AMPLITUDE MODULATION, FREQUENCY MODULATION, PHASE MODULATION

AMPLITUDE MODULATION, FREQUENCY MODULATION, PHASE MODULATION

CONTENTS:-

1.     ACKNOWLEDGEMENT

2.     OBJECTIVE

3.     BASIC COMMUNICATION SYSTEM

4.     MODULATION

5.     AMPLITUDE MODULATION

a.     Forms of amplitude modulation

b.    Designation and description

c.      Example

d.    Modulation index

6.     FREQUENCY MODULATION

a.     Fm spectrum

b.    Example

c.      Fm performance

1.     Band with

2.     Efficiency

3.     Noise

7.     PHASE MODULATION

a.     Modulation index

b.    Example

8.     CONCLUSION

9.     REFERENCES

AKNOWLEDGEMENT:-

A Term Paper as this would not have been written without the significant inputs and efforts of many people. I would thus like to first thank my respected MISS INDU RANA, for her guidance and help during the course of the making of this Term Paper. Without her support this term paper would have not been made.

My special thanks to my Friends and god who have helped me in developing innovative ideas

 

 

 

 

 

1.OBJECTIVE:-

1.     Know the relationship of carrier frequency, modulation frequency and modulation index to efficiency and bandwidth

2.     Compare FM systems to AM systems with regard to efficiency, bandwidth and noise.

2.BASIC SYSTEM:-

The basic communications system has:

Transmitter: The sub-system that takes the information signal and processes it prior to transmission. The transmitter modulates the information onto a carrier signal, amplifies the signal and broadcasts it over the channel.

Channel: The medium which transports the modulated signal to the receiver. Air acts as the channel for broadcasts like radio. May also be a wiring system like cable TV or the Internet.

Receiver: The sub-system that takes in the transmitted signal from the channel and processes it to retrieve the information signal. The receiver must be able to discriminate the signal from other signals which may using the same channel (called tuning), amplify the signal for processing and demodulate (remove the carrier) to retrieve the information. It also then processes the information for reception (for example, broadcast on a loudspeaker).

3.MODULATION:-

The information signal can rarely be transmitted as is, it must be processed. In order to use electromagnetic transmission, it must first be converted from audio into an electric signal. The conversion is accomplished by a transducer. After conversion it is used to modulate a carrier signal.

A carrier signal is used for two reasons:

• To reduce the wavelength for efficient transmission and reception (the optimum antenna size is ½ or ¼ of a wavelength). A typical audio frequency of 3000 Hz will have a wavelength of 100 km and would need an effective antenna length of 25 km! By comparison, a typical carrier for FM is 100 MHz, with a wavelength of 3 m, and could use an antenna only 80 cm long.
• To allow simultaneous use of the same channel, called multiplexing. Each unique signal can be assigned a different carrier frequency (like radio stations) and still share the same channel. The phone company actually invented modulation to allow phone conversations to be transmitted over common lines.

The process of modulation means to systematically use the information signal (what you want to transmit) to vary some parameter of the carrier signal. The carrier signal is usually just a simple, single-frequency sinusoid (varies in time like a sine wave).

The basic sine wave goes like V(t) = V_o sin (2 f t + ) where the parameters are defined below:

V(t) the voltage of the signal as a function of time.

V_o the amplitude of the signal (represents the maximum value achieved each cycle)

f the frequency of oscillation, the number of cycles per second (also known as Hertz = 1 cycle per second)

the phase of the signal, representing the starting point of the cycle.

To modulate the signal just means to systematically vary one of the three parameters of the signal: amplitude, frequency or phase. Therefore, the type of modulation may be categorized as either

AM: amplitude modulation

FM: frequency modulation or

PM: phase modulation

4.AMPLITUDE MODULATION:-

Amplitude modulation (AM) is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. AM works by varying the strength of the transmitted signal in relation to the information being sent. For example, changes in the signal strength can be used to reflect the sounds to be reproduced by a speaker, or to specify the light intensity of television pixels. (Contrast this with frequency modulation, also commonly used for sound transmissions, in which the frequency is varied; and phase modulation, often used in remote controls, in which the phase is varied)

In the mid-1870s, a form of amplitude modulation—initially called "undulatory currents"—was the first method to successfully produce quality audio over telephone lines. Beginning with Reginald Fessenden's audio demonstrations in 1906, it was also the original method used for audio radio transmissions, and remains in use today by many forms of communication—"AM" is often used to refer to the mediumwave broadcast band (see AM radio).

A.FORMS OF AMPITUDE MODULATION:-

As originally developed for the electric telephone, amplitude modulation was used to add audio information to the low-powered direct current flowing from a telephone transmitter to a receiver. As a simplified explanation, at the transmitting end, a telephone microphone was used to vary the strength of the transmitted current, according to the frequency and loudness of the sounds received. Then, at the receiving end of the telephone line, the transmitted electrical current affected an electromagnet, which strengthened and weakened in response to the strength of the current. In turn, the electromagnet produced vibrations in the receiver diaphragm, thus closely reproducing the frequency and loudness of the sounds originally heard at the transmitter.

In contrast to the telephone, in radio communication what is modulated is a continuous wave radio signal (carrier wave) produced by a radio transmitter. In its basic form, amplitude modulation produces a signal with power concentrated at the carrier frequency and in two adjacent sidebands. This process is known as heterodyning. Each sideband is equal in bandwidth to that of the modulating signal and is a mirror image of the other. Amplitude modulation that results in two sidebands and a carrier is often called double sideband amplitude modulation (DSB-AM). Amplitude modulation is inefficient in terms of power usage and much of it is wasted. At least two-thirds of the power is concentrated in the carrier signal, which carries no useful information (beyond the fact that a signal is present); the remaining power is split between two identical sidebands, though only one of these is needed since they contain identical information.

To increase transmitter efficiency, the carrier can be removed (suppressed) from the AM signal. This produces a reduced-carrier transmission or double-sideband suppressed-carrier (DSBSC) signal. A suppressed-carrier amplitude modulation scheme is three times more power-efficient than traditional DSB-AM. If the carrier is only partially suppressed, a double-sideband reduced-carrier (DSBRC) signal results. DSBSC and DSBRC signals need their carrier to be regenerated (by a beat frequency oscillator, for instance) to be demodulated using conventional techniques.

Even greater efficiency is achieved—at the expense of increased transmitter and receiver complexity—by completely suppressing both the carrier and one of the sidebands. This is single-sideband modulation, widely used in amateur radio due to its efficient use of both power and bandwidth.

A simple form of AM often used for digital communications is on-off keying, a type of amplitude-shift keying by which binary data is represented as the presence or absence of a carrier wave. This is commonly used at radio frequencies to transmit Morse code, referred to as continuous wave (CW) operation.

In 1982, the International Telecommunication Union (ITU) designated the various types of amplitude modulation as follows:

B.DESIGNATION		DESCRIPTION:-
A3E		double-sideband full-carrier - the basic AM modulation scheme
R3E		single-sideband reduced-carrier
H3E		single-sideband full-carrier
J3E		single-sideband suppressed-carrier
B8E		independent-sideband emission
C3F		vestigial-sideband
Lincompex		linked compressor and expander

C.EXAMPLE;DOUBLE SIDEBAND AM:-

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

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

For generality, and are arbitrary constants that represent the carrier amplitude and initial phase. For simplicity, we set their respective values 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:

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

For generality, and are arbitrary constants that represent the carrier amplitude and initial phase. For simplicity, we set their respective values 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 another constant we may choose. 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 u) whose frequencies are slightly above and below  

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

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

In mathmaticaly express as  the Fourier transform of:   using the following transform pairs:

In terms of the positive frequencies, the transmission bandwidth of AM is twice the signal's original (baseband) bandwidth—since both the positive and negative sidebands are shifted up to the carrier frequency. Thus, double-sideband AM (DSB-AM) is spectrally inefficient, meaning that fewer radio stations can be accommodated in a given broadcast band. The various suppression methods in Forms of AM can be readily understood in terms of the diagram in Figure 2. With the carrier suppressed there would be no energy at the center of a group. And with a sideband suppressed, the "group" would have the same bandwidth as the positive frequencies of   The transmitter power efficiency of DSB-AM is relatively poor (about 33%). The benefit of this system is that receivers are cheaper to produce. The forms of AM with suppressed carriers are found to be 100% power efficient, since no power is wasted on the carrier signal which conveys no information.

D.MODULATION INDEX:-

As with other modulation indices, in AM, this quantity, also called modulation depth, indicates by how much the modulated variable varies around its 'original' level. For AM, it relates to the variations in the carrier amplitude and is defined as:   where and were introduced above.

So if h = 0.5, the carrier amplitude varies by 50% above and below its unmodulated level, and for h = 1.0 it varies by 100%. To avoid distortion in the A3E transmission mode, modulation depth greater than 100% must be avoided. Practical transmitter systems will usually incorporate some kind of limiter circuit, such as a VOGAD, to ensure this

Variations of modulated signal with percentage modulation are shown below. In each image, the maximum amplitude is higher than in the previous image. Note that the scale changes from one image to the next.

Variations of modulated signal with percentage modulation are shown below. In each image, the maximum amplitude is higher than in the previous image. Note that the scale changes from one image to the next.

6.FREQUENCY MODULATION:-

Frequency modulation uses the information signal, V_m(t) to vary the carrier frequency within some small range about its original value. Here are the three signals in mathematical form:

• Information: V_m(t)
• Carrier: V_c(t) = V_co sin ( 2  f_c t + 
• FM: V_FM (t) = V_co sin (2 f_c + (f/V_mo) V_m (t)t + 

We have replaced the carrier frequency term, with a time-varying frequency. We have also introduced a new term: f, the peak frequency deviation. In this form, you should be able to see that the carrier frequency term: f_c + (f/V_mo) V_m (t) now varies between the extremes of f_c - f and f_c + f. The interpretation of f becomes clear: it is the farthest away from the original frequency that the FM signal can be. Sometimes it is referred to as the "swing" in the frequency.

We can also define a modulation index for FM, analogous to AM:

 = f/f_m , where f_m is the maximum modulating frequency used.

The simplest interpretation of the modulation index, is as a measure of the peak frequency deviation, f. In other words, represents a way to express the peak deviation frequency as a multiple of the maximum modulating frequency, f_m, i.e. f =  f_m.

Example: suppose in FM radio that the audio signal to be transmitted ranges from 20 to 15,000 Hz (it does). If the FM system used a maximum modulating index, , of 5.0, then the frequency would "swing" by a maximum of 5 x 15 kHz = 75 kHz above and below the carrier frequency.

Here is a simple FM signal:

Here, the carrier is at 30 Hz, and the modulating frequency is 5 Hz. The modulation index is about 3, making the peak frequency deviation about 15 Hz. That means the frequency will vary somewhere between 15 and 45 Hz. How fast the cycle is completed is a function of the modulating frequency.

A.FM SPECTRUM:-

A spectrum represents the relative amounts of different frequency components in any signal. Its like the display on the graphic-equalizer in your stereo which has leds showing the relative amounts of bass, midrange and treble. These correspond directly to increasing frequencies (treble being the high frequency components). It is a well-know fact of mathematics, that any function (signal) can be decomposed into purely sinusoidal components (with a few pathological exceptions) . In technical terms, the sines and cosines form a complete set of functions, also known as a basis in the infinite-dimensional vector space of real-valued functions (gag reflex). Given that any signal can be thought to be made up of sinusoidal signals, the spectrum then represents the "recipe card" of how to make the signal from sinusoids. Like: 1 part of 50 Hz and 2 parts of 200 Hz. Pure sinusoids have the simplest spectrum of all, just one component:

In this example, the carrier has 8 Hz and so the spectrum has a single component with value 1.0 at 8 Hz

The FM spectrum is considerably more complicated. The spectrum of a simple FM signal looks like:

The carrier is now 65 Hz, the modulating signal is a pure 5 Hz tone, and the modulation index is 2. What we see are multiple side-bands (spikes at other than the carrier frequency) separated by the modulating frequency, 5 Hz. There are roughly 3 side-bands on either side of the carrier. The shape of the spectrum may be explained using a simple heterodyne argument: when you mix the three frequencies (f_c, f_m and f) together you get the sum and difference frequencies. The largest combination is f_c + f_m + f, and the smallest is f_c - f_m - f. Since f =  f_m, the frequency varies ( + 1) f_m above and below the carrier.

A more realistic example is to use an audio spectrum to provide the modulation:

In this example, the information signal varies between 1 and 11 Hz. The carrier is at 65 Hz and the modulation index is 2. The individual side-band spikes are replaced by a more-or-less continuous spectrum. However, the extent of the side-bands is limited (approximately) to ( + 1) f_m above and below. Here, that would be 33 Hz above and below, making the bandwidth about 66 Hz. We see the side-bands extend from 35 to 90 Hz, so out observed bandwidth is 65 Hz.

You may have wondered why we ignored the smooth humps at the extreme ends of the spectrum. The truth is that they are in fact a by-product of frequency modulation (there is no random noise in this example). However, they may be safely ignored because they are have only a minute fraction of the total power. In practice, the random noise would obscure them anyway.

B.EXAMPLE: FM Radio

FM radio uses frequency modulation, of course. The frequency band for FM radio is about 88 to 108 MHz. The information signal is music and voice which falls in the audio spectrum. The full audio spectrum ranges form 20 to 20,000 Hz, but FM radio limits the upper modulating frequency to 15 kHz (cf. AM radio which limits the upper frequency to 5 kHz). Although, some of the signal may be lost above 15 kHz, most people can't hear it anyway, so there is little loss of fidelity. FM radio maybe appropriately referred to as "high-fidelity."

If FM transmitters use a maximum modulation index of about 5.0, so the resulting bandwidth is 180 kHz (roughly 0.2 MHz). The FCC assigns stations ) 0.2 MHz apart to prevent overlapping signals (coincidence? I think not!). If you were to fill up the FM band with stations, you could get 108 - 88 / .2 = 100 stations, about the same number as AM radio (107). This sounds convincing, but is actually more complicated (agh!).

FM radio is broadcast in stereo, meaning two channels of information. In practice, they generate three signals prior to applying the modulation:

• the L + R (left + right) signal in the range of 50 to 15,000 Hz.
• a 19 kHz pilot carrier.
• the L-R signal centered on a 38 kHz pilot carrier (which is suppressed) that ranges from 23 to 53 kHz .

So, the information signal actually has a maximum modulating frequency of 53 kHz, requiring a reduction in the modulation index to about 1.0 to keep the total signal bandwidth about 200 kHz.

C.FM PERFORMANCES:-

BANDWITH:

As we have already shown, the bandwidth of a FM signal may be predicted using:

BW = 2 ( + 1 ) f_m

where  is the modulation index and

f_m is the maximum modulating frequency used.

FM radio has a significantly larger bandwidth than AM radio, but the FM radio band is also larger. The combination keeps the number of available channels about the same.

The bandwidth of an FM signal has a more complicated dependency than in the AM case (recall, the bandwidth of AM signals depend only on the maximum modulation frequency). In FM, both the modulation index and the modulating frequency affect the bandwidth. As the information is made stronger, the bandwidth also grows.

EFFICIENCY:

The efficiency of a signal is the power in the side-bands as a fraction of the total. In FM signals, because of the considerable side-bands produced, the efficiency is generally high. Recall that conventional AM is limited to about 33 % efficiency to prevent distortion in the receiver when the modulation index was greater than 1. FM has no analogous problem.

The side-band structure is fairly complicated, but it is safe to say that the efficiency is generally improved by making the modulation index larger (as it should be). But if you make the modulation index larger, so make the bandwidth larger (unlike AM) which has its disadvantages. As is typical in engineering, a compromise between efficiency and performance is struck. The modulation index is normally limited to a value between 1 and 5, depending on the application.

NOISE:

FM systems are far better at rejecting noise than AM systems. Noise generally is spread uniformly across the spectrum (the so-called white noise, meaning wide spectrum). The amplitude of the noise varies randomly at these frequencies. The change in amplitude can actually modulate the signal and be picked up in the AM system. As a result, AM systems are very sensitive to random noise. An example might be ignition system noise in your car. Special filters need to be installed to keep the interference out of your car radio.

FM systems are inherently immune to random noise. In order for the noise to interfere, it would have to modulate the frequency somehow. But the noise is distributed uniformly in frequency and varies mostly in amplitude. As a result, there is virtually no interference picked up in the FM receiver. FM is sometimes called "static free, " referring to its superior immunity to random noise

7.PHASE MODULATION:-

Phase modulation (PM) is a form of modulation that represents information as variations in the instantaneous phase of a carrier wave.

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 determining whether, 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).

PM changes the phase angle of the complex envelope in direct proportion to the message 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

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 the mathematics 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 = ω_m / 2π and h is the modulation index defined below. This is also known as Carson's Rule for PM.

MODULATION INDEX:-

As with other modulation indices, this quantity indicates by how much the modulated variable varies around its unmodulated level. It relates to the variations in the phase of the carrier signal:

where Δθ is the peak phase deviation. Compare to the modulation index for frequency modulation

9.CONCLUSION:-                                                                        

By the virtue of this Term-Paper, working endlessly days and night, researching and gathering facts and figures. I have gained enough knowledge and experience in development of “AM,PM,FM” in particular and “COMMUNICATION SYSTEM ” in general so that I can deliver my very best in these fields.

                   Apart from these, I have gained a lot of knowledge about the recent development tools and techniques pursuing with the help of these concepts.

                   At the last but not the least I would like to thank to all my supporters for supporting me in such a project through which I have gained a lot of understanding about the above topic.