Contents
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What is Modulation and Demodulation? What is Sideband Communication?
In section 1.2.1, it has been mentioned that the process of superimposing the low frequency data signal on a high frequency carrier wave at the transmitting end is called modulation. On the other hand, the process of seperating the superimposed data signal from carrier wave at receiving end is called demodulation.
Let the equation of carrier wave be,
V = V0sin(Ωt + θ)
[Where, V0 = amplitude of the wave, Ω = angular frequency, Ωt + θ = phase of the wave = ϕ (say), θ = initial phase or epoch]
Linear frequency or simply the wave frequency,
n = \(\frac{\Omega}{2 \pi}\), where Ω = \(\frac{d \phi}{d t}\)
For convenience, the initial phase θ can be taken as zero.
In that case,
the carrier wave: V = V0sinΩt ….. (1)
Similarly, equation of the data signal,
v = c0sinωt …….. (2)
[where, v0 = amplitude of the wave and ω = angular frequency]
The instantaneous voltage v is called the modulating voltage.
Clearly, the condition of effective modulation of carrier wave of equation (1) by modulating data signal of equation (2) is,
ω \(\ll\)Ω
i.e., the frequency of carrier wave should be much higher than the frequency of the data signal. In practice, this frequency is 1000 times or even more than that of the data signal. The modulating voltage generally fluctuates very slowly with time and hence the wave indicating data signal is frequently called slow wave.
Amplitude Modulation (AM) and Amplitude Demodulation
Let, on the carrier wave of equation (1) of section 1.5, the data signal of equation (2) be superimposed in such a way, that the value of amplitude V0 changes with time. In fact, with the Stationary value of amplitude V0 of the carrier wave, a sinusoidal alternating voltage kv0 sinωt gets added. i.e.,
Vm0(t) = V0 + kv0sinωt
where, k is a dimensionless constant. Vm0 is the amplitude of generated modulated voltage due to modulation of carrier wave by data signal. As w\(\ll\)Ω, so the change of voltage is very slow.
Modulated voltage, Vm = VmosinΩt
= (V0 + kv0sin ωt)sinΩt
∴ Vm = V0(1 + βsinωt)sinΩt
where, β = k\(\frac{v_0}{V_0}\) = modulation index.
The significant of equation (2):
where β = k\(\frac{v_0}{V_0}\) = modulation index.
The significance of equation (2):
i) The existence of sinΩt indicates that, due to modulation, the frequency of carrier wave (Ω) does not change with time.
ii) sin ωt can be both negative and positive. As the value of ω is very low, the multiplier (1 + βsinωt) of the amplitude V0 indicates that the amplitude of the modulated wave fluctuates very slowly on either side of V0.
Definition: In case of a distant communication, after superimposition of a data signal on a carrier wave, if the frequency remains unchanged and only the amplitude changes in a slow, periodic way, then the process is called Amplitude Modulation or AM.
Carrier wave is shown as a sinusoidal curve of a particular frequency [Fig.(a)] and also a data signal is shown as a sinusoidal curve of another particular frequency[Fig.(b)]. In both the cases, with the two waves, their corresponding alternating sine-voltages are taken as the vertical axis.
A carrier wave, when modulated by a data signal, the nature of the AM wave thus produced is shown in Fig.
Sideband: From equation (2),
Vm = V0sinΩt + βV0sinΩtsinωt
= V0sinΩt + \(\frac{\beta V_0}{2}\)cos(Ω – ω)t – \(\frac{\beta V_0}{2}\)cos(Ω + ω)t ….. (3)
Equation (3) reveals that AM wave consists of sinusoidal-components of three frequencies Ω, Ω – ω and Ω + ω. Though the frequency of the carrier wave does not change with time, the other two frequencies get overlapped with the main frequency Ω (both cosine and sine functions are sinusoidal in nature).
In this discussion, the data signal has been taken as composed of a single frequency ω. In audio signal, it can be considered to be a signal generated from a pure tone and in video signal, a mono-chromatic signal. In most practical cases 0 however, quite a number of sinusoidal frequencies lie superimposed on the original data signal. Let us suppose, in a data signal, frequencies of range ω to ω±Δω are mixed up. In that case, if (ω → ω±Δω) range is considered in place of ω in equation (3), then the frequencies present in the amplitude modulated wave are [Fig.]:
Ω: Point O
The frequencies of(Ω + ω) to (Ω + ω + Δω) range:
Part BD
The frequencies of (Ω – ω – Δω) to (Ω – ω) range:
Here, the frequency range CA and BD are called the sidebands of the amplitude modulated wave. Clearly, the maximum and minimum frequencies of the full wave are (Ω + ω + Δω) (point D) and (Ω – ω – Δw) (point C). The CD stretch of the frequency is called bandwidth of AM wave. The magnitude of the bandwidth is,
d = CD = (Ω + ω + Δω) – (Ω – ω – Δω) = 2(w + Δw)
= 2 × maximum frequency on data signal
Obviously, to transmit the AM wave properly, a communication channel is to be selected, the transmission band of which should be extended at least from (Ω – ω – Δω) to (Ω + ω – Δω) i.e., from point C to D. However, instead of both the sidebands, transmission by using only one sideband is also in practice. In that case, transmission can be done with half bandwidth. This is called single sideband communication.
Demodulation principle of AM wave: A well selected circuit performs the function of amplitude modulation. Now the modulated wave is applied to a transmitting antenna. The wave form of the electromagnetic wave thus generated and spread all over is exactly similar to the modulated waveform. Transmitted through the communication medium, the electromagnetic wave reaches the receiving antenna (one or more than one), and in each antenna, an exactly similar potential wave is generated from the electromagnetic wave. Naturally, the intensity of the wave at the receiving end is much less than that at the transmitting end.
In the next step, keeping the waveform intact, the intensity of the wave is multiplied several times by using a suitable amplifier. Then, with a suitably selected çircuitry, the carrier wave and the data signal are separated from the mixed wave. This is the process of demodulation-its other popular name is detection. Demodulation of amplitude modulated wave is also called peak detection. At last the demodulated data signal is amplified again and with the right procedure (as in audio signal, through loud speaker) the data generated from the transmitting end, is traced [Fig.]. In audio signal, the entire machinery set-up is called radio receiver.
It can be mentioned here that, the process of demodulation of frequency modulated wave is also exactly similar to this (see section 1.5.2), though the circuitry is different.
Production of an AM wave: Fig. shows an n-p-n transistor T. At the very beginning, a dc circuit of the transistor is constructed by using necessary bias voltage and different resistances. An operating point is also fixed. These dc components of the circuit have not been shown in the Fig.
Now by using appropriate dc filter, the alternating voltage of the carrier wave is applied to base B of the transistor and the alternating voltage of the data signal is applied to collector C.
Depending on the fluctuation of voltage of data signal, the collector current changes and thus, at output of transistor, an identical replica of data signal gets mixed on the amplified carrier wave and an amplitude modulated wave is generated. Necessary filter arrangements are made so that no dc component of the current can mix with it.
Amplitude modulators are basically of two types—
- linear modulator, used in radio transmission
- square-law modulator, used in telephone conversation.
Detection of an AM wave: The circuit shown in Fig. is widely used as demodulator of AM wave. It is called envelope detector. It is a half-wave rectifier, specially made up of a semiconductor diode D, in the circuit of which an RC filter is connected. When the voltage reaches its highest value in the positive half cycle of the carrier wave of AM wave, the charge of capacitor C becomes maximum.
Now, as the carrier voltage gradually decreases, the charge of C starts to reduce due to dissipation through R. The time constant of RC circuit i.e., CR is kept at such a magnitude that, it becomes much more than the time period of the carrier wave and a little less than the time period of data signal. As a result, the charge of C does not increase or decrease as fast as that of the phases of carrier wave.
Rather, the waveform of the data signal is manifested through the increase or decrease of charge of C. At output, the waveform of carrier is not available, output wave mainly indicates the waveform of data signal. This envelope detector is a linear detector, because, here the output voltage becomes proportional to the input voltage. To ensure that no component of dc can pass over to output, capacitor C’ is used as filter in the circuit, as shown in Fig.
Frequency Modulation and Frequency Demodulation
Equation of carrier wave,
V = V0sinΩt = V0sinϕ ….. (1)
where phase angle, ϕ = Ωt
i.e., \(\frac{d \phi}{d t}\) = Ω …… (2)
and, equation of data signal,
v = v0sinωt …… (3)
Keeping the amplitude V0 of the carrier wave unchanged, the time dependent data signal is superimposed on it.
Due to modulation, the instantaneous value of frequency Ω is,
Ωm(t) = Ω + kv0sinωt …… (4)
Here, k is a coupling constant which converts v0sinωt into a frequency dependent term.
In this case, the unit of k will be V-1 ᐧ s-1 i.e., unit of (kv0 sinωt) will be s-1, i.e., Hz. Applying equation (2) for this time dependent frequency we get,
dϕm = Ωm(t)dt
or, ϕm = ∫Ωm(t) dt = Ω∫dt + kv0∫sinωtdt
or, ϕm = Ωt – \(\frac{k v_0}{\omega}\)cosωt + δ ….. (5)
Writing time dependent phase angle ϕm in place of ϕ in equation (1) of carrier wave we get.
Vm = V0sin(Ωt – βcosωt + δ) ….. (6)
where, β = \(\frac{k v_0}{\omega}\)
This is the equation of frequency modulated wave or FM wave.
In this equation,
β = \(\frac{k v_0}{\omega}\) = modulation index
In this case:
- The amplitude V0 of carrier wave does not change.
- For the term βcosωt, the frequency of carrier wave fluctuates with time.
As ω\(\ll\)Ω, so this change of frequency is a slow change. This phenomenon is called frequency modulation.
Definition: In a distant communication, after superimposing a data signal on a carrier wave, if the amplitude remains unchanged and only the frequency changes in a slow periodic way, then the phenomenon is called Frequency Modulation or FM.
In Fig.(a), (b) and (c) a carrier wave, a data signal and a form of a FM wave, generated due to the superimposition of these two waves, are shown respectively.
It is observed that in AM wave, besides the frequency Ω of carrier wave, two more sine components of frequencies (Ω – ω) and (Ω + ω) are present. But on mathematical analysis of frequency modulated wave, it is found that the number of sine components is infinite. The frequency of the components are Ω±ω, Ω±2ω, Ω±3ω, ……. etc.
Clearly, these frequencies lie symmetrically on either side of the frequency of the carrier wave Ω.
In transmission through Low Frequency (LF) or Medium Frequency (MF) carrier wave, amplitude modulation is generally employed while in transmission through High Frequency (HF) or Very High Frequency (VHF) carrier wave, frequency modulation is employed. As range of frequency of HF or VHF is very high, so the differences in frequency of the carrier waves, transmitted from different transmitting centres, are also very high. Hence, inspite of the presence of sideband frequencies in FM wave, the possibility of overlapping of different waves and noise and distortion of data signal due to this, becomes very low. For this reason, the sound of FM radio is very clear and in TV chance of mixing pictures transmitted from two stations is almost nil.
Demodulation principle of FM wave: In most of the cases, the receiver generates another waveform from the frequency modulated wave and the slow change of amplitude gets associated with the slow change of frequency. The wave is then applied to a suitable detector circuit and almost in the same method as in demodulation of amplitude modulated wave, the data signal is separated.
Nowadays, in demodulation of FM wave, use of superheterodyne receiver is prevalent. Here an oscillator is kept inside the receiver from which a wave of properly selected frequency is mixed with the FM wave. The process is very useful for detecting correct frequency of data signal.
Power Dissipated due to Modulation
If the potential difference across the two ends of a transmitting antenna is time dependent and the potential difference is expressed as V( t), then dissipated power of the antenna is
P = \(\frac{\overline{V^2(t)}}{R}\) ….. (1)
Here, the symbol \(\overline{V^2(t)}\) indicates the mean of the quantity V2(t) with respect to time. R is the effective resistance of the antenna. In the case of time dependent voltage, due to metallic elements of the antenna and electromagnetic radiation from it, the effective resistance R is not equal to the dc resistance of the antenna.
Now, according to equation (1) of section 1.5,
carrier wave: V = V0sinΩt …… (2)
Again, from equation (2) of section 1.5.1, we get,
AM wave: = V0(1 + βsinωt)sinΩt …. (3)
Similarly from equation (6) of section 1.5.2 we get,
FM wave: VFM = V0sin(Ωt – βcosωt) ….. (4)
In both equations (3) and (4), the term β is modulation index, which is sometimes expressed by the symbol ‘m’ also.
Clearly, each of V, VAM and VFM indicated by above three equations is time dependent potential difference. Hence, in each case, power dissipated in antenna is to be evaluated by using equation (1).
Power dissipated in transmission of carrier wave:
From equation (2),
V2 = \(V_0^2\)sin2 Ωt i.e., \(\overline{v^2}\) = \(V_0^2 \overline{\sin ^2 \Omega t}\)
We know that functions like sinΩt or cosΩt are time dependent sinusoidal functions. In each complete cycle, the average of sine-function or cosin-function is zero, but the average of sin2 or cos2 function is \(\frac{1}{2}\)
∴ \(\overline{\sin ^2 \Omega t}\) = \(\frac{1}{2}\)
Hence, power dissipated in antenna for transmitting carrier wave only:
PC = \(\frac{\overline{V^2}}{R}\) = \(\frac{V_0^2 \cdot \frac{1}{2}}{R}\) = \(=\frac{V_0^2}{2 R}\) ….. (5)
Power dissipated in transmission of amplitude modulated wave: From equation (3) we get,
The significance of this equation is that the power dissipated in antenna increases in transmitting amplitude modulated wave compared to that in transmitting only the carrier wave. The amount of increase is
P’ = PAM – PC = PC(1 + \(\frac{\beta^2}{2}\)) – P’C = PCᐧ\(\frac{\beta^2}{2}\) ……. (7)
i.e., the rate of dissipation of additional power or energy is proportional to the square of modulation index.
As for example, for 100% modulation, β = 100% = 1.
So, PAM = PC(1 + \(\frac{1^2}{2}\)) = \(\frac{3}{2} P_C\)
In this case, increase in dissipated power,
P’ = \(\frac{3}{2}\)PC – PC = \(\frac{1}{2}\)PC
i.e., amount of increase is 50%.
It may be noted that the additional dissipated power due to amplitude modulation is equally divided between the two side bands. i.e., dissipated power for each sideband
= \(\frac{P^{\prime}}{2}\) = PCᐧ\(\frac{\beta^2}{4}\)
Power dissipated in transmission of frequency modulated wave: From equation (4),
The significance of this equation is that, the power dissipated in antenna remains unchanged in transmitting frequency modulated wave compared to that in transmitting only the carrier wave. That is, for frequency modulation, there is no change in dissipated power. This power is not at all dependent on modulation index, β.
Modulator-Demodulator or Modem
It is a device which converts a digital data to an analogue data and an analogue data to digital data.
Modern computers function In a digital set-up. All the data avail able from it are digital. In a localised area (as in an office), where the local area network or LAN is formed by connecting the computers of the office, direct exchange of digital data takes place. In such cases, the data need not be converted to analogue data, hence there is no need to use modem. In this type of direct exchange of digital data, mainly coaxial cable is used as the medium.
On the other hand, in distant communication, the computer is connected with telephone line through modem. The digital data of the computer is converted into amplitude modulated or frequency modulated analogue data by modem. Then this analogue data reaches the computers of worldwide network through telephone system. The modem connected with the receiving computer on its part, separates the primary digital data from modulated analogue data.