Lecture 6 Angle Modulation and Demodulationeng.staff.alexu.edu.eg/~bmokhtar/courses/analog_comm/spring_2018/... · AM systems do not have the feature of exchanging signal power for

Lecture 6

Angle Modulation and Demodulation

Agenda

Introduction to Angle Modulation and

Demodulation

Frequency and Phase Modulation

Angle Demodulation

FM Applications

Angle Modulation

Introduction

The other two parameters (frequency and phase) of the carrier sinusoid can be varied by the message signal m(t)

We will start by discussing the Frequency Modulation (FM)

Previously, it was thought that the bandwidth required by the FM is less than the one needed by the AM bandwidth

However, the bandwidth at FM is greater with several times than that of AM

Angle Modulation

Introduction

While AM signals carry a message with their varying amplitude, FM signals can vary instantaneous frequency in proportion to the modulating signal m(t)

The carrier frequency is changing continuously every instant

Instantaneous frequency Consider a general sinusoid

Conventional sinusoid

Angle Modulation

Introduction

The relation between the instantaneous angular frequency and the generalized angle

Now, at transmitting the information of m(t), the angle of the carrier varies (Phase Modulation or PM)

Angle Modulation

Introduction

The resulting PM wave

In PM, the instantaneous angular frequency is given by

The instantaneous angular frequency varies linearly

with the derivative of the modulating signal (FM)

In FM, the instantaneous angular frequency is

Angle Modulation

Introduction

The angle is now

From

The FM wave is

Angle Modulation

Introduction

Angle Modulation

Introduction In both PM and FM, the angle of the

carrier is varied in proportion to some measure of m(t)

In PM, it is directly proportional to m(t)

In FM, it is proportional to the integral of m(t)

As shown in the figure in the previous slide, A frequency modulator can be directly used to

generate an FM signal or the message m(t) can be processed by a differentiator to generate PM signals

Angle Modulation

Introduction The generalized angle-modulated carrier can

be

The message m(t) can be recovered from

by passing it through a system with transfer function

Angle Modulation

Bandwidth of Angle-Modulated Waves

Unlike AM, angle modulation is nonlinear and no properties if Fourier transform can be directly applied for its bandwidth analysis

To determine the bandwidth of an FM wave

and define

Angle Modulation


Such that its relationship to the FM signal is

Expanding the exponential in power series yields

and

Angle Modulation


The modulated wave consists of an unmodulated carrier plus various amplitude-modulated terms

The signal a(t) is an integral of m(t)

If M(f) is bandlimited to B, A(f) is also bandlimited to B Integration is a linear operation equivalent to passing

a signal through a transfer function

The spectrum of is bandlimited to nB

Angle Modulation


Although the bandwidth of an FM wave is theoretically infinite, for practical signals with bounded will remain finite

Angle Modulation

Narrowband Angle Modulation Approximation

Unlike AM, angle modulations are nonlinear

When

Then, the equation

becomes

Angle Modulation

Narrowband Angle Modulation Approximation

This approximation is a linear modulation that has an expression similar to that of the AM signal with message signal a(t)

Because the bandwidth of a(t) is B Hz, the bandwidth of is 2B Hz according to the frequency-shifting property due to the term

For this case, the FM signal at the case of

is called narrowband FM (NBFM) Angle Modulation

Wideband FM (WBFM) Bandwidth Analysis

Note that an FM signal is meaningful only if its frequency deviation is large enough

In other words, practical FM chooses the constant large enough that the condition is not satisfied

At this case, we have Wideband FM (WBFM)

The maximum and minimum carrier frequencies are

Angle Modulation


The peak frequency deviation from the carrier frequency

The estimated FM bandwidth

This estimated bandwidth is calculated based

on the staircase approximation of m(t)

This bandwidth is somewhat higher that the actual value Angle Modulation


Better FM bandwidth approximation is between

In case of very small is very small that we have NBFM

So,

However, we showed previously that for NBFM, the FM bandwidth is approximately 2B Hz

Angle Modulation


So, better estimate for bandwidth of FM

In case

We define a deviation ratio

The bandwidth of FM

β is called modulation index

Angle Modulation

Phase Modulation

All results derived for FM can be directly applied to PM

The instantaneous frequency

The peak frequency deviation

Angle Modulation

Phase Modulation

If we assume

Then

Angle Modulation

Notes In FM,

Depends only on the peak of m(t) not the spectrum

of m(t)

In PM,

Depends on the peak of

However, depends strongly on the spectral composition of m(t)

PM depends on the spectral shape of m(t) [not in FM]

So, for m(t) spectrum concentrated at lower frequencies, bandwidth of PM will be smaller than the one at case of m(t) spectrum concentrated at higher frequencies

Generating FM Waves

There are two ways of generating FM waves Indirect

• Narrowband FM generator

Direct • Voltage-controlled oscillator

Angle Modulation

Narrowband FM (NBFM) Generation

Indirect FM generators are used for generating wideband angle modulation signals

For NBFM and NBPM signals In case of and the modulated

signals can be approximated by

Both approximations are linear and similar to the expression of the AM wave

Angle Modulation

NBFM Generation The equations

Possible methods of generating narrowband FM and PM signals by using DSB-SC modulators

Angle Modulation

NBFM Generation

Because the approximation in

The NBFM generated by

has some distortion and amplitude variations

NBFM Generation

A nonlinear device designed to limit the amplitude of a bandpass signal can remove most of the distortion

Bandpass Limiter The amplitude variations of an angle-modulated

carrier can be eliminated by what is known as a bandpass limiter, consists of a hard limiter followed by a bandpass filter

Angle Modulation

NBFM Generation

Bandpass Limiter The input output characteristic of a hard limiter is

shown

The limiter output will be a square wave of unit amplitude regardless of the incoming sinusoidal amplitude

Angle Modulation

NBFM Generation

Angle-modulated sinusoidal input

Results in a constant amplitude angle-modulated square wave

Angle Modulation

Indirect Method of Armstrong

In this method, NBFM is generated as shown

Then converted to WBFM by using additional frequency multipliers

Angle Modulation


A frequency multiplier can be realized by a nonlinear device followed by a bandpass filter

For a nonlinear device with output y(t) and input x(t)

If an FM signal passes through the device, the output signal will be

Angle Modulation


Simplified commercial FM transmitter using Armstrong’s method

Angle Modulation

Direct Generation

In a voltage-controlled oscillator (VCO), the frequency is controlled by an external voltage

The oscillation frequency varies linearly with the control voltage

An FM wave by using the modulating signal m(t), as a control signal, can be generated

VCO can be built by varying one of the reactive parameters (C or L) of the resonant circuit

Angle Modulation

Features of Angle Modulation The transmission bandwidth of AM systems

cannot be changed

In angle modulation, the transmission bandwidth can be adjusted by adjusting ∆f

AM systems do not have the feature of exchanging signal power for transmission bandwidth

For angle-modulated systems, the SNR is roughly proportional to the square of the transmission bandwidth

Angle Modulation

Demodulation of FM Signals The information in an FM signal

resides in the instantaneous frequency

Frequency-selective network with a transfer function of the form

Over the FM band would yield an output proportional to the instantaneous frequency

Angle Demodulation

Demodulation of FM Signals FM demodulator frequency response

Output of the differentiator to the input FM wave

Angle Demodulation

Demodulation of FM Signals FM demodulation by direct differentiation

Ideal differentiator with transfer function is j2πf

The output if we apply to the ideal differentiator

.

Demodulation of FM Signals Both the amplitude and the frequency of the

signal are modulated

Because , we have for all t

Then, m(t) can be obtained by envelope detection

The amplitude A of the carrier should be constant

Channel noise and fading cause A to vary

Demodulation of FM Signals Practical Frequency Demodulators

The differentiator is only one way to convert frequency variation of FM signals into amplitude variation [envelope detectors]

Another method for detection using Operational amplifier differentiator

The role of the differentiator can be replaced by any linear system (frequency response contains a linear segment of positive slope) [slope detection]

Demodulation of FM Signals Practical Frequency Demodulators

One simple device for FM demodulation is an RC high-pass filter

The RC frequency response

If the parameter RC << that The RC filter approximates a differentiator

Demodulation of FM Signals FM Demodulation via Phase Locked Loop (PLL)

Voltage Controlled Oscillator

Angle Demodulation

Demodulation of FM Signals FM Demodulation via Phase Locked Loop (PLL)

Consider a PLL with input signal

and output error signal

When the input signal is an FM signal

The loop filter output signal

If the incoming signal is a PM wave, then

Angle Demodulation

Effects of Nonlinear Distortion and Interference

Immunity of Angle Modulation to Nonlinearities Very useful feature of angle modulation is its constant

amplitude, which makes it less susceptible to nonlinearities

Amplifier with second order nonlinear distortion

Clearly, the first term is the desired signal amplification term, the remaining terms are the unwanted nonlinear distortion


Immunity of Angle Modulation to Nonlinearities For the angle modulated signal

The nonideal system output

A bandpass filter centered at with bandwidth equaling to can extract the desired FM signal component without any distortion

For a DSB-SC signal passes through a nonlinearity , the output is


Interference Effect Angle modulation is also less vulnerable than AM to small-

signal interference from adjacent channels

Let us consider the interference of an unmodulated carrier with another sinusoid

The received signal

where


Interference Effect When the interfering signal is small in comparison to the

carrier

then

The output

The interference output is inversely proportional to the carrier amplitude A

The larger A, the smaller interference effect in FM


Interference due to Channel Noise The channel noise acts as interference in an angle-

modulated signal

We will consider the most common form of noise, white noise, which has a constant power spectral density

Such noise may be considered as a sum of sinusoids of all frequencies in the band

All components have the same amplitudes (uniform density)

This means that the interference I is constant for all frequencies


Interference due to Channel Noise The amplitude spectrum of the interference at the

receiver output is shown

Effect of interference in PM, FM, and FM with preemphasis-deemphasis (PDE)


Interference due to Channel Noise

Preemphasis and Deemphasis in FM Broadcasting In FM, interference increases linearly with frequency

The noise power in the receiver output is concentrated at higher frequencies

To consider this issue • At the transmitter, the weaker high frequency components are

boosted before modulation

• At the receiver, attenuating the higher frequency components



Preemphasis and Deemphasis in FM Broadcasting



Preemphasis and Deemphasis Filters Assignment

• Prepare a report about those filters discussing their comprising components and their works

Superheterodyne Analog AM/FM Receivers

The radio receiver used in broadcast AM and FM systems is called superheterodyne receiver


It consists of

an RF (radio-frequency) section

• Tunable filter and an amplifier

a frequency converter or mixer

• Translates the carrier from to a fixed IF frequency

An intermediate-frequency (IF) amplifier

An envelope detector

An audio amplifier


The importance of the superheterodyne receiver

Used in radio and television broadcasting

Adequate selectivity of frequencies

Accommodate many carrier frequencies

FM Broadcasting System

FM Transmitter

The FCC has assigned a frequency range of 88 to 108

MHz for FM broadcasting with a separation of 200 KHz between adjacent stations


Spectrum of a baseband stereo signal


FM Stereo Receiver

Lecture Summary

Covered material Introduction to Angle Modulation and Demodulation

Frequency and Phase Modulation Angle Demodulation FM Applications

Material to be covered next lecture Performance Study of Angle Modulation in the

Existence of Noise

Angle Modulation

Documents

Lecture 6 Angle Modulation and Demodulationeng.staff.alexu.edu.eg/~bmokhtar/courses/analog_comm/spring_2018/... · AM systems do not have the feature of exchanging signal power for