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Radio Systems III
A textbook covering the Level III syllabus. of the Technician Education Council DeGreen
MTech. CEng. MIERE Senior Lecturer in Telecommunication Willesden College of Technology Engineering
Pitman
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Fig.1.4 Amplitude-modulatedwave of modulation depth greater than 100%
v
The maximum value of the modulation factor is limited to 1 since this gives a minimum value to the envelope of Ve(1-I) or zero. If a greater value of modulation factor is used, the envelope will no longer be sinusoidal (Fig. 1.4) and the waveform will contain a number of extra, unwanted frequency components.
Power Contained in an Amplitude-modulated Wave
The expression for the instantaneous voltage of an amplitudemodulated wave, equation (1.2), can be rewritten in terms of the modulation factor m:
(1.7)
(1.8)
The power developed by an amplitude-modulated wave is the sum of the powers developed by the carrier frequency, upper sidefrequency and lower sidefrequency components. The carrier power is
(V)2I R .J~
2.J2 R
V2 or 2~ watts
and the power developed by each of the two sidefrequencies is mVe)2 1 m2V~ - or --watts ( -8R
so that the TOTAL POWER is
AMPLITUDE MODULATION
7
As previously mentioned, the maximum modulation factor used in practice is m = 1, and for this condition PI is one and a half times the carrier power. For maximum modulation conditions, therefore, only one-third of the total power is contained in the sidefrequencies. Since it is the sidefrequencies that carry the intelligence, amplitude modulation is not a very efficient system when ~~!C"!(t on a power basis.
EXAMPLE 1.4
The power dissipated by an amplitude-modulated wave is 100 W when its depth of modulation is 40%. What modulation depth m is necessary to increase the power to 120 W?
Solution
From equation (1.9), 100=Pc (
0 4 l+T
2 )
or
P c =--watts is altered to m, the total power
100 1.08
When the depth of modulation increases to 120 W. Therefore
120x 1.08 = 1 +.!m2 100 2
!m2 = 1.2 x 1.08-1 m = ";0.592 = 0.769 (Ans.)
EXAMPLE 1.5
A 1 kW carrier is amplitude modulated by a sinusoidal signal to a depth of 50%. Calculate the power at the lower sidefrequency and determine what percentage it is of the total power.
Solution
From equation (1.9) P,=1000(1 +!0.52) = 1000+ 125 The carrier power is 1000 W so clearly the total sidefrequency power is 125 W. The amplitudes of the two sidefrequencies are equal and so the sidefrequencies will dissipate equal powers. Therefore Lower sidefrequency power = 125 2 = 62.5 W (Ans.) power
The total power is 1125 W, hence the lower sidefrequency expressed as a percentage of the total power is 62.5 x 100 1125 or 5.56% (Ans.)
8
AMPLITUDE MODULATION
R.M.S. Value of an Amplitude-modulated Wave
If the r.m.s. voltage of an amplitude-modulated wave is V, then the power PI dissipated by that wave in a resistance R is given by P,
VZ =R" = r; (1 +!m
2 )
W alone is
The power dissipated by the carrier component
p c =
V~W 2R
Therefore P, 2V 2
= ~
Pc
Pc (1 +!m2) Pc
2 VZ = V~(1+!m2)
V = ~;J(1 +4m2)
EXAMPLE 1.6
(1.10)
The r.m.s. value of the current flowing in an aerial is 50 A when the current is unmodulated. When the current is sinusoidally modulated, the output current rises to 56 A. Determine the depth of modulation of the current waveform. Solution From equation (1.10)
56)2 ( 50 m=
= 1+~m2
~2[ (~~r =0.713 -1]
(Ans.)
The double-sideband full-carrier (d.s.b.) system of amplitude modulation can be demodulated by a relativ~ly shJl~e circuit which responds to the variations of the envelope of the wave. Mainly for this reason the d.s.b. system is used for sound ___;..broadcasting in the long and medium wavebands. The dis. advantage of d.s.b. working, made apparent by Example 1.5, is that the greater part of the transmitted power is associated with the carrier component and this carries no information. Many radio-telephony systems use a more efficient method of amplitude modulation. .'..
AMPLITUDE MODULATION
9
Double-sideband tion
Suppressed-carrier
Amplitude
Modula-
The majority of the power contained in an amplitudemodulated wave is developed by the carrier component. Since this component carries no information, it may be suppressed -during the modulation process by means of a BALANCED MODULATOR. All the transmitted power is then associated with the upper and lower sidebands. The waveform of a double-sideband suppressed-carrier (d.s.b.s.c.) voltage is shown in Fig. 1.5. Fig. 1.5 has been drawn on the assumption that a 10 kHz carrier wave is amplitude modulated by a 1 kHz sinusoidal wave to produce lower and upper sidefrequencies of 9 kHz and 11 kHz respectively. With the carrier component suppressed, the d.s.b.s.c. waveform is the resultant of the 9 kHz and 11 kHz waveforms (Figs 1.5a and b) and is shown in Fig. 1.5c. The envelope of the resultant waveform is not sinusoidal and this is an indication that a
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Fig. 1.5 The formation of a d.s.b.s.c. wave by adding the components at the lower and upper sidefreq uencies
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Time (ms
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10 AMPLITUDE MODULATION
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d.s.b.s.c. signal cannot be demodulated with the simple envelope detector which is available for d.s.b. full carrier demodulation. For demodulation to be achieved, it is necessary for the carrier component to be re-inserted at the receiver with both the correct frequency and phase. The first of these requirements can be satisfied if the receiver circuitry includes an oscillator of sufficiently high stability, such as a crystal oscillator. The second requirement is much more difficultto satisfy and led to the rejection of this version of amplitude modulation in the past. Nowadays, modern developments, particularly in the field of integrated circuits, have considerably reduced these difficulties, and d.s.b.s.c. finds an application in two particular systems. These ar6-tlfe''lransmission of the colour information in the colour television system of the U.K., and the transmission of the stereo information in v.h.f. frequencymodulated sound broadcast signals.
Single-sideband tion Suppressed-carrier Amplitude Modula-
The information represented by the modulating signal is contained in both the upper and the lower sidebands, since each modulating frequency t, produces corresponding upper and lower sidefrequencies t: ± fl' It is therefore unnecessary to transmit both sidebands; either sideband can be suppressed at the transmitter without any loss of information. When the modulating signal is of sinusoidal waveform, the transmitted sidefrequency will be a sine wave of constant amplitude. Should this signal be applied to an envelope d.s.b. detector, a direct voltage output would be obtained and not the original modulating signal. This means that, once again, demodulation using an envelope detector is not possible. For demodulation to be achieved, the carrier component must be re-inserted at the correct frequency. Now, however, the phase of the re-inserted carrier does not matter and the design of the receiver is considerably eased. This method of operation is known as single-sideband suppressed-carrier (s.s.b.s.c.) amplitude modulation, frequently known simply as s.s.b. The basic principle of operation of an s.s.b. system is shown in Fig. 1.6. The modulating signal is applied to a balanced modulator along with the carrier wave generated by a highstability oscillator. The output of the balanced modulator consists of the upper and lower sidebands only. The carrier component is not present having been suppressed by the action of the modulator. The d.s.b.s.c. signal is then applied to the band-pass filter whose function is to remove the unwanted sideband.
AMPLITUDE
d.s.b.s.c. signal fe ±
MODULATION
s.s.b.s.c. signal fe- fm
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Fig. 1.6 The
s.s.b.s.c. signal
production
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Carrier frequency'"
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Single Sideband compared with Double Sideband
Single-sideband operation of a radio system has a number of advantages over double-sideband working. These advantages are as follows:
(a) The bandwidth required for an s.s.b. transmission is one
half the bandwidth that must be provided for a d.s.b. signal carrying the same information. The reduced bandwidth per channel allows a greater number of channels to be provided by the transmission medium. (b) The signal-to-noise ratio at the output of an s.s.b system is higher than at the output of the equivalent d.s.b. system. The improvement in signal-to-noise ratio has a minimum value of 9 dB when the depth of modulation is 100% and becomes larger as the depth of modulation is reduced. Exactly 3 dB of this improvement comes about because the necessary bandwidth is reduced by half, and n~e P9~er is prop()rtional to bandwidth. The rest of the improvement arisesas a result of an increase in the ratio sideband-power/total-power. (c) A d.s.b. transmitter produces a power output at all times whereas an s.s.b. transmitter does not. This results in an increase in the overall efficiencyof the transmitter. (d) Selective fading of d.s.b. radio waves may cause considerable distortion because the carrier component may fade below the sideband level. This allows the sidebands to beat together and generate a large number of unwanted frequencies. This type of distortion does not occur in an s.s.b. system since the signal is demodulated against a locally generated carrier of constant amplitude. (e) In a multi-channel telephony system, any non-linearity generates intermodulation products, many of which would lead to inter-channel crosstalk. The most likely sources of non-linearity distortion are the output stages of amplifiers since these are expected to handle the largest amplitude signals. Suppression of the carrier component reduces the amplitude of the signals that are applied to the output stages and in so doing minimizes the effect of non-linearity. The main disadvantage of s.s.b. working is the need for the carrier to be re-inserted at the receiver before demodulation
12
AMPLITUDE
MODULATION
,/1
can take place. This requirement increases the complexity, and therefore, the cost of the radio receiver. It is for this reason that sound broadc~§1,sY!>le.n;ls 9 