass signals that are linearly related to the message signal m ( t ).

In-Phase and Quadrature Components of Linear Modulation: 

In-Phase and Quadrature Components of Linear Modulation Depending on s I ( t ) and s Q ( t ), three types of linear modulation are defined: 1) DSB SC modulation , where only the upper and lower sidebands are transmitted. 2) SSB modulation , where only the lower or the upper sideband is transmitted. 3) VSB modulation , where only a vestige of one of the sidebands and a modified version of the other sideband are transmitted.

In-Phase and Quadrature Components of Linear Modulation: 

In-Phase and Quadrature Components of Linear Modulation There are 2 important points to be noted from this table: 1). The in-phase component s I ( t ) is solely dependent on the message m ( t ). 2). The quadrature component s Q ( t ) is a filtered version of m ( t ). Spectral modification of the modulated wave s ( t ) is solely due to s Q ( t ) .

Linear Modulation Schemes: 

Linear Modulation Schemes AM DSB SC (AM Double Side Band Suppressed Carrier) SSB (Single Side Band) VSB (Vestigial Side Band)

AM DSB SC: 

AM DSB SC Derivation Signal & Spectra Modulators Product Modulator Balanced Modulator Ring Modulator (Double Balanced Modulator) Demodulator Coherent Detector Costas Receiver

Introduction: 

Introduction DSB-SC modulation is generated by using a product modulator that simply multiplies the message signal m ( t ) by the carrier wave A c cos (2  f c t ). Specifically, we write: s ( t ) = A c m ( t ) cos(2  f c t ) (2.8)

Introduction: 

The modulated signal s ( t ) undergoes a phase reversal whenever the message signal m ( t ) crosses zero. This is called double side-band suppressed carrier (DSB-SC) modulation . Introduction Transmission bandwidth is same as standard AM. Transmitted power is less than that used by standard AM.

Signal Representation: 

Signal Representation Double-sideband-suppressed carrier modulation. (a) Message signal. (b) DSB-SC modulated wave, resulting from multiplication of the message signal by the sinusoidal carrier wave.

Signal Representation: 

Signal Representation

Spectrum Representation: 

Spectrum Representation The envelope of a DSB-SC signal is different from the message signal; unlike the case of an AM wave that has a percentage modulation < 100 %. From Equ. (2.8), the Fourier transform of s ( t ) is obtained as:

Spectrum of AM DSB SC: 

Spectrum of AM DSB SC When m ( t ) is limited to the interval - W < f < W , as in Figure 2.6a, the spectrum S ( f ) of the DSB-SC wave s ( t ) is as illustrated in Figure 2.6b.

Spectrum Representation: 

Spectrum Representation

Spectrum of AM DSB SC: 

Spectrum of AM DSB SC Because it doesn’t have components of the carrier, we call this kind of modulation suppressed carrier

Time domain Vs Frequency domain: 

Time domain Vs Frequency domain Time-domain (on the left) and frequency-domain (on the right) characteristics of DSB-SC modulation produced by a sinusoidal modulating wave. (a) Modulating wave. (b) Carrier wave. (c) DSB-SC modulated wave. Note that  = 2  .

Modulators: 

Modulators Product Modulator Balanced Modulator Ring Modulator (Double Balanced Modulator)

Product Modulator: 

Product Modulator

Balanced Modulator: 

Balanced Modulator

Ring Modulator: 

Ring Modulator

Ring Modulator: 

Ring Modulator

Ring Modulator: 

Ring Modulator

Ring Modulator: 

Ring Modulator

Ring Modulator: 

Ring Modulator Therefore, we have Since c(t) is a periodic function, the Fourier series can be expressed as: The desired DSB-SC AM signal is obtained by passing through a bandpass filter with center frequency and bandwidth 2W .

Demodulators: 

Demodulators Coherent Detector AM DSB SC Modulator + Filter Also called Synchronous or Homodyne Detector. Quadrature Null Effect – Phase Error. Costas Receiver Employs two Coherent detectors. Avoids Quadrature Null Effect.

Coherent Detector: 

Coherent Detector

Coherent Detector: 

Coherent Detector

Coherent Detector – Quadrature Null Effect: 

Coherent Detector – Quadrature Null Effect Assume the Local Oscillator signal have same frequency of that of the Carrier, but a different phase. Let the Phase difference is Ø. The LO signal is:

Coherent Detector – Quadrature Null Effect: 

Coherent Detector – Quadrature Null Effect

Costas Receiver: 

Costas Receiver

Costas Receiver: 

Costas Receiver I-channel: After downconverwsion, At the output of the lowpass filter, with |H(0)| = 1, Q-channel :

Costas Receiver: 

Costas Receiver Feedback path: At the output of the multiplier, At the output of the lowpass filter, The purpose of h f ( t ) is to smooth out fast time variations of m e ( t ). The output of the VCO is described by

Costas Receiver: 

Costas Receiver Where  c is the VCO’s reference frequency and is the residual phase angle due to the tracking error. The constant k v is the frequency sensitivity of the VCO in rad/s/volt. The instantaneous frequency in radians/sec of the VCO’s output is given by: Clearly, if  (t) were small, then the instantaneous frequency would be close to  c and the output of the I-path would also be proportional to m ( t ) .

Why SSB?: 

Why SSB? The carrier contains no audio information . The sidebands contains duplicated information

AM SSB SC (SSB): 

AM SSB SC (SSB) Hilbert Transform Derivation Signal and Spectrum Modulators Frequency Discriminator Phase Discriminator (Hartley Modulator) Demodulators Coherent Detector Envelope Detector

Introduction to SSB: 

Introduction to SSB Two main parameters to be considered while designing a Communication System are : Transmission Power Transmission Bandwidth. In AM DSB FC, both are very high. In AM DSB SC Transmission Power is less than AM DSB FC, but Transmission Bandwidth is same as that of AM DSB FC.

Introduction to SSB: 

Introduction to SSB In AM SSB SC or SSB, only one Sideband will be Transmitted (Both the Sidebands contain the same information). The Transmission Power as well as the Transmission Bandwidth can be reduced. Transmission Bandwidth will be reduced to half of that of AM DSB FC & AM DSB SC. To accomplish these merits, the Equipment Design in more Complex .

SSB Derivation: 

SSB Derivation A single sideband AM signal can be represented mathematically as: USSB AM LSSB AM

Spectrum of SSB: 

Spectrum of SSB Suppose we want to transmit the upper sideband, then using an ideal bandpass filter with center frequency yields the desired result, namely,

Spectrum of SSB: 

Spectrum of SSB

SSB Modulators: 

SSB Modulators Frequency Discriminator Generating SSB signal from DSB SC signal by using BPF Phase Discriminator Generating SSB signal by using Hilbert Transform

Frequency Discriminator: 

Frequency Discriminator

Frequency Discriminator: 

Frequency Discriminator

Phase Discriminator: 

Phase Discriminator

SSB Demodulators: 

SSB Demodulators Coherent Detector Envelope Detector

Coherent Detector: 

Coherent Detector Same Coherent Detector used for AM DSB SC.

Envelope Detector (Modified): 

Envelope Detector (Modified)

Spectrum of SSB: 

Spectrum of SSB

Demerit of SSB: 

Demerit of SSB Selective Filtering using filters with sharp cutoff characteristics. Sharp cutoff filters are difficult to design. The audio signal spectrum has no dc component, therefore , the spectrum of the modulated audio signal has a null around the carrier frequency. This means a less than perfect filter can do a reasonably good job of filtering the DSB to produce SSB signals .

VSB: 

VSB Derivation Signal and Spectra Modulators Frequency Discriminator Demodulators

Introduction to VSB: 

Introduction to VSB

Introduction to VSB: 

Introduction to VSB To produce SSB signal from DSB signal ideal filters should be used. In VSB system one sideband and a vestige of other sideband are transmitted together. The resulting signal has a bandwidth > the bandwidth of the modulating (baseband) signal but < the DSB signal bandwidth.

Spectrum of DSB SC, SSB & VSB: 

Spectrum of DSB SC, SSB & VSB

Generation of VSB: 

Generation of VSB Generation of VSB AM generate a DSB-SC AM signal pass the DSB-SC AM signal through a sideband filter with frequency response H(f)

Response of the Filter: 

Response of the Filter

Response of the Filter: 

Response of the Filter

Demodulation of VSB: 

Demodulation of VSB

Basics of Signal to Noise Ratio: 

Basics of Signal to Noise Ratio

Basics of Signal to Noise Ratio: 

Basics of Signal to Noise Ratio