+ All Categories
Home > Documents > 49141143 Modulation

49141143 Modulation

Date post: 06-Apr-2018
Category:
Upload: awaisjinnah
View: 217 times
Download: 0 times
Share this document with a friend
41
Analog Modulation What is Modulation? Modulation the process of varying one or more properties of a high-frequency  periodic waveform, called the carrier signal , with respect to a modulating signal . This is done in a similar fashion as a musician may modulate a tone (a periodic waveform) from a musical instrument by varying its volume, timing and pitch. The three key parameters of a periodic waveform are its amplitude ("volume"), its  phase ("timing") and its frequency ("pitch"), all of which can be modified in accordance with a low frequency signal to obtain the modulated signal. Typically a high-frequency sinusoid waveform is used as carrier signal, but a square wave  pulse train may also occur. In telecommunications, modulation is the process of conveying a message signal, for example a digital bit stream or an analog audio signal, inside another signal that can be physically transmitted. Modulation of a sine waveform is used to transform a baseband message signal into a passband signal, for example low- fr eque ncy audi o si gnal into a ra di o- fr equenc y si gnal (RF si gnal ). In radi o communications, cable TV systems or the public switched telephone network for ins tan ce, el ect ric al si gna ls can onl y be tra ns fer red over a limite d pas sba nd frequency spectrum, with specific (non-zero) lower and upper cutoff frequencies. Modulating a sine-wave carrier makes it possible to keep the frequency content of the transferred signal as close as possible to the centre frequency (typically the carrier frequency) of the passband. A device that performs modulation is known as a modulator and a device that  performs the inverse operation of modulation is known as a demodulator (sometimes detector or demod ). A device that can do both operations is a modem (modulator–demodulator). Modulation is a process in which a modulator changes some attribute of a higher frequency carrier signal proportional to a lower frequency message signal. If the carrier is represented by the equation
Transcript
Page 1: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 1/41

Page 2: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 2/41

 

Carrier Signal Equation

a change in the message signal will produce a corresponding change in either the

amplitude, frequency, or phase of the carrier. A transmitter can then send thiscarrier signal through the communication medium more efficiently than the

message signal alone. Finally, a receiver will demodulate the signal, recovering

the original message.

Page 3: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 3/41

Modulations are of Two Types:

1. Digital Modulation

2. Analog Modulation

Digital Modulation

Digital modulation is similar to analog modulation, but rather than being able to

continuously change the amplitude, frequency, or phase of the carrier, there are

only discrete values of these attributes that correspond to digital codes. There areseveral common digital modulation schemes, each varying separate sets of  parameters. The simplest type is called On Off Keying (OOK) where the

amplitude of the carrier corresponds to one of two digital states. A nonzero

amplitude represents a digital one while a zero amplitude is a digital zero. A

specific implementation of OOK is Morse Code. Frequency Shift Keying (FSK),

seen in Figure, is a form of frequency modulation where a certain frequency

represents each binary value.

Frequency Shift Keying (FSK)

Page 4: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 4/41

Finally, Quadrature Amplitude Modulation (QAM) uses combinations of 

amplitudes and phases to represent more than 2 digital states, as many as 1024.

I and Q Data

I/Q data shows the changes in magnitude (or amplitude) and phase of a sine wave.

If amplitude and phase changes are made in an orderly, predetermined fashion,

one can use these amplitude and phase changes to encode information upon a sine

wave; a process known as modulation.

Modulation is the process of changing a higher frequency carrier signal in

 proportion to a lower frequency message, or information, signal. I/Q data is highly

 prevalent in RF communications systems, and more generally in signal

modulation, because it is a convenient way to modulate signals. This discussion

covers the theoretical background of I/Q data as well as practical considerations

which make the use of I/Q data in communication so desirable.

Common Analog Modulation Techniques

Amplitude modulation (AM) 

The amplitude of the carrier signal is varied in accordance to the

instantaneous amplitude of the modulating signal)

o Double-sideband modulation (DSB)

Double-sideband modulation with carrier (DSB-WC) (usedon the AM radio broadcasting band)

Double-sideband suppressed-carrier transmission (DSB-SC)

Double-sideband reduced carrier transmission (DSB-RC)

o Single-sideband modulation (SSB, or SSB-AM),

SSB with carrier (SSB-WC)

SSB suppressed carrier modulation (SSB-SC)

o Vestigial sideband modulation (VSB, or VSB-AM)

o Quadrature amplitude modulation (QAM)

Page 5: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 5/41

Angle Modulation o Frequency modulation (FM) (here the frequency of the carrier 

signal is varied in accordance to the instantaneous amplitude of the

modulating signal)

o Phase modulation (PM) (here the phase shift of the carrier signal is

varied in accordance to the instantaneous amplitude of the

modulating signal)

In Amplitude Modulation (AM), pictured below, the amplitude of the carrier 

sinusoid changes based on the amplitude of the message.

Amplitude Modulation

The message signal (red) rides on top of the carrier as the amplitudes of both vary

with time. The frequency of the carrier, however, is much higher than the

frequency of the message. This carrier frequency is the center of the 'channel,' or frequency allocation of this RF signal. Frequency allocations vary depending on

the medium of transmission. For broadcast transmissions, where signals are sentthrough the air, the government regulates frequency allocation. If the RF signal is

transmitted over wire, such as in cable television, there is more freedom in the

choice of carrier.

In addition to amplitude modulation, frequency modulation varies the frequency of 

the carrier sinusoid based on the amplitude of the message signal. Similarly, phase

Page 6: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 6/41

modulation changes the phase of the carrier in response to a change in amplitude

of the message.

Amplitude Modulation

Modulation is the process of varying a higher frequency carrier wave to transmitinformation. Though it is theoretically possible to transmit baseband signals (or 

information) without modulating it, it is far more efficient to send data by

modulating it onto a higher frequency "carrier wave." Higher frequency waves

require smaller antennas, use the available bandwidth more efficiently, and are

flexible enough to carry different types of data. AM radio stations transmit audio

signals, which range from 20 Hz to 20 kHz, using carrier waves that range from500 kHz to 1.7 MHz. If we were to transmit audio signals directly we would need

an antenna that is around 10,000 km! Modulation techniques can be broadly

divided into analog modulation and digital modulation. Amplitude modulation

(AM) is one form of analog modulation.

Basic Stages of AM

Page 7: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 7/41

Mathematical Background

The carrier signal is generally a high-frequency sine wave. There are three parameters of a sine wave that can be varied: amplitude, frequency, and phase.

Any of these can be modulated, or varied, to transmit information. A sine wave

can be mathematically described by a sine or cosine function with amplitude Ac,

frequency f c, and phase φ.

Carrier Wave

The carrier signal is modulated by varying its amplitude in proportion to the

message, or baseband, signal. The message signal can be represented by

m(t) = M b cos(2πf  b + φ)

and the carrier signal can be represented by

c(t) = Ac cos(2πf c + φ)

To make the equations simpler, assume that there is no phase difference between

the carrier signal and the message signal and thus φ = 0.

Page 8: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 8/41

The modulated signal can be represented by multiplying the carrier signal and the

summation of 1 and the message signal, as shown below.

Ac(1 + m(t)) cos(2πf c)

With some basic trigonometric manipulation, the above waveform can be writtenas

Ac cos(2πf c) + (M b/2) cos(2π(f c – f  b)) + (M b/2) cos(2π(f c + f  b)).

Types of AM Modulation

As described in the previous section, the modulated signal has waves at three

frequencies: f c, f c – f  b and f c + f  b. Transmitting at all three frequencies wastes

 power and bandwidth. To avoid that problem use a filter to remove one of the

sidebands (usually the lower sideband, f c – f  b). Use a highpass filter to remove thelower sideband signal; this process is single sideband (SSB) modulation.

However, by removing one of the sidebands we lose some of the original power of 

the modulated signal. To maximize the power transmitted, transmit both the lower 

and the upper sideband. This process is double sideband (DSB) modulation. The

following figure illustrates DSB.

Figure 3. Frequency Domain View of Double Sideband – Full Carrier

One of the components of the modulated signal is the pure carrier wave. Because

the carrier wave does not have any information, we can remove the carrier wave

component from the signal before we transmit it. This process is called single

 sideband/double sideband – suppressed carrier (SSB-SC, DSB-SC) modulation.

Page 9: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 9/41

However, we need the carrier when demodulating the signal. Special circuits can

extract information about the carrier from one of the sidebands; these circuits are

used when demodulating SSB-SC or DSB-SC signals.

We can also use amplitude modulation to send digital data. Quadrature amplitude

modulation (QAM) uses four predetermined amplitude levels to determine digital bits.

Background on Signals

Signal modulation involves changes made to sine waves in order to encode

information. The mathematical equation representing a sine wave is as follows:

Figure 1: Equation of a Sine Wave

If we think about possible sine wave parameters that we can manipulate, the

equation above makes it clear we are limited to making changes to the amplitude,

frequency, and phase of a sine wave to encode information. Frequency is simply

the rate of change of phase of a sine wave (frequency is the first derivative of 

 phase), so these two components of the sine wave equation can be collectively

referred to as the phase angle. Therefore, we can represent the instantaneous state

of a sine wave with a vector in the complex plane containing amplitude

(magnitude) and phase coordinates in a polar coordinate system.

Page 10: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 10/41

Polar Representation of a Sine Wave

In the graphic above, the distance from the origin to the black point represents the

amplitude (magnitude) of the sine wave, and the angle from the horizontal axis

represents the phase. Thus, the distance from the origin to the point will remain

fixed as long as the amplitude of the sine wave is not changing (modulating). The

 phase of the point will change according to the current state of the sine wave. For 

example, a sine wave with a frequency of 1 Hz (2π radians/second) rotates

counter-clockwise around the origin at a rate of one revolution per second. If the

amplitude doesn't change during one revolution, the dot maps out a circle around

the origin with radius equal to the amplitude along which the point will travel at a

rate of one cycle per second.

Because phase is a relative measurement, imagine that the phase reference used is

a sine wave of frequency equal to the sine wave that is being represented by the

amplitude and phase points. If the reference sine wave frequency and the plotted

sine wave frequency are the same, then the rate of change that the phase of the two

signals experience will be the same, and the rotation of the sine wave around theorigin will become stationary. In this case, a single amplitude/phase point can be

used to represent a sine wave of frequency equal to the reference frequency. Any

 phase rotation around the origin indicates a frequency difference between the

reference sine wave and the sine wave being plotted. We will return to this pointlater.

Up to this point, this tutorial has covered amplitude and phase data in a polar 

coordinate system. All the concepts discussed above apply to I/Q data, and in fact,

I/Q data is merely a translation of amplitude and phase data from a polar 

Page 11: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 11/41

coordinate system to a cartesian (X,Y) coordinate system. Using trigonometry,

you can now convert the polar coordinate sine wave information into cartesian I/Q

sine wave data. These two representations are equivalent and contain the exact

same information, just in different forms. This equivalence is show in Figure.

I and Q Represented in Polar Form

The figure below shows a Lab View example demonstrating the relationship

 between polar and cartesian coordinates.

Page 12: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 12/41

 

I/Q Data in Lab

I/Q Data in Communication Systems

At this point, we have discussed technically what I/Q data is, but to explain why

I/Q data is used, we must first discuss modulation basics.

RF communication systems use advanced forms of modulation to increase the

amount of data that can be transmitted in a given amount of frequency spectrum.Signal modulation can be divided into two broad categories: analog modulation

and digital modulation. Analog or digital refers to how the data is modulated onto

a sine wave. If analog audio data is modulated onto a carrier sine wave, then this is

referred to as analog modulation. If analog audio data is sampled by an analog to

digital converter (ADC) with the resulting digital bits modulated onto a carrier 

sine wave, this is digital modulation because digital data is being encoded. Both

analog modulation and digital modulation are performed by changing the carrier 

wave amplitude, frequency, or phase (or combination of amplitude and phase

simultaneously) according to the message data.

Amplitude modulation (AM), frequency modulation (FM), or phase modulation(PM) are all examples of analog modulation. With amplitude modulation, the

carrier sine wave amplitude is modulated according to the message signal. The

same idea holds true for frequency and phase modulation.

Page 13: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 13/41

Time

Domain of AM, FM, and PM Signals

Above figure represents various analog techniques—AM, FM, and PM—applied

to a carrier signal. In the AM case, the message signal is the blue sine wave that

forms the "envelope" of the higher frequency carrier sine wave. In the FM case,

the message data is the dashed square wave. As the figure illustrates, the resulting

carrier signal changes between two distinct frequency states. Each of these

frequency states represents the high and low state of the message signal. If themessage signal were a sine wave in this case, there would be a more gradual

change in frequency, which would be more difficult to see. In the PM case, notice

the distinct phase change at the edges of the dashed square wave message signal.

Applying this to the earlier discussion, if only the carrier sine wave amplitude

changes with respect to time (proportional to the message signal), as is the case

with AM modulation, we should see changes in the I/Q plane only with respect to

the distance from the origin to the I/Q points. This is evidenced by the following

image:

Page 14: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 14/41

I/Q Data in the Complex Domain

The preceding figure shows the I/Q data points vary in amplitude only, with the

 phase fixed of 45 degrees. We cannot tell from Figure 6 the nature of the message

signal—only that it is amplitude modulated. However, if we can see how the I/Q

data points vary in magnitude with respect to time, we can essentially see arepresentation of the message signal. Using Lab View’s 3D graph control, we can

show the third axis of time to illustrate the message signal.

Page 15: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 15/41

Representation of Magnitude vs. Time

The preceding figure shows the same data as the 2D I vs. Q plot in Figure 6. The

magnitude of the signal trace modulates in a sinusoidal pattern indicating that the

message signal is a sine wave. The green trace represents the amplitude and phase

data in a polar coordinate system, while the red traces represent the projections of 

this waveform onto the I and Q axes, representing the individual I and Qwaveforms.

We can show the same type of example using PM. An image of the same message

signal sine wave using PM instead of AM is shown below.

Page 16: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 16/41

Polar Representation of Phase vs. Time

Once again, we can tell that the message signal is phase modulated as the

amplitude is constant but the phase is changing (modulating). We cannot tell whatthe shape of the message signal is with respect to time, but we can tell the

minimum and maximum signal levels of the message signal are represented by

 phase deviations of -45 degrees and +45 degrees respectively.

Once again, the time axis can be used to better understand this concept.

Page 17: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 17/41

3D Representation of Phase Modulation

The preceding figure shown in the LabVIEW 3D graph, shows the green trace

varying in a sinusoidal fashion with respect to time. The projections onto the I andQ axes represent the individual I and Q waveforms corresponding to the PM sine

wave with fixed magnitude and oscillating phase.

In essence, the I/Q data represents the message signal. Because the I/Q datawaveforms are Cartesian translations of the polar amplitude and phase waveforms,

it is not easy to visually tell what the nature of the message signal is from the I/Q

data. To illustrate this, compare the red I and Q traces on the 3D I vs. Q plots in

Figure 9 to the green trace in Figure 9. If we plot amplitude vs. time for the AM

sine wave, we would display the message signal. If we plot the phase data vs. time

for the AM sine wave, we would have a straight line. We would see sine waves for 

the I vs. time and Q vs. time waveforms as well, but the scale would be off, andthis would not necessarily be the case for more complex digital modulation

schemes where both amplitude and phase are modulated simultaneously.

Page 18: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 18/41

So Why Use I/Q Data?

Because amplitude and phase data seem more intuitive, it would seem that we

should use polar amplitude and phase data instead of cartesian I and Q data.However, practical hardware design concerns make I and Q data the better choice

in this matter.

It is difficult to vary precisely the phase of a high-frequency carrier sine wave in a

hardware circuit according to an input message signal. A hardware signalmodulator that manipulates the amplitude and phase of a carrier sine wave would

therefore be expensive and difficult to design and build, and, as it turns out, not as

flexible as a circuit that uses I and Q waveforms. To understand how we to avoid

manipulating the phase of an RF carrier directly, we first return to trigonometry.

 

Mathematical Background of I/Q Modulation

According to the trigonometric identity shown in the first line of Figure 10,multiply both sides of the equation by A and substitute 2πf ct in place of α and φ in

 place of β to arrive at the equation shown in line 2. Then substitute I for  A cos(φ)

and Q for  A sin(φ) to represent a sine wave with the equation shown on line 3.

Remember that the difference between a sine wave and a cosine wave of the samefrequency is a 90-degree phase offset between them. The implications of this are

very important. What this essentially means is that we can control the amplitude,

Page 19: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 19/41

frequency, and phase of a modulating RF carrier sine wave by simply

manipulating the amplitudes of separate I and Q input signals! With this method,

we no longer have to directly vary the phase of an RF carrier sine wave. We can

achieve the same effect by manipulating the amplitudes of input I and Q signals.

Of course, the second half of the equation is a sine wave and the first half is a

cosine wave, so we must include a device in the hardware circuit to induce a 90-degree phase shift between the carrier signals used for the I and Q mixers, but this

is a much simpler design issue than the aforementioned direct phase manipulation.

Hardware Diagram of an I/Q Modulator

The preceding figure shows a block diagram of an I/Q modulator. The circles with

an 'X' represent mixers—devices that perform frequency multiplication and either upconvert or downconvert signals (upconverting here). The I/Q modulator mixes

the I waveform with the RF carrier sine wave, and mixes the Q signal with the

same RF carrier sine wave yet with a 90-degree phase offset. The Q signal is

subtracted from the I signal (just as in the equation shown in line 3 in Figure 10)

 producing the final RF modulated waveform. In fact, the 90-degree shift of thecarrier is the source of the names for the I and Q data—I refers to in-phase data

(because the carrier is in phase) and Q refers to quadrature data (because the

carrier is offset by 90 degrees). This technique is known as quadrature

upconversion and the same I/Q modulator can be used for any modulation scheme.

This is because the I/Q modulator is merely reacting to changes in I and Qwaveform amplitudes, and I and Q data can be used to represent any changes inmagnitude and phase of a message signal. The flexibility and simplicity (relative

to other options) of the design of an I/Q modulator is the reason for its widespread

use and popularity.

Page 20: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 20/41

IQ vs. IF Modulators

After calculating digital I and Q data from the baseband message signal, there are

two methods of converting this data into an analog RF signal. The first methodinvolves converting I and Q data into analog signals, then feeding them into a

quadrature encoder. There, they control the amplitudes of two oscillators,

operating 90 degrees out of phase. The output of these oscillators is summed,

resulting in an RF signal with the appropriate amplitude, phase, and frequency.

 

IQ Modulation

The next method of converting digital I and Q data to analog RF performs the

oscillator scaling and summing in the digital domain. That is, digital sinusoidswith a phase difference of 90 degrees are scaled by the digital I and Q values, then

added together. These digital sinusoids are of a lower frequency than the analog

oscillators in the IQ modulation scheme, but still at a significantly higher 

frequency than the message signal. A digital to analog converter (DAC), which

operates at a much higher frequency than the DAC used in IQ modulation,

converts the resulting digital waveform to low frequency analog RF. Finally, ananalog IF to RF upconverter uses several stages of mixing and filtering to shift the

analog RF signal to the desired RF frequency.

Page 21: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 21/41

 

IF Modulation

Analog Modulation Methods

In analog modulation, the modulation is applied continuously in response to the

analog information signal.

 

A low-frequency message signal (top) may be carried by an AM or FM radio

wave.

The following figure shows the modulation techniques that Communications

Blockset supports for analog signals. As the figure suggests, some categories of techniques include named special cases.

Page 22: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 22/41

 

For a given modulation technique, two ways to simulate modulation techniques

are called baseband and passband . This blockset supports passband simulation for 

analog modulation.

The modulation and demodulation blocks also let you control such features as the

initial phase of the modulated signal and post-demodulation filtering.

Representing Signals for Analog Modulation

Analog modulation blocks in this blockset process only sample-based scalar 

signals. The input and output of the analog modulator and demodulator are all real

signals.

All analog demodulators in this blockset produce discrete-time, not continuous-

time, output.

Sampling Issues in Analog Modulation

The proper simulation of analog modulation requires that the Nyquist criterion be

satisfied, taking into account the signal bandwidth.

Specifically, the sample rate of the system must be greater than twice the sum of 

the carrier frequency and the signal bandwidth.

Page 23: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 23/41

Filter Design Issues

After demodulating, you might want to filter out the carrier signal. The particular 

filter used, such as butter , cheby1, cheby2, and ellip, can be selected on the mask 

of the demodulator block. Different filtering methods have different properties,

and you might need to test your application with several filters before decidingwhich is most suitable.

Example: Varying the Filter's Cutoff Frequency

In many situations, a suitable cutoff frequency is half the carrier frequency. Since

the carrier frequency must be higher than the bandwidth of the message signal, acutoff frequency chosen in this way properly filters out unwanted frequency

components. If the cutoff frequency is too high, those components may not be

filtered out. If the cutoff frequency is too low, it might narrow the bandwidth of 

the message signal.The following example modulates a sawtooth message signal, demodulates the

resulting signal using a Butterworth filter, and plots the original and recovered

signals. The Butterworth filter is implemented within the SSB AM Demodulator

Passband block.

To build the model, gather and configure these blocks:

Signal Generator in the Simulink Sources library

Set Wave form to Sawtooth.

Set Amplitude to 4.

Set Frequency to .3.

Zero-Order Hold: in the Simulink Discrete library

Set Sample time to .01.

Page 24: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 24/41

SSB AM Modulator Passband:In the Analog Passband sublibrary of 

the Modulation library

Set Carrier frequency to 25.

Set Initial phase to 0.

Set Sideband to modulate to Upper.

Set Hilbert transform filter order to 200.

SSB AM Demodulator Passband: In the Analog Passband sublibrary of 

the Modulation library

Set Carrier frequency to 25.

Set Initial phase to 0.

Set Lowpass filter design method to Butterworth.

Set Filter order to 2.

Set Cutoff frequency to 30

Frequency Modulation

In telecommunications and signal processing, frequency modulation (FM)conveys information over a carrier wave by varying its instantaneous frequency.

This is in contrast with amplitude modulation, in which the amplitude of the

carrier is varied while its frequency remains constant. In analog applications, the

difference between the instantaneous and the base frequency of the carrier isdirectly proportional to the instantaneous value of the input signal amplitude.

Digital data can be sent by shifting the carrier's frequency among a set of discrete

values, a technique known as frequency-shift keying.

Frequency modulation can be regarded as phase modulation where the carrier 

 phase modulation is the time integral of the FM modulating signal.

FM is widely used for broadcasting of music and speech, and in two-way radio

systems, in magnetic tape recording systems, and certain video transmission

systems. In radio systems, frequency modulation with sufficient bandwidth

 provides an advantage in cancelling naturally-occurring noise. Frequency-shift

keying (digital FM) is widely used in data and fax modems.

Page 25: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 25/41

Theory of Frequency Modulation

Suppose the baseband data signal (the message) to be transmitted is xm(t ) and the

sinusoidal carrier is , where f c is the carrier's base

frequency and Ac is the carrier's amplitude. The modulator combines the carrier 

with the baseband data signal to get the transmitted signal:

In this equation, is the instantaneous frequency of the oscillator and is the frequency deviation, which represents the maximum shift away from f c in one

direction, assuming xm(t ) is limited to the range ±1.

Although it may seem that this limits the frequencies in use to f c ± f Δ, this neglects

the distinction between instantaneous frequency and spectral frequency. The

frequency spectrum of an actual FM signal has components extending out to

infinite frequency, although they become negligibly small beyond a point.

Sinusoidal Base band signal:

While it is an over-simplification, a baseband modulated signal may beapproximated by a sinusoidal Continuous Wave signal with a frequency f m. The

integral of such a signal is

Thus, in this specific case, equation (1) above simplifies to:

Page 26: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 26/41

where the amplitude of the modulating sinusoid, is represented by the peak 

deviation (see frequency deviation).

The harmonic distribution of a sine wave carrier modulated by such a sinusoidal

signal can be represented with Bessel functions - this provides a basis for a

mathematical understanding of frequency modulation in the frequency domain.

Frequency Modulation (FM) is a form of modulation in which changes in the

carrier wave frequency correspond directly to changes in the baseband signal. FM

is considered an analog form of modulation because the baseband signal is

typically an analog waveform without discrete, digital values.

Common Applications

Frequency modulation (FM) is most commonly used for radio and television

 broadcast. The FM band is divided between a variety of purposes. Analog

television channels 0 through 72 utilize bandwidths between 54 MHz and 825MHz. In addition, the FM band also includes FM radio, which operates from 88

MHz to 108 MHz. Each radio station utilizes a 38 kHz frequency band to

 broadcast audio.

FM Theory

The basic principle behind FM is that the amplitude of an analog baseband signalcan be represented by a slightly different frequency of the carrier. We represent

this relationship in the graph below.

Page 27: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 27/41

 

Frequency Modulation

As this graph illustrates, various amplitudes of the baseband signal (shown in

white) relate to specific frequencies of the carrier signal (shown in red).

Mathematically, we represent this by describing the equations which characterize

FM.

First, we represent our message, or baseband, signal by the simple designation

m(t). Second, we represent a sinusoidal carrier by the equation:

 xc(t) = Ac cos (2πf ct).

The actual mathematical process to modulate a baseband signal, m(t), onto the

carrier requires a two-step process. First, the message signal must be integrated

with respect to time to get an equation for phase with respect to time, θ(t). This

integration enables the modulation process because phase modulation is fairlystraightforward with typical I/Q modulator circuitry. A block diagram description

of an FM transmitter follows.

 

FM Transmitter Block Diagram

As the block diagram above illustrates, the integration of a message signal results

in an equation for phase with respect to time. This equation is defined by the

following equation:

Page 28: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 28/41

where k  f  is the frequency sensitivity. Again, the resulting modulation that must

occur is phase modulation, which involves changing the phase of the carrier over time. This process is fairly straightforward and requires a quadrature modulator,

shown below.

Quadrature Modulator

As a result of phase modulation, the resulting FM signal, s(t), now represents the

frequency modulated signal. This equation is shown below.

where m(τ) = M cos (2πf mτ). More simply, we can also represent this equation as:

Page 29: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 29/41

Modulation Index

One important aspect of frequency modulation is the modulation index. We

already have established that changes in amplitude of the baseband correspond to

changes in carrier frequency. The factor that determines exactly how much the

carrier deviates from its center frequency is known as the modulation index.

Mathematically, we have already identified our integrated baseband signal as the

following equation.

We can simplify this equation to the following:

In the equation above, ∆ƒ is the frequency deviation, which represents the

maximum frequency difference between the instantaneous frequency and the

carrier frequency. In fact, the ratio of ∆ƒ to the carrier frequency is the modulation

index. This index, β , is thus defined by the equation

The integrated message signal can be represented as:

As a result, we can substitute this new representation of θ(t) into our originalformula to represent the final modulated FM signal as the following equation:

The modulation index affects the modulated sinusoid in that the larger the

modulation index, the greater the instantaneous frequency can be from the carrier.

Below we illustrate an FM modulated signal in which the center frequency is 500

kHz. In the graph below, the FM deviation has been selected as 425 kHz. As a

result, the modulated signal will have instantaneous frequencies from 75 kHz to

925 kHz. The wide range of frequencies is evident by observing the minimumamplitude of the baseband, when the modulated frequency is very small.

Page 30: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 30/41

 

FM Signal with 425 kHz FM Deviation

Contrast the image above to an FM signal where the frequency deviation issmaller. Below, we have chosen a 200 kHz FM deviation instead.

 

FM Signal with 200 kHz FM Deviation

Conclusions

Frequency Modulation (FM) is an important modulation scheme both because of 

its widespread commercial use, and because of its simplicity. As we have seen inthis document, frequency modulation can be simplified to angle modulation with a

simple integrator. As a result, we can generate frequency modulated signals with

the National Instruments vector signal generator, because they require nothing

more than an I/Q modulator.

Page 31: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 31/41

Applications

Magnetic tape storage

FM is also used at intermediate frequencies by all analog VCR systems, including

VHS, to record both the luminance (black and white) and the chrominance

 portions of the video signal. FM is the only feasible method of recording video to

and retrieving video from Magnetic tape without extreme distortion, as video

signals have a very large range of frequency components — from a few hertz to

several megahertz, too wide for equalizers to work with due to electronic noise

 below −60 dB. FM also keeps the tape at saturation level, and therefore acts as a

form of noise reduction, and a simple limiter can mask variations in the playback output, and the FM capture effect removes print-through and pre-echo. Acontinuous pilot-tone, if added to the signal — as was done on V2000 and many

Hi-band formats — can keep mechanical jitter under control and assist time base

correction.

These FM systems are unusual in that they have a ratio of carrier to maximum

modulation frequency of less than two; contrast this with FM audio broadcasting

where the ratio is around 10,000. Consider for example a 6 MHz carrier modulated

at a 3.5 MHz rate; by Bessel analysis the first sidebands are on 9.5 and 2.5 MHz,

while the second sidebands are on 13 MHz and −1 MHz. The result is a sidebandof reversed phase on +1 MHz; on demodulation, this results in an unwanted output

at 6−1 = 5 MHz. The system must be designed so that this is at an acceptable level

Sound

Page 32: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 32/41

FM is also used at audio frequencies to synthesize sound. This technique, known

as FM synthesis, was popularized by early digital synthesizers and became a

standard feature for several generations of personal computer sound cards.

Radio

Edwin Howard Armstrong (1890–1954) was an American electrical engineer who

invented frequency modulation (FM) radio. He patented the regenerative circuit in

1914, the superheterodyne receiver in 1918 and the super-regenerative circuit in

1922. He presented his paper: "A Method of Reducing Disturbances in Radio

Signaling by a System of Frequency Modulation", which first described FM radio

Example of Double-sideband AM

 

The (2-sided) spectrum of an AM signal.

A carrier wave is modeled as a simple sine wave, such as:

 

where the radio frequency (in Hz) is given by:

Page 33: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 33/41

 

The constants and represent the carrier amplitude and initial phase, and areintroduced for generality. For simplicity however, their respective values can be

set to 1 and 0.

Let m(t ) represent an arbitrary waveform that is the message to be transmitted.

And let the constant M represent its largest magnitude. For instance:

 

Thus, the message might be just a simple audio tone of frequency

It is generally assumed that and that

Then amplitude modulation is created by forming the product:

represents the carrier amplitude which is a constant that we would choose to

demonstrate the modulation index. The values A=1, and M =0.5, produce a y(t )

depicted by the graph labelled "50% Modulation" in Figure 4.

For this simple example, y(t ) can be trigonometrically manipulated into the

following equivalent form:

Therefore, the modulated signal has three components, a carrier wave and two

sinusoidal waves (known as sidebands) whose frequencies are slightly above and

 below

Also notice that the choice A=0 eliminates the carrier component, but leaves thesidebands. That is the DSBSC transmission mode. To generate double-sidebandfull carrier (A3E), we must choose:

Spectrum:

Page 34: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 34/41

For more general forms of m(t ), trigonometry is not sufficient. But if the top trace

of Figure 2 depicts the frequency spectrum, of m(t ), then the bottom trace depicts

the modulated carrier. It has two groups of components: one at positive

frequencies (centered on + ωc) and one at negative frequencies (centered on − ωc).

Each group contains the two sidebands and a narrow component in between that

represents the energy at the carrier frequency. We need only be concerned with the positive frequencies. The negative ones are a mathematical artifact that contains

no additional information. Therefore, we see that an AM signal's spectrum consists

 basically of its original (2-sided) spectrum shifted up to the carrier frequency.

Figure 2 is a result of computing the Fourier transform of:

using the following transform pairs:

Amplitude Modulator Designs

Circuits

A wide range of different circuits have been used for AM, but one of the simplest

circuits uses anode or collector modulation applied via a transformer. While it is

 perfectly possible to create good designs using solid-state electronics, valved

Page 35: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 35/41

(vacuum tube) circuits are shown here. In general, valves are able to more easily

yield RF powers, in excess of what can be easily achieved using solid-state

transistors. Many high-power broadcast stations still use valves.

 

Anode modulation using a transformer. The tetrode is supplied with an anode

supply (and screen grid supply) which is modulated via the transformer. The

resistor R1 sets the grid bias; both the input and outputs are tuned LC circuits

which are tapped into by inductive coupling

Modulation circuit designs can be broadly divided into low and high level.

Low level

Here a small audio stage is used to modulate a low power stage; the output of this

stage is then amplified using a linear RF amplifier. Wideband power amplifiers are

used to preserve the sidebands of the modulated waves. In this arrangement,

modulation is done at low power. To amplify it we use a wideband power 

amplifier at the output.

Page 36: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 36/41

Advantages:

The advantage of using a linear RF amplifier is that the smaller early stages can be

modulated, which only requires a small audio amplifier to drive the modulator.

Disadvantages:

The great disadvantage of this system is that the amplifier chain is less efficient,

 because it has to be linear to preserve the modulation. Hence Class C amplifiers

cannot be employed.

An approach which marries the advantages of low-level modulation with the

efficiency of a Class C power amplifier chain is to arrange a feedback system to

compensate for the substantial distortion of the AM envelope. A simple detector at

the transmitter output (which can be little more than a loosely coupled diode)

recovers the audio signal, and this is used as negative feedback to the audio

modulator stage. The overall chain then acts as a linear amplifier as far as the

actual modulation is concerned, though the RF amplifier itself still retains the

Class C efficiency. This approach is widely used in practical medium power 

transmitters, such as AM radiotelephones.

High level

With high level modulation, the modulation takes place at the final amplifier stage

where the carrier signal is at its maximum

Advantages:

One advantage of using class C amplifiers in a broadcast AM transmitter is that

only the final stage needs to be modulated, and that all the earlier stages can bedriven at a constant level. These class C stages will be able to generate the drive

for the final stage for a smaller DC power input. However, in many designs in

Page 37: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 37/41

order to obtain better quality AM the penultimate RF stages will need to be subject

to modulation as well as the final stage.

Disadvantages:

A large audio amplifier will be needed for the modulation stage, at least equal tothe power of the transmitter output itself. Traditionally the modulation is applied

using an audio transformer, and this can be bulky. Direct coupling from the audio

amplifier is also possible (known as a cascode arrangement), though this

Phase modulation (PM)

Phase modulation is a form of modulation that represents information as variations

in the instantaneous phase of a carrier wave.

Frequency modulation requires the oscillator frequency to deviate both above and

 below the carrier frequency. During the process of frequency modulation, the

 peaks of each successive cycle in the modulated waveform occur at times other 

than they would if the carrier were unmodulated. This is actually an incidental

 phase shift that takes place along with the frequency shift in fm. Just the opposite

action takes place in phase modulation. The af signal is applied to a PHASEMODULATOR in pm. The resultant wave from the phase modulator shifts in

 phase, as illustrated in figure 2-17. Notice that the time period of each successive

cycle varies in the modulated wave according to the audio-wave variation. Since

frequency is a function of time period per cycle, we can see that such a phase shift

in the carrier will cause its frequency to change. The frequency change in fm is

vital, but in pm it is merely incidental. The amount of frequency change has

nothing to do with the resultant modulated wave shape in pm. At this point the

comparison of fm to pm may seem a little hazy, but it will clear up as we progress.

.

Page 38: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 38/41

Phase modulation

Unlike its more popular counterpart, frequency modulation (FM), PM is not very

widely used for radio transmissions. This is because it tends to require more

complex receiving hardware and there can be ambiguity problems in determiningwhether, for example, the signal has changed phase by +180° or -180°. PM is

used, however, in digital music synthesizers such as the Yamaha DX7, even

though these instruments are usually referred to as "FM" synthesizers (both

modulation types sound very similar, but PM is usually easier to implement in this

area).

Phase Modulation Basics

Before looking at phase modulation it is first necessary to look at phase itself. A

radio frequency signal consists of an oscillating carrier in the form of a sine wave

is the basis of the signal. The instantaneous amplitude follows this curve moving

 positive and then negative, returning to the start point after one complete cycle - itfollows the curve of the sine wave. This can also be represented by the movement

of a point around a circle, the phase at any given point being the angle between the

start point and the point on the waveform as shown.

Phase modulation works by modulating the phase of the signal, i.e. changing the

rate at which the point moves around the circle. This changes the phase of the

signal from what it would have been if no modulation was applied. In other words

Page 39: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 39/41

the speed of rotation around the circle is modulated about the mean value. To

achieve this it is necessary to change the frequency of the signal for a short time.

In other words when phase modulation is applied to a signal there are frequency

changes and vice versa. Phase and frequency are inseparably linked as phase is the

integral of frequency. Frequency modulation can be changed to phase modulation

 by simply adding a CR network to the modulating signal that integrates themodulating signal. As such the information regarding sidebands, bandwidth and

the like also hold true for phase modulation as they do for frequency modulation,

 bearing in mind their relationship.

Forms of Phase Modulation

Although phase modulation is used for some analogue transmissions, it is far more

widely used as a digital form of modulation where it switches between different phases. This is known as phase shift keying, PSK, and there are many flavours of 

this. It is even possible to combine phase shift keying and amplitude keying in a

form of modulation known as quadrature amplitude modulation, QAM.

The list below gives some of the forms of phase shift keying that are used:

• PM - Phase Modulation

• PSK - Phase Shift Keying

• BPSK - Binary Phase Shift Keying

QPSK - Quadrature Phase Shift Keying• 8 PSK - 8 Point Phase Shift Keying

• 16 PSK - 16 Point Phase Shift Keying

• QAM - Quadrature Amplitude Modulation

• 16 QAM - 16 Point Quadrature Amplitude Modulation

• 64 QAM - 64 Point Quadrature Amplitude Modulation

• MSK - Minimum Shift Keying

• GMSK - Gaussian filtered Minimum Shift Keying

These are just some of the major forms of phase modulation that are widely used

in radio communications applications today. With today's highly software

adaptable radio communications systems, it is possible to change between the

different types of modulation to best meet the prevailing conditions.

Page 40: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 40/41

Theory of Phase Modulation:

 

An example of phase modulation. The top diagram shows the modulating signalsuperimposed on the carrier wave. The bottom diagram shows the resulting phase-

modulated signal.

PM changes the phase angle of the complex envelope in direct proportion to themessage signal.

Suppose that the signal to be sent (called the modulating or message signal) is m(t )

and the carrier onto which the signal is to be modulated is

 

Page 41: 49141143 Modulation

8/2/2019 49141143 Modulation

http://slidepdf.com/reader/full/49141143-modulation 41/41

Annotated:

carrier(time) = (carrier amplitude)*sin(carrier frequency*time + phase

shift)

This makes the modulated signal

 

This shows how m(t ) modulates the phase - the greater m(t) is at a point in time,

the greater the phase shift of the modulated signal at that point. It can also be

viewed as a change of the frequency of the carrier signal, and phase modulation

can thus be considered a special case of FM in which the carrier frequency

modulation is given by the time derivative of the phase modulation.

The spectral behaviour of phase modulation is difficult to derive, but themathematics reveals that there are two regions of particular interest:

• For small amplitude signals, PM is similar to amplitude modulation (AM)

and exhibits its unfortunate doubling of baseband bandwidth and poor 

efficiency.

• For a single large sinusoidal signal, PM is similar to FM, and its bandwidth

is approximately

,

where f M = ωm / 2π and h is the modulation index defined below. This isalso known as Carson's Rule for PM.

Overview of Phase Modulation:

Phase modulation, PM, is widely used in today's radio communications scene, with phase

shift keying being widely used for digital modulation and data transmission. It is used inall forms of radio communications from cellular technology to Wi-Fi, WiMAX, radio

 broadcasting of digital audio and TV, and many more forms of transmission.


Recommended