TOPIC 2

ANALOG MODULATION

Modulation Principle

In understanding the concept of modulation and demodulation, student must studying the condition happened by referring to the table below.

Table 2.1: Modulation and demodulation process

Definition of Modulation

Modulation is a process of transmit a lower frequency of information spectrum band to the higher frequency of information spectrum band. Modulation is necessary in order to transmit the information signal.

Figure 2.1 : The Frequency Spectrum of the Information Signal

In the other words, modulation is a process of modifying a carrier signal (example:- electromagneticwave (emf)) by the information signal by varying one of the parameters (example: - amplitude, frequency or phase) of the car rier signal. Usually the information signal or modulating signal would be in the voice, video, binar y data or some other information in the lower audio frequency signal (AF) into the higher radio frequency signal (RF) in order to make the signal suitable for transmission in a long distance. The component2 that has been used when modulation process happened are:

i. Information Signal (fm) As known as Intelligence Signal, modulating signal and audio signal or base band signal.

ii. Carrier Signal (fc) as known as Carrier fr equency

The Purpose of Modulation Process.

(a) An easier transmission because of the size of antenna can reduced. This is happened because the lower frequency can be transmit or sent to the higher frequency and can decrease the antenna size. Example the frequency of transmission FM (88 108MHz) is 1metre. You can calculate to get antenna size. If one information didnt do modulation, imaging the information frequency is 500 Hz and by using this equation v = f , get the answer of, from this answer ,you must divide with 4, this is because in the theory antenna size can effective to received the signal is /4.

(b) To reduce the noise and distortion By using wideband like PCM (The signal has been converting to pulse condition. The information signal has been transmit directly will be produce suddenly distortions. This is because the combination of radio waveform has same with range frequency.

(c) Can make frequency division. Where the user can choose the station, because each station has own wideband.

(d) Multiplication technique. Allow only one or some signal can transmit with parallel in one difference wideband. The type of multiplexing is frequency division multiplexing (FM) and time division multiplexing (TDM).

Demodulation Process

Demodulation is the act of extracting the original information-bearing signal from a modulated carrier wave. A demodulator is an electronic circuit (or computer program in a software defined radio) that is used to recover the information content from the modulated carrier wave. These terms are traditionally used in connection with radio receivers, but many other systems use many kinds of demodulators. Another common one is in a modem, which is a contraction of the terms modulator/demodulator.

Exercise 1

Give the definition of modulation and demodulation

Answer:

Modulation is the process of transmit one of the information spectra band that has lower frequency to spectra band that has higher frequency and through this process the characteristic of amplitude and the carrier will be changing.

Demodulation is the process of to get back the information signal from signal modulation.

Exercise 2

Define the main component must needed in modulation process.

Answer:

Two main component must needed in modulation process are i. Information signal. ii. Carrier Signal

Exercise 3

Define three reasons why modulation process is important for make far distance communication

Answer 2: i. Easier to transmit signal process, because of the antenna size can make reduce. ii. Multiplexing process can be done, so frequency division can be happened. iii. To reduce noise and distortion.

AMPLITUDE MODULATION

Definition of Amplitude Modulation (AM)

It is a process of the carrier amplitude signal changes accordingly with the amplitude of the modulating signal. That means, carrier amplitude is proportional with the amplitude of information signal. The frequency and phase of the carrier signal has not change before and after modulation process.

Definition of Demodulation Amplitude

It is a process to recover the information signal that has been transmitted and pass it on the user. The most commonly DSB System used diode detector, transistor detector, tuned radio frequency (TRF) and superhetodin detector.

Amplitude Modulation process

Figure 2.2 : Amplitude modulation process

Amplitude Modulated Signal Waveform

The figure below is shown the example of information signal, carrier signal and amplitude modulated signal.

Figure 2.3 : AM Waveform Signal

Fundamental Concept:

In amplitude modulation (AM), Carrier signal will be change following the amplitude information signal, which means when the amplitude of the information signal at the maximum level, the amplitude of the carrier signal also in maximum level and vice versa. Refer in Figure 2.3 above.

Exercise 4

By using the signal below, draw the waveform has been produced from the Amplitude modulator.

Answer

Refer Figure 2.3

Exercise 5

Differentiate between carrier waveform and modulated waveform

Answer

Refer to block diagram of modulation process (Figure 2.2)

Exercise 6

Give three frequencies that have been produced after Amplitude Modulation process (AM).

Answer

i. Carrier Frequency (fp). ii. upper side frequency (fp + fm). iii. lower side frequency (fp fm).

Mathematic equation of amplitude modulation (AM)

Lets say the instantaneous wave of sinusoidal carrier given by Vc and modulating /information signal given by Vm

Where: vc = carrier voltage Vc = peak voltge of carrier signal fc = c / 2 = carrier frequency

and

vm = information voltge fm = m / 2 = information frequency

From two equation above and by using explanation of mathematic, so the equation of amplitude modulation equation is like this :

Where are: Vc = Peak voltage of carrier waveform m = Modulation index c = 2 fc m = 2 fm

AM Frequency Spectrum

Imaging the component of frequency consist in AM Modulation signal. AM modulation waveform is Sinus Form that consists of the component at three difference frequency. That is:

i. Carrier frequency, fc. ii. Lower sideband Frequency, fc - fm iii. Upper sideband Frequency, fc + fm

Amplitude maximum value = ( Vc + Vm ) i.e sin mt = +1 Amplitude minimum value = ( Vc - Vm ) i.e sin mt = -1

BW

Bandwidth (BW) for AM signal :

BW = maximum frequency minimum frequency = ( fc + fm ) ( fc - fm ) = 2fm

Modulation waveform equation shows you there are three components have differentiated. There are:

i. Fc ii. fc + fm iii. fc - fm

*all this equation can shows you in amplitude spectrum form

Modulation index, Power and Efficiency transmission

Modulation Index (m) Shows you the carrier amplitude waveform can change after modulation happened by using information waveform

BW

Vc

mVc/2 mVc/2

Figure 2.4 : AM frequency spectrum

fc - fm fc + fm fc

Modulation Index definition:

Or from figure amplitude modulation waveform, Modulation percentage (% m)

Figure 2.6 : AM waveform

Refer to Figure 2.6 above, to get modulation percentage value is :

Vm Vmaksima Vm + Vc

Vminima Vc - Vm

Figure 2.5 : Amplitude modulation waveform

Vc

Maximum value for m is 1. If m > 1 modulation envelope is not in sinus form.

Figure 2.7 : AM Waveform for m < 1, m = 1, m>1

The usage Oscilloscope in measuring m

There are two techniques to verify modulation percentage for amplitude modulation waveform:

i. Insert the modulation waveform to input x or input y and verify result can display at OSK as shown figure below.

ii. Connect the modulation waveform to input y and information signal to input x. The waveform will display in trapezoid form as shown in figure below

Figure 2.8: Trapezium form in amplitude waveform

A B

Power component in amplitude modulation waveform

Figure 2.9 : Power spectrum signal AM

The power has develop by amplitude modulation waveform K that all the carrier power Pc, upper sideband power, PUSB and lower sideband power,PLSB.

)2

1(2mK p +=

44

22cc

c

PmPmP ++=

Example 1

One amplitude modulation waveform can be presented in this equation

V = 20 (1 + 0.8 sin 10 000t) sin 150 000t

Calculate: 1). Carrier amplitude 2). Carrier Frequency 3). Modulation Frequency 4). Modulation Percentage 5). If carrier power is 3kw, how much the total of modulation power and inside power for each

sideband.

Answer:

i. Carrier amplitude, V = 20V ii. Carrier Frequency, fc = c / 2

= 150 x 103 / 2p = 23873.24Hz

iii. Modulation Frequency, fm = m / 2 = 10 x 10 3 / 2p = 1591.55Hz

iv. Modulation percentage, m = 0.8 x 100 = 80%

v. Power total , PT = Pc (1 + m2 / 2) = 3000 (1 + 0.82 / 2)

= 3960W

The power for each sideband is

PT = Pc + PLSB + PUSB ; PUSB = PLSB = Pc + 2PUSB

3960 = 3000 + 2PUSB 2PUSB = 960 PUSB = 480 watt

PUSB = PLSB = 480 watt

The power for each sideband

Exercise 7

One amplitude modulation waveform as presented by this equation :

Get this answer: i. Carrier Amplitude. ii. Carrier Frequency. iii. Information Frequency. iv. Modulation Index. v. Modulation Percentage. vi. Component Upper sideband and Lower sideband

Answer

i. Carrier Amplitude, Vc = 20 Vpeak ii. Carrier Frequency, fc = 0.6MHz iii. Information Frequency, fm = 5kHz iv. Modulation Index, m = 0.5 v. Modulation Percentage, % m = 50 % vi. Upper sideband, fUSB = 605kHz

Lower sideband, fLSB = 595kHz

Exercise 8

Based on one of an experiment , frequency carrier 46kHz has 0.5V amplitude,has been modulated by one audio signal frequency 300Hz that has 0.2V amplitude. Find :

i. Modulation percentage. ii. Frequency-frequency in this modulated signal. iii. Draw a spectra frequency and calculate a bandwidth. iv. Draw the amplitude modulation waveform

Answer:

i. %m = 40% ii. fc = 465kHz

fUSB = 465.3 kHz fLSB = 464.7kHz

iii. Bw = 600 Hz

iv. Amplitude modulation signal

AM signal waveform

fc fUSB fLSB

AM spectrum frequency

SELF ASSESSMENT

1). Give the definition of amplitude modulation process and state three reasons why this process is needed.

2). One of amplitude modulation waveform transmitter has antenna resistor 50O.Carrier waveform frequency and maximum waveform has 1 MHz and 1 KHz. Peak to peak RF for amplitude modulation waveform can up to maximum 15V and down to minimum 5V.With Imaging sinusoidal modulation, get the answer for :

i. Maximum Amplitude Waveform, Carrier Waveform, demodulation and modulation index.

ii. Equation mathematics of amplitude modulation waveform. iii. Total of the power transmission and power of each sideband. iv. Efficiency transmitter percentage of amplitude modulation waveform

3). State the function of modulation and demodulation in system amplitude modulation. 4). One amplitude modulation waveform can be presented in this equation :

Calculate : i. Carrier amplitude. ii. Carrier Frequency. iii. Modulation Frequency. iv. Modulation Percentage. v. If power of carrier is 3Kw , how much the power for each sideband

Answer

1). Refer notes. 2). i. Maximum Amplitude, Vm = 5V

Carrier Amplitude, Vc = 10V Modulation index, m = 0.5V

ii. Vam = 10 sin 2 1 x 106 t + 2.5 cos 2 999 x 103 t - 2.5 cos 2 1001 x 103 t iii. Total of power transmission = 1.125 W iv. The power for each sideband = 0.0625 W

Transmission Efficiency, % = 11.11%

3). Refer notes. 4). i. Vc = 20V

ii. fc = 28.87kHz iii. fm = 159Hz iv. % m = 80 % v. Pt = 3960 Watt

Theoretical Background

Modulation is a process by which a parameter of a high frequency sinusoid is modified in accordance with the message signal to be transmitted. The high frequency sinusoid is known as the carrier and the message signal is the modulating signal. The modified carrier signal is called the modulated signal. A consequence of modulation is a translation or shifting of the message spectrum to a higher frequency band. Message signals, by nature, are low frequency or baseband signals. A baseband signal is a signal whose spectrum is positioned close to dc ( =0). Examples of baseband signals include speech signals whose spectrum occupies the frequency band from 0 to 3.5 Khz and video signals whose spectrum occupies the frequency band. 0 to 6 MHz. There are two broad classes of communication baseband communication and carrier (Passband) communication. Modulation is required to match the signal to the channel (or link). Baseband communication requires no modulation whereas carrier communication requires modulation. Links such as local telephones using a pair of wires, coaxial cables and optical fibers do not need modulation. Radio links (radio and TV broadcast, microwave links, cellular phones and satellite links), on the other hand, must utilize modulation. The reverse of modulation is called demodulation (or detection). Demodulation is a process which extracts the message signal from the modulated signal.

In linear modulation the amplitude of the carrier signal is a linear function of the message signal. Depending on the nature of the spectral (frequency domain) relationship between the modulated signal and the message signal, we have the following types of linear modulation schemes:

i. Double-Sideband Suppressed Carrier (DSB-SC) Modulation. ii. Amplitude Modulation (AM). iii. Single-sideband modulation (SSB). iv. Vestigial-Sideband Modulation (VSB).

Each of these schemes has its own distinct advantages, disadvantages, and practical applications. We will examine these different types of linear modulation schemes. The emphasis is characteristics such as signal spectrum, power and bandwidth, demodulation methods, and the complexity of transmitters and receivers.

Double Sideband Suppressed Carrier Modulation

In amplitude modulation the amplitude of a high-frequency carrier is varied in direct proportion to the low-frequency (baseband) message signal. The carrier is usually a sinusoidal waveform, that is,

c (t) = Ac cos( ct + c)

Or

c (t) = Ac sin( ct + c)

Where: A is the unmodulated carrier amplitude c is the unmodulated carrier angular frequency in radians/s ; c = 2pfc c is the unmodulated carrier phase, which we shall assume is zero.

The amplitude modulated carrier has the mathematical form

DSB-SC (t) = A(t) cos( ct )

Where:

A(t) is the instantaneous amplitude of the modulated carrier, and is a linear function of the message signal m(t). A(t) is also known as the envelope of the modulated signal For double-sideband suppressed carrier (DSB-SC) modulation the amplitude is related to the message as follows:

A (t) = Ac(t) m(t)

Consider a message signal with spectrum (Fourier transform) M() which is band limited to 2B as shown in Figure 1(b). The bandwidth of this signal is B Hz and is c is chosen such that c >> 2B. Applying the modulation theorem, the modulated Fourier transform is

A(t) cos( ct )t) = m(t) cos( ct ) ( M ( - c) + M ( + c))

Figure 1-a shows a DSBSC modulator. Figure 1-B shows an example of the baseband signal waveform and spectrum .The time domain waveform and the frequency spectrum for the modulated signal are shown in Figure 1(c). The dashed lines represent the positive (+A(t) = +m(t)) and negative (-A(t) = -m(t)) amplitudes, respectively

Figure 2.30 : Amplitude modulated signal in time and frequency domains

Properties of DSB-SC Modulation:

i. There is a 180 phase reversal at the point where +A(t) = +m(t) goes negative. This is typical of DSB-SC modulation.

ii. The bandwidth of the DSB-SC signal is double that of the message signal, that is, BWDSB-SC

= 2B (Hz). iii. The modulated signal is centered at the carrier frequency c

with two identical sidebands (double-sideband) the lower sideband (LSB) and the upper sideband (USB). Being identical, they both convey the same message component.

iv. The spectrum contains no isolated carrier. Thus the name suppressed carrier.

v. The 180 phase reversal causes the positive (or negative) side of the envelope to have a shape different from that of the message signal, see Figure 2(a) and (b). This is known as envelope distortion, which is typical of DSB-SC modulation.

vi. The power in the modulated signal is contained in all four sidebands.

Figure 2.31 : DSB-SC Modulation

Generation of DSB-SC Signals

The circuits for generating modulated signals are known as modulators. The basic modulators are Nonlinear, Switching and Ring modulators. Conceptually, the simplest modulator is the product or multiplier modulator which is shown in figure 1-a. However, it is very difficult (and expensive) in practice to design a product modulator that maintains amplitude linearity at high carrier frequencies. One way of replacing the modulator stage is by using a non-linear device. We use the non-linearity to generate a harmonic that contains the product term then use a BPF to separate the term of interest. Figure 3 shows a block diagram of a nonlinear DSBSC modulator. Figure 4 shows a double balanced modulator that use the diode as a non-linear device, then use the BPF to separate the product term.

Figure 2.32 : A nonlinear modulator for DSB-SC

Figure 2.33 : A circuit diagram of a double-balanced modulator

Another method for generation DSBSC is to use a switching circuit. This is similar to modulating a signal with a square wave rather than a sinusoid. Then, we use a BPF to separate the harmonic of interest. Figure 5 shows the block diagram and the associated waveforms and spectrums of a switching modulator. Figure 6 represents a circuit diagram for a ring modulator that uses diodes as switching device rather than a non-linear device. The schematic diagrams and waveforms for a ring modulator are shown in Figures 6 and 7. Semi- conductor diodes are ideally suited for use in balanced modulator circuits because they are stable, require no external power source, have a long life, and require virtually no maintenance. A balanced modulator has two inputs: a single-frequency carrier and the modulating signal. For the modulator to operate properly, the amplitude of the carrier must be sufficiently greater than the amplitude of the modulating signal (approximately six to seven times greater). This ensures that the carrier and not the modulating signal controls the on or off condition of the four diode switches (D1 to D4). Figure 7 shows the input and output waveforms associated with a ring modulator for a single-frequency modulating signal. It can be seen that D1 and D2 conduct only during the positive half-cycles of the carrier input signal, and D3 and D4 conduct only during the negative half-cycles.

(1) Block diagram of basic switching modulator.

Associated waveforms and spectrum

Figure 2.34 : (1) Switching modulator block diagram for DSB-SC. (2) Associated waveforms and spectrum

Figure 2.35 : Circuit Diagram for Ring modulator

Figure 2.36 : Ring modulator waveforms

Demodulation of DSB-SC Signals

Demodulation or detection is the process of recovering the message signal from the modulated waveform. The method used to recover message signals from DSB-SC waveforms is known as coherent or synchronous detection (or demodulation).

Coherent detection

The block diagram for coherent detection is shown in Figure 8. This is similar to the modulator except that the band-pass filter is replaced by a low-pass filter. The received DSB-SC signal is

Sm(t) = DSB-SC (t) = Ac(t) m(t) cos( ct )

The receiver first generates an exact (coherent) replica (same phase and frequency) of the unmodulated carrier

Sc(t) = Cos( ct )

The coherent carrier is then multiplied with the received signal to give

Sm(t)* Sc(t) (t) = Ac(t) m(t) cos( ct ) * Cos( ct )c = Ac(t) m(t) + Ac(t) m(t) Cos( 2ct )

The first term is the desired baseband signal while the second is a band-pass signal centered at 2c. A low-pass filter with bandwidth equal to that of the m(t) will pass the first term and reject the band-pass component.

Figure 2.37 : Coherent demodulator for DSB-SC signals

Figure 9 shows a block diagram for the DSBSC system that will be used in the virtual lab experiment.

Figure 2.38: A block diagram of a DSBSC system

Single sideband

Single sideband modulation is widely used in the HF portion, or short wave portion of the radio spectrum for two way radio communication. There are many users of single sideband modulation. Many users requiring two way radio communications will use single sideband and they range from marine applications, generally HF point to point transmissions, military as well as radio amateurs or radio hams.

Single sideband modulation or SSB is derived from amplitude modulation (AM) and SSB modulation overcomes a number of the disadvantages of AM. Single sideband modulation is normally used for voice transmission, but technically it can be used for many other applications where two way radio communication using analogue signals is required.

As a result of its widespread use there are many items of radio communication equipment designed to use single sideband radio including: SSB receiver, SSB transmitter and SSB transceiver equipments.

What is single sideband modulation?

Single sideband, SSB modulation is basically a derivative of amplitude modulation, AM. By removing some of the components of the ordinary AM signal it is possible to significantly improve its efficiency.

A more complete explanation of the way amplitude modulated signals are formed and work can been seen on the pages relating to AM. These can be accessed via the "Related Articles" links that can be found on the left hand side of the page below the main menu.

It is possible to see how an AM signal can be improved by looking at the spectrum of the signal. When a steady state carrier is modulated with an audio signal, for example a tone of 1 kHz, then two smaller signals is seen at frequencies 1 kHz above and below the main carrier. If the steady state tones are replaced with audio like that encountered with speech of music, these comprise many different frequencies and an audio spectrum with frequencies over a band of frequencies is seen. When modulated onto the carrier, these spectra are seen above and below the carrier.

It can be seen that if the top frequency that is modulated onto the carrier is 6 kHz, then the top spectra will extend to 6 kHz above and below the signal. In other words the bandwidth occupied by the AM signal is twice the maximum frequency of the signal that is used to modulate the carrier, i.e. it is twice the bandwidth of the audio signal to be carried. Amplitude modulation is very inefficient from two points. The first is that it occupies twice the bandwidth of the maximum audio frequency, and the second is that it is inefficient in terms of the power used. The carrier is a steady state signal and in itself carries no information, only providing a reference for the demodulation process. Single sideband modulation improves the efficiency of the transmission by removing some unnecessary elements. In the first instance, the carrier is removed - it can be re-introduced in the receiver, and secondly one sideband is removed - both sidebands are mirror images of one another and the carry the same information. This leaves only one sideband - hence the name Single SideBand / SSB.

Single sideband power measurement

It is often necessary to define the output power of a single sideband transmitter or single sideband transmission. For example it is necessary to know the power of a transmitter sued for two way radio communication to enable its effectiveness to be judged for particular applications. Power measurement for an SSB signal is not as easy as it is for many other types of transmission because the actual output power is dependent upon the level of the modulating signal. To overcome this a measure known as the peak envelope power (PEP) is used. This takes the power of the RF envelope of the transmission and uses the peak level of the signal at any instant and it includes any components that may be present. Obviously this includes the sideband being used, but it also includes any residual carrier that may be transmitted. The level of the peak envelope power may be stated in Watts, or nowadays figures quoted in dBW or dBm may be used. These are simply the power levels relative to 1 Watt or 1 milliwatt respectively. As an example a signal of 10 watts peak envelope power is 10 dB above a 1 Watt signal and therefore it has a power of 10 dBW. Similar logic can be used to determine powers in dBm.

Single sideband modulation variants

There are many variants of single sideband modulation that are used, and there are several different abbreviations for them. These are explained below.

LSB: This stands for Lower Sideband. This form of single sideband modulation is formed when the lower sideband only of the original signal is transmitted. Typically this is used by radio amateurs or radio hams on their allocations below 9 MHz.

USB: This stands for Upper Sideband. This form of single sideband modulation is formed when the upper sideband only of the original signal is transmitted. Typically this form of SSB modulation is used by professional users on all frequencies and by radio amateurs or radio hams on their allocations above 9 MHz.

DSB: This is Double Sideband and it is a form of modulation where an AM signal is taken and the carrier is removed to leave the two sidebands. Although easy to generate, it does not give any improvements in spectrum efficiency and it is also not particularly easy to resolve. Accordingly it is rarely used.

SSB SC: This stands for Single Sideband Suppressed Carrier. It is the form of SSB modulation where the carrier is removed completely as opposed to SSB reduced carrier where some of the carrier is left.

VSB: This stands for Vestigial Sideband. It is a form is signal where one sideband is completely present, and the other sideband that has been only partly cut off or suppressed. It is widely used for analogue television transmissions. It comes in useful because the baseband video signal is wide (typically 6 MHz). To transmit this using AM would require a bandwidth of 12 MHz. To reduce the amount of spectrum used, one sideband is transmitted fully, whereas only the lower frequencies of the other are transmitted. The high frequencies can be later enhanced using filters.

SSB reduced carrier : In this form of SSB modulation one sideband is present along with a small amount of the carrier. For some applications, a small amount of carrier is kept. This may be used to provide a reference signal for accurate demodulation.

SSB advantages

Single sideband modulation is often compared to AM, of which it is a derivative. It has several advantages for two way radio communication that more than outweigh the additional complexity required in the SSB receiver and SSB transmitter required for its reception and transmission.

i. As the carrier is not transmitted, this enables a 50% reduction in transmitter power level for the same level of information carrying signal. [NB for an AM transmission using 100% modulation, half of the power is used in the carrier and a total of half the power in the two sideband - each sideband has a quarter of the power.]

ii. As only one sideband is transmitted there is a further reduction in transmitter power. iii. As only one sideband is transmitted the receiver bandwidth can be reduced by half. This

improves the signal to noise ratio by a factor of two, i.e. 3 dB, because the narrower bandwidth used will allow through less noise and interference.

The summary of this is that SSB modulation offers a far more effective solution for two way radio communication because it provides a significant improvement in efficiency. Single sideband modulation, SSB is the main modulation format used for analogue voice transmission for two way radio communication on the HF portion of the radio spectrum. Its efficiency in terms of spectrum and power when compared to other modes means that for many years it has been the most effective option to use. Now some forms of digital voice transmission are being used, but it is unlikely that single sideband will be ousted for many years as the main format used on these bands.

Vestigial sideband (VSB)

A vestigial sideband (in radio communication) is a sideband that has been only partly cut off or suppressed. Television broadcasts (in analog video formats) use this method if the video is transmitted in AM, due to the large bandwidth used. It may also be used in digital transmission, such as the ATSC standardized 8-VSB. The Milgo 4400/48 modem (circa 1967) used vestigial sideband and phase-shift keying to provide 4800-bit/s transmission over a 1600 Hz channel. The video baseband signal used in TV in countries that use NTSC or ATSC has a bandwidth of 6 MHz. To conserve bandwidth, SSB would be desirable, but the video signal has significant low frequency content (average brightness) and has rectangular synchronising pulses. The engineering compromise is vestigial sideband modulation. In vestigial sideband the full upper sideband of bandwidth W2 = 4 MHz is transmitted, but only W1 = 1.25 MHz of the lower sideband is transmitted, along with a carrier. This effectively makes the system AM at low modulation frequencies and SSB at high modulation frequencies. The absence of the lower sideband components at high frequencies must be compensated for, and this is done by the RF and IF filters.

FREQUENCY MODULATION

In telecommunications, frequency modulation (FM) conveys information over a carrier wave by varying its frequency (contrast this with amplitude modulation, in which the amplitude of the carrier is varied while its frequency remains constant). In analog applications, the instantaneous frequency of the carrier is directly proportional to the instantaneous value of the input signal. Digital data can be sent by shifting the carriers frequency among a set of discrete values, a technique known as frequency-shift keying.

Mathematical expression for Frequency Modulation (FM)

To get mathematical expression for Frequency Modulation, assume carrier frequency as a topic:

where:

and audio signal,

frequency at carrier signal,

Figure 2.30 : Frequency modulation waveform

so,

If this signal is used to modulate the carrier frequency,

By integrating,

where, frequency deviation,

modulation index,

where,

So, the equation of Frequency Modulation is:

Modulator sensitivity, S = f d / V a

Frequency spectrum and Bessel Function Table

Frequency modulation has frequency and numbers of pairs of significant sidebands. These sidebands are separated by fm, 2fm, 3fm and so on.

where,

J0 = carrier J1 = first sideband (upper & lower) J2 = second sideband (upper & lower) J3 = third sideband (upper & lower)

where, carrier amplitude = J0mf

sidebands amplitude =

Equation below can be used to solve any problem of frequency component of sidebands

fp-2fm

2f m

Figure 2.31 : Spectrum frequency of FM

fp fp-fm fp-3fm fp+fm

fm

3f m

fp+2fm fp+3fm

J1 J2

J0

J3

J1 J2

J3

FM Bandwidth

In theory, an FM signal contains an infinite number of side frequencies, so that the bandwidth required to transmit such a signal is similarly infinite in extent. In practical, significant sidebands is limited, depending on the value of mf. A sideband is considered significant if its relative amplitude is greater or equal to 1%. For FM signal analysis, an advanced calculus equation called Bessel functions is required. Bessel functions can be obtained in a tabulated form (Bessel Function Table) or in a graph form. Using Bessel Function Table, the bandwidth BW is given by,

BW = 2nfm where, n = number of pairs of the significant sidebands.

fm = frequency of the modulating signal.

For smaller values of m for the m 0.25, the FM bandwidth is equal to the bandwidth of AM.

Carsons rule:

This is a rule of thumb to estimate the bandwidth for an FM signal transmission. The minimum bandwidth is twice the sum of the peak frequency deviation and the highest modulating signal frequency. Mathematically, Carsons rule is,

BW = 2 [fd + fm]

Table 2.2 : Bessel function

Advantages and dis advantages of FM compare to AM.

The advantages of FM over AM are: 1. A Much better signal-to-noise ratio. There is as much as a 25-dB increases in this ratio over

AM. You can notice this while listening to the car radio during a thunder storm. 2. When two FM transmitters are nearby operating on the same frequency, there is a much

smaller geographical interference area as compared to AM transmitters operating on one frequency.

3. Less radiated power required for the same signal-to-noise ratio for FM over AM.

There are also some serious disadvantages of FM. 1. An FM wave typically requires 15 to 20 times the bandwith of an AM wave. 2. FM systems are much more complicated to analyze and build than AM systems. 3. More expensive equipment required to transmit

Example 1

Get the value of the FM modulation index which has a frequency deviation of 30 kHz, while the frequency of the input signal is 10 kHz.

Solution :

fD = 30 Khz fm = 10 Khz

so,

Example 2

A FM signal equation is given as :

Vfm = 2 sin (5 X 106 t + 3 sin 1250t)

Calculate the maximum frequency deviation for that FM signal

Solution :

Compare the given equation with the general equation FM signal :

General equation : Vfm = Vp sin (p t + mf sin m t ) From the question : Vfm = 2 sin (5 X 106 t + 3 sin 1250 t)

From Example 1, mf = 3

m = 2pifm = 1250

so,

fm = pi2

1250 = 198.9 Hz

as we known, mf = fmf D

,

therefore, fD = mffm = 3 X 198.9 Hz = 596.7 Hz

31030

===

KhzKhz

ff

mm

D

Example 3

If m = 0.25, draw the frequency spectrum with reference to the Bessel function table.

Solution :

From the Bessel function table : J0 = carrier amplitude = 0.98 J1 = 1st sideband = 0.12

J2, J3, J4 - values that can be ignored

Example 4

A frequency modulation (FM) signal has the following equation :

V fm = 10 sin ( 2 pipipipi x 10 6 t - 2 cos 2 pipipipi x 10 3 t )

i. Find the number of sideband pairs whose it amplitude is greater than 1%. ii. The amplitude of carrier signal. iii. The frequency of information signal. iv. Frequency deviation. v. Sensitivity value of modulator if the frequency deviation needs 100 mV. vi. Sketch the frequency spectrum of the modulated signal. vii. Calculate the bandwidth of this signal.

Solution :

V fm = 10 sin ( 2 pi x 10 6 t - 2 cos 2 pi x 10 3 t )

= Vp sin ( 2 pi fp t - m f kos 2 pi f a t )

i. Refer to the Bessel function table, the number of sideband pairs are 4 pairs.

0.98 Vp

0.12 Vp 0.12 Vp

fp fp + fm fp - fm

ii. V p = 10 V.

iii. f m = 1000 Hz.

iv. m f = 2

f d = m f x f a

= 2 x 1000 = 2 kHz.

v. Modulator sensitivity, S = f d / V a

= 2000 Hz / 100 mV = 20 Hz / mV.

vi. Spectrum frequency

0.576 0.576

0.352 0.352

0.223

0.128 0.128

0.034 0.034

(kHz)

996 997 998 999 1000 1001 1002 1003 1004

vii. Bandwidth, B = 2 ( f d + f a )

= 2 (2 k + 1 k ) = 6 kHz.

SELF ASSESSMENT

1. The equation of a frequency modulation (FM) signal, Vfm is given as :

V fm = 20 sin ( 200 x 10 6 pipipipi t - 5 kos 30 x 10 3 pipipipi t )

Find : i. Amplitude of the carrier signal.

ii. Modulation index. iii. Frequency of modulation signal. iv. Frequency of carrier signal.

2. An FM transmitter produces a FM signal and transmits the signal to the free space by an antenna with a resistance of 50 . If the FM signal equation is :

V fm = 100 cos ( 2 pipipipi 10 6 t - 0.5 cos 2 pipipipi 10 4 t )

Calculate :

i. Total power. ii. Modulation index.

iii. Frequency deviation. iv. Frequency spectrum. v. Modulation sensitivity if frequency deviation needs 200 mv.

vi. Bandwidth. vii. Power at the lower sideband.

viii. Total power of information signal.

3. Refers to the FM signal equation below, calculate the maximum frequency deviation. Also determine the frequency of carrier and information signal.

V fm = 12 sin ( 6 x 10 6 t + 2 sin 1250 t )

SELF ASSESSMENT ANSWERS

Question 1

i. Vp = 20V ii. mf = 5 iii. fm = 15 Khz iv. fp = 200 Mhz

Question 2

i. Total power, P =100 Watt ii. mf = 0.5 iii. fd = 5 Khz iv. Frequency spectrum :

v. Bandwidth, B = 30 Khz vi. Power of information signal, Pm = 0.09 watt

Question 3

Frekuensi pembawa, fp = 954.92 Khz Frekuensi maklumat, fm = 198.94 Hz Sisihan frekeunsi maksima, fd = 397.89 Hz

f2 f1 fp f1 f2

94 V

24 V 24 V

3 V 3 V

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 mathematics of the spectral behaviour reveals that there are two regions of particular interest :

i. For small amplitude signals, PM is similar to amplitude modulation (AM) and exhibits its unfortunate doubling of baseband bandwidth and poor efficiency.

ii. For a single large sinusoidal signal, PM is similar to FM, and its bandwidth is approximately

where : fM = m / 2 h = the modulation index.

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

Figure 2.32 Phase modulation waveform