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LOVELY PROFESSIONAL UNIVERSITY

ELE 102

TERM PAPER

Applications of Frequency Modulation

Submitted to: Arvind Chandan Submitted by: Deepak kumar

Sr. lecturer Roll no. RB 4802 B37

Lovely Professional University B. tech Mechanical

Phagwara

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Acknowledgement

I am very thankful to Sir Arvind Chandan (Sr. lecturer) for his valueable guideance to

the preparation of the assignment on the title Applications of Frequency Modulation.

Deepak kumar

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Introduction

The history and evolution of angle modulation basically revolves around one man, Major

Edwin Armstrong, a radio pioneer who invented first the regenerative and then the

superheterodyne receiver in the 1910s, worked on the principles of frequency and phase

modulation starting in the 1920s. It was not until the 1930s, however, that he finally completedwork on a practical technique for wideband frequencymodulation broadcasting. At the turn of

the last century, the very early Paulson arc transmitter actually used the simplest form of FM,

frequency-shift keying (FSK), to transmit a wireless telegraph signal. With this type of wireless

transmitter, a continuous electrical arc would have its fundamental output frequency altered by

closing a telegraph key. When the key was closed, it would short out several turns of a tuning

inductor, thus changing the transmitter output frequency. For this reasons it was a form of

FSK.

Despite Armstrongs efforts, the implementation of FM broadcasting was fought by RCA and

NBC through 1945, only becoming popular in the United States during the late 1960s and early

1970s when technological advances reduced the cost of equipment and improved the quality of

service. AMPS cellular-telephone service, an FM-based system, was introduced in the United

States in 1983. Today FM is used for the legacy FM broadcast band, standard TV-broadcasting

sound transmission, Direct-satellite TV service, cordless telephones, and just about every type

of business band and mobile-radio service. FM is capable of much more noise immunity than

AM, and is now the most popular form of analog modulation.

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Frequency-Modulation Theory

The classic definition of FM is that the instantaneous output frequency of a transmitter is

varied in accordance with the modulating signal. Recall that we can write an equation for a sine

wave as follows:

While amplitude modulation is achieved by varying EP, frequency modulation is realized by

varying (omega) in accordance with the modulating signal or message. Notice that one can

also vary to obtain another form of angle modulation known as phase modulation (PM).

Figure below for a time display of a typical FM signal.

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Definition

An important concept in the understanding of FM is that of frequency deviation. The amount

of frequency deviation a signal experiences is a measure of the change in transmitter outputfrequency from the rest frequency of the transmitter. The rest frequency of a transmitter is

defined as the output frequency with no modulating signal applied. For a transmitter with linear

modulation characteristics, the frequency deviation of the carrier is directly proportional to the

amplitude of the applied modulating signal. Thus an FM transmitter is said to have modulation

sensitivity, represented by a constant, kf, of so many kHz/V, kf = frequency deviation/V = kf

kHz/V

For a single modulating tone of eM (t) = eM sin (Mt), the amount of frequency deviation is given

by

Where is the instantaneous frequency deviation and eM(t) represents the modulating signal.

The peak deviation is given by

Where EM is the peak value.

1. Frequency Modulation Techniques for the control of LED Colour Mixing

and Intensity.

The technology is relevant to both single colour intensity colour and colourmixing

applications. Most existing production designs for LED colour mixing use a technique called

Pulse Width Modulation (PWM). PWM is characterised by a fixed frequency control

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waveform, where the intensity of each LED colour is controlled by the width of the pulse. This

technology has been widely used in the first generation of LED colour mixing products. Whilst

the technique works, it has a number of drawbacks:

1. The response of control input to LED current is largely linear. As LEDs are non-linear

devices, this does not produce a linear intensity response.

2. PWM is a fixed frequency system, this means that all LEDs switch on at the same time in

the cycle. In larger systems this leads to asymmetric loading of the power source and can

complicate EMC issues.

A number of patents have been issued covering the use of PWM in such applications. The

latest developments by Artistic Licence are intended to solve these problems. The technique of

Frequency Modulation uses the concept of a fixed width control pulse delivered at a variable

frequency as shown in the figures below. The average current supplied to the LEDs is of the

ratio

X/(X+Y). As the frequency increases, the intensity of the LEDs is reduced. It can be seen that

the technique is inherently non-linear. However, the benefit is that this nonlinearity opposes the

inherent non-linear LED response. The result is to increase the resolution over the low intensity

end of the control range. The power supply loading issue is also addressed by Frequency

Modulation. As the frequency varies, the switch on point for each circuit varies in time. This

effect reduces the asymmetric power supply loading.

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2. Radio and television broadcast

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

The FM band is divided between varieties of purposes. Analog television channels 0

through 72 utilize bandwidths between 54 MHz and 825 MHz. 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 signal can be

represented by a slightly different frequency of the carrier. We represent this relationship

in the graph below.

Figure 1. Frequency Modulation

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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 (2fct).

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, (t). This integration enables the

modulation process because phase modulation is fairly straightforward with typical I/Q

modulator circuitry. A block diagram description of an FM transmitter follows.

Figure 2. 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:

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where kf 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.

Figure 3. 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() = M cos (2fm). More simply, we can also represent this equation as:

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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, is the frequency deviation, which represents the maximum

frequency difference between the instantaneous frequency and the carrier frequency. In

fact, the ratio of to the carrier frequency is the modulation index. This index, , is

thus defined by

The integrated message signal can be represented as:

As a result, we can substitute this new representation of (t) into our original formula to

represent the final modulated FM signal as the following equation:

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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 minimum amplitude of the baseband, when the

modulated frequency is very small.

Figure 4. FM Signal with 425 kHz FM Deviation

Contrast the image above to an FM signal where the frequency deviation is smaller.

Below, we have chosen a 200 kHz FM deviation instead.

Figure 5. FM Signal with 200 kHz FM Deviation

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As Figure 5 illustrates, the instantaneous frequency range of the modulated signal is

much smaller with a smaller FM deviation.

Conclusion

1. Finally this suggests that the frequency modulation technique is widely open to the

lighting industry.The technique is clearly applicable to all forms of additive colour mixing

including light sources other than LEDs. Additionally it is clear that the FM modulation could

be set by local controls.

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

its widespread commercial use, and because of its simplicity. As we have seen in

this 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.

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References

1. R. G. Driggers, C. E. Halford, G. D. Boreman, D. J. Lattman, and K. F. Williams,

"Parameters of spinning FM reticles," Appl. Opt. 29, (Dec. 10, 1990).

2. R. 0. Carpenter, "Comparison of AM and FM reticle systems," AppI. Opt. 2(3),

229 (1963).

3. R. C. Anderson and P. R. Callary, "Computer modeling of optical trackers, Opt.

Eng. 20(6), 861865 (1981).

4. K. Suzuki, "Analysis of rising sun reticle," Opt. Eng. 18(3), 350-351 (1979).

5. Craubner, ' 'Digital simulation of reticle systems,' ' in Image Processing for

Missile Guidance, Proc. SPIE 238, 414424 (1980).

6. T. Buttweiler, "Optimum modulation characteristics for amplitude-modulated and

frequency-modulated infrared systems," JOSA 5 1(9), 1011(1961).

7. P. Menger and K. O'Brien, "Analysis of error response of amplitude modulated

reticles," JOSA 54(5), 668 (1964).

8. A. Gedance, "Comparison of infrared tracking systems," AppI. Opt. 51, 1127

(1961).

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Thank you