Modulation in Communication Systems

Introduction

Modulation is the process of changing some characteristics (e.g. Amplitude, Frequency, or Phase) of a carrier wave in accordance with the intensity of the message signal.

Modulation means to ‘’change’’. In Modulation, some characteristics of the carrier wave is changed in accordance with the intensity i.e. amplitude of the message signal. The resultant wave is called modulated wave or radio wave and contains the audio signal. Hence, modulation permits the transmission to occur at high frequency while it simultaneously allows the carrying of the audio signal.

Reasons why Modulation is required in Communication Systems

Modulation is needed in communication systems due to the following reasons:

Practical Antenna Length

Theory shows that in order to transmit a wave effectively, the length of the transmitting antenna should be approximately equal to the wavelength of the wave.

As the audio frequencies range from 20 Hz – 20 kHz, hence, if they are transmitted directly into space, the length of the transmitting antenna required would be extremely large. For example to radiate a frequency of 20 kHz directly into space, we would need an antenna length equal to:

This is too long antenna to be constructed practically. As a result, it is impracticable to radiate audio signal directly into space. Alternatively, if a carrier wave say of 1000 kHz is used to carry the signal, we need an antenna length of only 300 metres and this size is practically possible to construct.

Operating Range

The energy of a wave depends on its frequency, the greater the frequency of the wave, the greater the energy possessed by it. As the audio signal frequencies are small (20 Hz – 20 kHz), hence they cannot be transmitted over large distances if they are radiated directly into space. The only practical solution is to modulate a high frequency carrier wave with audio signal and permit the transmission to occur at this high frequency i.e. carrier frequency.

Wireless communication

Radio transmission doesn’t require wires i.e. it is radiated into space but with audio frequencies, radiation is not practicable because the efficiency of radiation is poor. However, efficient radiation of electrical energy is possible at high frequencies i.e. greater than 20 kHz. Therefore, modulation is always done in communication systems.

Types of Modulation in Communication Systems

We have two types of modulation

1. Analog Modulation
2. Digital Modulation

Analog Modulation Techniques

In analog modulation, the characteristic parameters of a high-frequency sinusoidal signal (carrier signal), is varied according to the message signal/information signal.

Generally the carrier wave is represented as:

A_Ccos (2ℼf_Ct +Φ)

Where, A_C is the amplitude

f_C is the frequency of the carrier

Φ is the phase of the carrier

The 3 characteristic parameters of the carrier signal are:

• Amplitude
• Frequency
• Phase

These parameters can be varied according to the information/message signal. Therefore, analog modulation techniques are classified as:

• Amplitude Modulation (AM)
• Frequency Modulation (FM)
• Phase Modulation (PM)

Amplitude Modulation

When the amplitude of carrier signal is varied in accordance with the information/message signal, amplitude modulation is produced. This method is mainly used where large power outputs are required for long-distance communications.

Figures (a, b, c) shows a constant-amplitude, constant-frequency carrier being modulated, by a single tone (in practice, many modulating signals may be used).

The general expression of the waveform in Figure (a) is:

v_c = V_cSin (w_c + ϴ)     -equation 1

Where,

v_c is the instantaneous carrier voltage

V_c is the peak amplitude

w_c, is the frequency of the carrier in radians

ϴ is the phase of the carrier (we will ignore this in our analysis below)

The modulating signal in Figure (b) is given by

v_m = V_msin w_mt       -equation 2

Where, v_m is the instantaneous amplitude of the modulating signal while V_m is the peak of the amplitude and w_m is the frequency of the modulating signal in radians.

The amplitude-modulated wave shown in Figure (c) above is given by:

v= (V_c + V_msin w_mt) sin w_ct    -equation 3

 = V_csin w_ct + V_msin w_mt Sin w_ct     -equation 4

Using trigonometric identity

sin A sin B = ½ cos (A-B) – ½ cos (A+B)

equation 4 becomes

From equation 5, the modulated wave has three frequency components, namely the carrier frequency (f_c), lower sideband (f_c –f_m) and the upper side sideband (f_c + f_m). These 3 components are represented in the form of a line or spectrum diagram as illustrated below:

If several modulating tones were present in the speech band, they would be as illustrated below:

Figure (c) above shows two important factors used in practice:

• The modulating factor
• Depth of modulation

The modulation factor (m) is given by:

Expressed as a percentage, this is termed as the depth of modulation. Hence, the depth to which the carrier is modulated depends on the amplitude of the carrier and the modulating voltage. The maximum modulation factor used is unity. Exceeding this causes over modulation and break-up of the signal and hence some figure that is less than unity is used in practice.

The Power Distribution in Amplitude Modulated (AM) Wave

The power which is coupled to an antenna by an AM wave is developed across its resistance. An antenna must be coupled to a transmitter by means of a transmission line or waveguide in order to be excited and produce radiation. The antenna input impedance which the feeder ‘sees’ must be known in order to achieve efficient coupling.

Note, however that the antenna input impedance generally has a resistive and reactive part. The reactive element originates from the inherent inductance and capacitance in the antenna. The resistive element of the input impedance originates from the numerous losses that occur in the antenna.

The radiated loss (radiation resistance) is the actual power transmitted and is a necessary loss caused by the modulated wave generating power in the antenna but other losses are present such as ohmic losses and those due to current lost in the ground. Because of this, it is important that the radiation resistance be much greater than all other losses.

The radiation resistance is defined as the equivalent resistance that would dissipate an amount of power equal to the total radiated power when the current through the resistance is equal to the current at the antenna input terminals.

Rearranging equation 6

The r.m.s. power developed across the antenna resistance (R_a) by the carrier and two side bands will be given by:

If several sidebands are involved, the equation 8 becomes:

The above method of amplitude modulation is known as double sideband modulation (d.s.b.). This method has a number of disadvantages which can be overcome by filtering out the carrier, one of the sidebands, or both. If this is done, you would have a better system with the following advantages:

• More channels available.
• Reduced bandwidth, hence less noise.
• Increase in efficiency, as power is only transmitted when information is sent.
• Selective fading is reduced as there is no carrier component to fade below the sideband level and cause sideband beating which would produce unwanted components.
• Non-linearity is reduced as the carrier amplitude is the largest of all the components and this can cause saturation.

Double sideband suppressed carrier modulation (d.s.b.s.c.) requires the carrier to be reinserted at the receiver with the correct phase and frequency. Single sideband suppressed carrier modulation (s.s.b.s.c.) only requires the frequency of the reinserted carrier to be correct.

The basic principle of operation of single sideband suppressed carrier modulation is illustrated in the figure below:

The carrier and modulating signal are applied to a balanced modulator. The output of the modulator consists of the upper and lower sidebands, but the carrier is suppressed. The bandpass filter then removes one of the sidebands.

Limitations of Amplitude Modulation (AM)

Although AM is theoretically highly effective, it has the following drawbacks:

Low Efficiency

In amplitude modulation, useful power is in the sidebands, as they contain the signal. However, an AM wave has low sideband power e.g. if modulation is 100% the sideband power is only one third of the total of AM wave hence the efficiency of AM modulation is low.

Noisy Reception

In an AM wave, the signal is in the amplitude variations of the carrier. Practically all the natural and man-made noises consist of electrical amplitude disturbances. As a radio receiver cannot distinguish between amplitude variation that represent noise and those that contain the desired signal, hence the reception is generally noisy.

Lack of Audio Quality

In order to attain high-fidelity reception, all audio frequencies up to 15 kHz must be reproduced. This necessitates bandwidth of 30 kHz since both sidebands must be reproduced. However AM broadcasting stations are assigned bandwidth of only 10 kHz to minimize the interference from adjacent broadcasting stations. This means that the highest modulating frequency can be 5 KHz which is insufficient to reproduce the sound quality e.g. music properly.

Small Operating Range

Due to low efficiency of amplitude modulation, transmitters employing this method have a small operating range i.e. messages cannot be transmitted over larger distances.

Frequency Modulation

In frequency modulation (FM), the amplitude of the carrier is kept constant but the frequency f_c of the carrier is varied by the modulating signal. The carrier frequency f_c varies at the rate of the signal/message frequency f_m, the frequency deviation being proportional to the instantaneous amplitude of the modulating signal. Note that the maximum frequency deviation is (f_c(max) – f_c) and occurs at the peak voltage of the modulating signal.

Assume we modulate a 100 MHz by 1 V, 1 KHz modulating signal and the maximum deviation is 35 kHz. This means that the carrier frequency will vary sinusoidally between (100 + 0.035) MHz and (100 -0.035) MHz at the rate of 1000 times per second.

Let’s consider a modulating sine-wave signal:

v = V_msin w_mt that is used to vary the carrier frequency f_c. Let the change in the carrier frequency be kv, where k is a constant known as the frequency deviation constant. Therefore the instantaneous carrier frequency f_i will be given by:

f_i = f_c + kv

fi = f_c + kV_msin w_mt

The factor KV_m represent the maximum frequency deviation and is denoted by Δf i.e.

Maximum frequency deviation Δf = KV_m

Hence f_i = f_c + Δfsin w_mt

The Equation of Frequency Modulated (FM) wave

In frequency modulation, the carrier frequency is varied sinusoidally at signal/message frequency. The instantaneous deviation in frequency from the carrier is proportional to the instantaneous amplitude of the modulating signal. Thus the instantaneous angular frequency of FM is given by:

w_i = w_c + Δw_csin w_mt

Total phase angle ϴ = wt so that if w is varied, then

Hence ϴ = w_ct – βcos w_mt

The instantaneous value of FM voltage is given by

v = V_csin ϴ

   = V_csin (w_ct – βcos w_mt)

We know that

Unlike amplitude modulation, the modulation index β for Frequency modulation can be greater than unity.

The above equation for β is for a constant frequency, constant amplitude modulating signals. In practice the modulating signal varies in amplitude and frequency. This leads to two further parameters: A maximum value of the modulating signal f_m(max); and a maximum allowable frequency shift; which is defined as the frequency deviation (f_d).

The deviation ratio δ is then defined as:

For any given FM system, the frequency will swing to a maximum value of frequency deviation known as the rated system deviation. This parameter determines the maximum allowable modulating signal voltage.

We know that, the frequency-modulated wave can be written as:

v = V_csin (w_ct –βcos w_mt)   -equation 1(a)

For a constant-amplitude constant-frequency modulating signal such as a square wave, and is written as:

v = V_csin (w_ct –δcos w_mt)   -equation 1(b)

For a variable amplitude, variable frequency modulating signal such as sinusoidal wave.

Expanding equation 1(b) using the identity:

sin (A + B) = sin A cos B – cos A sin B

gives

sin w_ct cos (δcos w_mt) – cos w_ct sin (δcos w_mt)

The second factor of each term expands into an infinite series whose coefficients are a function of δ. These coefficients are called Bessel functions, denoted by J_n(δ), which vary as δ varies. They are Bessel functions of the first kind and of order n. Expanding the second factor gives:

cos (δcos w_mt) = J₀(δ) – 2J₂(δ) cos 2w_m + 2J₄(δ) cos 4w_mt -…

and,

sin (δcos w_mt) = 2J₁(δ) cos w_mt – 2J₃(δ) cos 3w_mt +…

Using relationships

sin A cos B = ½ [sin (A + B) + sin (A – B)]

cos A sin B = ½ [sin (A + B) –sin (A – B)]

we obtain

v = Vc{ J₀(δ) sin w_ct + J₁(δ)[sin (w_c + w_m)t – sin (w_c-w_m)t] – J₂(δ)[sin (w_c + 2w_m)t + sin (w_c –w_m)t] + J₃(δ) [sin (w_c + 3w_m)t – sin(w_c-3w_m)t] – …}

Hence the modulated wave consists of a carrier and an infinite number of upper and lower side frequencies spaced at intervals equal to the modulation frequency. Also, since the amplitude of the unmodulated and modulated waves is the same, the powers in the unmodulated and modulated waves are equal.

Note the Bessel coefficients can be determined either from graphs or tables.

Carson’s Bandwidth Rule

As a rule of thumb, Carson’s rule states that the nearly all ≈ 98% of the power of a frequency lies within a bandwidth B_T of:

B_T = 2(Δf + f_m) = 2f_m(β + 1)

Where Δf, is defined above, is the peak deviation of the instantaneous frequency f(t) from the center frequency f_c, β is the modulation index which is the ratio of frequency deviation to highest frequency in the modulating signal and f_m is the highest frequency in the modulating signal.

The condition of application of Carson’s rule is only sinusoidal signals.

Advantages of Frequency Modulation FM over Amplitude Modulation (AM)

• It is almost total immune from noise interference as noise is a form of amplitude variations and FM receivers will reject such signals.
• It gives high-fidelity reception.
• The operating range is quite large.
• The efficiency of transmission is very large.

You can also read: Components that make up a RF Communication System

Phase Modulation (PM)

Phase modulation is defined as a process in which the phase of the carrier is varied linearly according to the message signal.

If m(t) is the message signal/information signal to be transmitted with the help of a carrier signal of amplitude A_c, frequency w_c and phase angle Φ_c, then he time domain equation of the phase modulated signal will become:

s(t) = A_c sin (w_ct + m(t) + Φ_c)

Digital Modulation Techniques

The digital-modulation process involves switching or keying the amplitude, frequency or phase of the carrier according to the incoming data. The input to the digital modulators is in binary digits. Based upon the keying, these digital modulation techniques are divided into 3 types:

• Amplitude Shift Keying (ASK)
• Frequency Shift Keying (FSK)
• Phase Shift Keying (PSK)

Amplitude Shift Keying (ASK)

In ASK, the amplitude of the carrier is changed according to the modulating waveform which is a digital signal bit. The level of amplitude can be used to represent binary logic 0s and 1s. Here, either of the two states of the carrier signal is considered i.e. ON or OFF. In the modulated signal, logic 0 is represented by the absence of a carrier, thus it is said to be an OFF/ON keying operation.

ASK demonstrates poor performance, as it is heavily affected by noise and interference. Mathematically we can represent it as:

Frequency Shift Keying (FSK)

In FSK, the frequency of the carrier is varied according to the modulating waveform which is a digital signal.

The simplest FSK is binary FSK (BFSK). BFSK literally means using a couple of discrete frequencies to transmit binary (0s and 1s) information. With this scheme, the ‘’1’’ is called the space frequency. Mathematically, it can be represented as:

Phase Shift Keying (PSK)

In PSK, the phase of the carrier is changed according to the modulating waveform which is a digital signal. PSK uses a finite number of phases; each assigned a unique pattern of binary bits.

Usually, each phase encodes an equal number of bits. Each pattern of bits forms the symbol that is represented by the particular base.

Mathematically, it can be represented as:

Where f_c is the frequency of the carrier wave, and E_b and T_b are energy per bit and bit duration respectively.

Key Points about Phase Shift Keying (PSK)

• PSK has a better power and frequency efficiencies compared to ASK and FSK.
• PSK achieves small bit error rate (BER) for the same C/N (carrier-noise ratio).
• PSK has constant envelope, and is robust to time-varying fading channel.
• PSK is popularly used in many communication systems such as satellite and mobile communication systems.

Advantages of Digital Modulation over Analogue Modulation

• A large amount of information can be conveyed by digital modulation.
• Digital modulation provides more information capacity and compatibility with digital data services.
• By digital modulation, we have better quality communications and quicker system availability.

You can also check: Telecommunication Tools