Amplitude Modulation (AM) is preferred for picture transmission in TV because of the following reasons:
On the other hand, FM is preferred for sound because of the following reasons:
A wave has 3 parameters Amplitude, Phase, and Frequency. Thus there are 3 types of modulation techniques.
Amplitude Modulation: The amplitude of the carrier is varied according to the amplitude of the message signal.
Frequency Modulation: The frequency of the carrier is varied according to the amplitude of the message signal.
Phase Modulation: The Phase of the carrier is varied according to the amplitude of the message signal.
Concept:
Power of a transmitted AM wave is given as:
\(P_t = {P_c}\left( {1 + \frac{{{μ ^2}}}{2}} \right)\)
\(P_t = {P_c} + P_c\frac{μ ^2}{2}\)
Power in the carrier = Pc
Power in both the sidebands is given by:
\(P_s= \frac{{{P_c}{μ^2}}}{2}\)
Since the power is distributed equally to the left and to the right side of the sideband, the power in one of the sidebands is given by:
\(P_{s1}= \frac{{{P_c}{u^2}}}{4}\)
Analysis:
We know that:
\({P_t} = {P_c}\left( {1 + \frac{{{\mu ^2}}}{2}} \right)\)
\(2.09 = {P_c}\left( {1 + \frac{{0.09}}{2}} \right)\)
\(\therefore {P_c} = 2\;Watts\)
Power in each sideband is:
\({P_{SB}} = {P_c}~\frac{{{\mu ^2}}}{4} = \frac{{2\left( {0.09} \right)}}{4}\)
\( = 0.045\;Watts\)
Concept:
Signal to noise ratio in case of WBFM is given by
\({\left( {\frac{S}{N}} \right)_{WBFM}} = \frac{3}{2}m_f^2\)
Signal to noise ratio in case of AM is given by
\({\left( {\frac{S}{N}} \right)_{AM}} = \frac{{{\mu ^2}}}{{{\mu^2} + 2}}\)
Calculation:
Given:
100% amplitude modulation i.e.
μ = 1
\({\left( {\frac{S}{N}} \right)_{WBFM}} = \frac{3}{2}m_f^2\)
\({\left( {\frac{S}{N}} \right)_{AM}} = \frac{{{1^2}}}{{{1^2} + 2}} = \frac{1}{3}\)
\(\frac{{{{\left( {\frac{S}{N}} \right)}_{WBFM}}}}{{{{\left( {\frac{S}{N}} \right)}_{AM}}}} = \frac{{\frac{3}{2}m_f^2}}{{\frac{1}{3}}} = \frac{9}{2}\;m_f^2\)
Schemes 
(S/N) 
AM 
\({\left( {\frac{S}{N}} \right)_{AM}} = \frac{{{\mu ^2}}}{{{\mu^2} + 2}}\) 
FM 
\({\left( {\frac{S}{N}} \right)_{WBFM}} = \frac{3}{2}m_f^2\) 
PM 
\({\left( {\frac{S}{N}} \right)_{PM}} = \frac{1}{2}m_f^2\) 
Concept:
The total transmitted power for an AM system is given by:
\({P_t} = {P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)\)
Pc = Carrier Power
μ = Modulation Index
Analysis:
When the carrier is not modulated, i.e. modulation index = 0, the transmitted power is the carrier power only, i.e.
P_{t} = P_{C}
When modulated with a modulation index of 40%, the total power is calculated as:
\({P_t} = {P_c}\left( {1 + \frac{{{0.4^2}}}{2}} \right)\)
The percentage increase in power will be:
\(=\frac{{P_c}\left( {1 + \frac{{{0.4^2}}}{2}} \right)P_c}{P_c}\times 100\)
\(=\frac{0.4^2}{2}\times 100~\%\)
= 8 %
Concept:
AM modulated wave equation is given as:
\(S\left( t \right) = {A_c}\left[ {1 +\mu\cos 2\pi fm\left( t \right)} \right]\cos 2\pi fct\)
\(= {A_c}\cos 2\pi \;f_ct + {A_c}\mu\cos 2\pi f_mt\cos 2\pi f_ct\)
\(= {A_c}\cos 2\pi f_ct + \frac{{{A_c}\mu}}{2}\cos 2\pi \left( {f_c + f_m} \right)t+\frac{{{A_c}\mu}}{2}\cos 2\pi \left( {fc  fm} \right)t\)
Frequency of USB: (fc + fm) and (fc  fm)
Frequency of LSB: (fc + fm) and (fc  fm)
Calculation:
Given:
f_{c} = 20 kHz
Speech band = 300 to 3300 Hz
The range of LSB is given as:
(fc + fm_{1}) and (fc  fm_{1}) = 19.7 kHz and 19.7 kHz
(fc + fm_{2}) and (fc  fm_{2}) = 16.7 kHz and 16.7 kHz
Note:
Negative frequency does not exist practically so:
The range of LSB is: 16.7 kHz to 19.7 kHz
Which of the following requires the least bandwidth?
DSB SC:
1) It is a form of Amplitude modulation where only the sidebands are transmitted and the carrier is suppressed.
2) The advantage is 66% power saving compared to conventional AM.
3) The Bandwidth requirement is of 2f_{m}, with f_{m} being the maximum frequency component of the message signal.
4) It is used for transmitting stereo information.
Single Side Band (SSB SC):
1) SSB SC is a form of amplitude modulation where only a single sideband is transmitted and 1 sideband and carrier are suppressed.
2) The advantage of SSB is bandwidth and powersaving over both conventional AM and DSB SC, i.e. DSB SC has more power consumption than SSB SC.
3) The Bandwidth requirement is only fm, ∴ It needs half the bandwidth than the DSBSC transmission.
Comparison:
Parameter 
SSB 
DSB 
VSB 
Power 
Less 
High 
Medium 
Bandwidth 
fm 
2 fm 
fm < BW < 2fm 
Carrier Suppression 
Complete 
Complete 
No 
Sideband Suppression 
One sideband completely 
No 
One sideband suppressed partially. 
Concept:
The frequency spectrum of an Amplitude Modulated wave is given by:
Bandwidth in AM = (f_{c} + f_{m})  (fc  fm)
Bandwidth in AM = 2fm
Calculation:
fc = 10 kHz
Upper sideband = fc + fm = 11 kHz
∴ The message frequency is:
fm = 11 – 10 = 1 kHz
Hence, Bandwidth is:
= 2f_{m} = 2 × 1 kHz = 2 kHz
What is the total power carried by sidebands of the AM wave (DSB) for tone modulation of μ = 0.4 ?
Concept:
The generalized AM expression is represented as:
s(t) = Ac [1 + μa mn (t)] cos ωc t
The total transmitted power for an AM system is given by:
\({P_t} = {P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)\)
Pc = Carrier Power
μ = Modulation Index
The above expression can be expanded to get:
\({P_t} = {P_c} + P_c\frac{{{μ^2}}}{2}\)
The total power is the sum of the carrier power and the sideband power, i.e.
\({P_s} = P_c\frac{{{μ^2}}}{2}\)
Analysis:
Total sideband power is calculated as:
\({P_s} = P_c\frac{{{μ^2}}}{2}\)
% of sideband power is given as:
⇒ \( \frac{P_c \frac{μ^2}{2}}{{P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)}\)
⇒ \( \frac{μ^2}{μ^2+2}\)
putting μ = 0.4, we get
⇒ \( \frac{0.4^2}{0.4^2\;+\;2} \times 100 = 0.074 \times 100\)
= 7.4 %
The ring modulator is generally used for generating
The ring modulator and balanced modulator is generally used for the modulation of DSB SC signal.
SSB/SC is generated using a balanced modulator
Concept:
The transmission efficiency of an AM wave is defined as the percentage of total power contributed by the sidebands.
For a sinusoidal AM signal, it is given by:
\(η=\frac{{{μ ^2}}}{{2 + {μ ^2}}} \times 100\)
μ = Modulation index
The maximum efficiency is obtained for μ = 1, i.e.
\(η_{max}=\frac{{{1}}}{{2 + {1}}} \times 100\)
η_{max} = 33.33 %
Derivation:
Mathematically, the efficiency can be expressed as:
\(\eta = \frac{{{P}_{SB}}}{{{P_t}}} \times 100\%\)
For sinusoidal input
PSB = Sideband power given by:
\({P_{SB}} = \frac{{{P_c}\;{\mu ^2}}}{2}\)
Pt = Total power given by:
\({P_t} = {P_c}\;\left( {1 + \frac{{{\mu ^2}}}{2}} \right)\),
\(\eta = \frac{{{P_c}{\mu ^2}}}{{2\left( {{P_c}\left( {1 + \frac{{{\mu ^2}}}{2}} \right)} \right)}}\)
\(\eta = \frac{{{P_c}{\mu ^2}}}{{{P_c}\left( {2 + {\mu ^2}} \right)}} = \frac{{{\mu ^2}}}{{2 + {\mu ^2}}} \times 100\)
The frequency spectrum of all the given modulation schemes is as shown:
Total power = Carrier power + Sideband power
In SSB, we have one sideband only hence the power is less than DSB and VSB.
In VSB, we have one sideband and some part of the other sideband and hence power is more than SSB and less than DSB.
Parameter 
SSB 
DSB 
VSB 
Power 
Less 
High 
Medium 
Bandwidth 
f_{m} 
2 f_{m} 
f_{m}< BW< 2f_{m} 
Carrier Suppression 
Complete 
Complete 
No 
Sideband Suppression 
One sideband completely 
No 
One sideband suppressed partially. 
Explanation:
Electromagnetic spectrum: It is a collection of a range of different waves in sequential order from radio to gamma electromagnetic waves.
Radio waves:
Concept:
The power of a transmitted AM wave is given as:
\(P_t = {P_c}\left( {1 + \frac{{{μ ^2}}}{2}} \right)\)
\(P_t = {P_c} + P_c\frac{μ ^2}{2}\)
Power in the carrier = Pc
\(P_c=\frac{{A_m}^2}{2}\)
Power in both the sidebands is given by:
\(P_s= \frac{{{P_c}{μ^2}}}{2}\)
Since the power is distributed equally to the left and to the right side of the sideband, the power in one of the sidebands is given by:
\(P_{s1}= \frac{{{P_c}{u^2}}}{4}\)
Calculation:
Given μ = 20% = 0.2
\(P_c=\frac{{A_m}^2}{2}\)
Total Sideband power is:
\(P_{sb}=\frac{{A_m}^2\mu^2}{4}\)
Assume A_{m} = 1
\(P_{sb}=\frac{0.2^2}{4} \ \times \ 100\)
P_{sb} = 1%
Hence option (3) is the correct answer.
Amplitude Modulation (AM) is preferred for picture transmission on TV because of the following reasons:
On the other hand, FM is preferred for sound because of the following reasons:
A wave has 3 parameters Amplitude, Phase, and Frequency. Thus there are 3 types of modulation techniques.
Amplitude Modulation: The amplitude of the carrier is varied according to the amplitude of the message signal.
Frequency Modulation: The frequency of the carrier is varied according to the amplitude of the message signal.
Phase Modulation: The Phase of the carrier is varied according to the amplitude of the message signal.
The modulation technique that takes the lowest bandwidth is SSBSC
Single Side Band (SSB SC):
1) SSB SC is a form of amplitude modulation where only a single sideband is transmitted and 1 sideband and carrier are suppressed.
2) The advantage of SSB is bandwidth and powersaving over both conventional AM and DSB SC, i.e. DSB SC has a more power consumption than SSB SC.
3) The Bandwidth requirement is only fm, ∴ It needs half the bandwidth than the DSBSC transmission.
Comparison:
Parameter 
SSB 
DSB 
VSB 
Power 
Less 
High 
Medium 
Bandwidth 
fm 
2 fm 
fm < BW < 2fm 
Carrier Suppression 
Complete 
Complete 
No 
Sideband Suppression 
One sideband completely 
No 
One sideband suppressed partially. 
Consider the following amplitude modulated signal: s(𝑡) = cos(2000 𝜋𝑡) + 4 cos(2400 𝜋𝑡) + cos(2800 𝜋𝑡).The ratio (accurate to three decimal places) of the power of the message signal to the power of the carrier signal is ________.
Concept:
For a single tone sinusoidal signal, the expression for amplitude modulated wave is given by:
\({x_{AM}}\left( t \right) = {A_c}\left( {1 + {m_a}\cos {\omega _m}t} \right)\cos {\omega _c}t\)
\({A_c}\cos {\omega _c}t + \frac{{{A_c}{m_a}}}{2}\cos \left( {{\omega _c} + {\omega _m}} \right)t + \frac{{{A_c}{m_a}}}{2}\cos \left( {{\omega _c}  {\omega _m}} \right)t\)
Calculation:
Comparing the given expression with the standard expression, the given AM signal can be written as:
\({x_{AM}}\left( t \right) = 4\left( {1 + \frac{1}{2}\cos {\omega _m}t} \right)\cos {\omega _c}t\)
\(So,\;{m_a} = \frac{1}{2}\;and\;{A_c} = 4\)
The modulation index is given by;
\({m_a} = \frac{{{A_m}}}{{{A_c}}} = \frac{1}{2}\)
\({A_m} = \frac{{{A_c}}}{2} = \frac{4}{2} = 2\)
Power of the message signal is, therefore:
\({P_m} = \frac{{A_m^2}}{2} = \frac{4}{2} = 2\;W\)
Power of the carrier signal:
\({P_c} = \frac{{A_c^2}}{2} = \frac{{{4^2}}}{2} = 8\;W\)
So, the required ratio of the message power to the carrier power:
\(\frac{{{P_m}}}{{{P_c}}} = \frac{2}{8} = \frac{1}{4} = 0.25\)
Concept:
The power of a transmitted AM wave is given as:
\(P_t = {P_c}\left( {1 + \frac{{{μ ^2}}}{2}} \right)\)
\(P_t = {P_c} + P_c\frac{μ ^2}{2}\)
Power in the carrier = Pc
Power in both the sidebands is given by:
\(P_s= \frac{{{P_c}{μ^2}}}{2}\)
Calculation:
Given:
μ = 0.7
P_{c} = 71.14 W
\(P_s= \frac{{{P_c}{μ^2}}}{2}\)
\(P_s= \frac{{{71.14} \ \times \ 0.7{^2}}}{2}\)
P_{s} = 17.43 W
Concept:
VSB modulation is the process where a part of a signal called vestige is modulated along with one of the sidebands.
A VSB signal is plotted as shown in the following figure:
A guard band is a very small frequency width used to avoid interference.
The mathematical representation of the VSB wave is:
\(s\left( t \right) = \frac{{{V_m}}}{2}\cos 2\pi {f_c}t \pm \frac{{{V_m}\left( q \right)}}{2}\sin 2\pi {f_c}t\)
V_{m}, q = Quardature component of V_{m.}
f_{c} = Carrier frequency
Power relation in VSB wave:
\({P_{VSB}} = \frac{{{K^2}}}{4}{P_c} + F\;\left( {\frac{{{K^2}}}{4}{P_c}} \right)\)
F = represents a fraction
K = modulation index
Advantage of VSB 
Disadvantage of VSB 
Highly efficient 
Bandwidth compared to SSB is greater 
Reduction in Bandwidth 
Demodulation is complex 
Good phase characteristics 

Calculation:
Given that:
P_{VSB} = 0.625, K = 60% = 0.6, F = 25% = 0.25
P_{C} = ?
Then:
\({P_{VSB}} = \frac{{{K^2}}}{4}{P_c} + F\;\left( {\frac{{{K^2}}}{4}{P_c}} \right)\)
\({P_{VSB}} = \frac{{{K^2}}}{4}{P_c}\left( {1 + F} \right)\)
\(0.625 = \frac{{{{\left( {0.6} \right)}^2}}}{4}{P_c}\left( {1 + 0.25} \right)\)
\({P_c} = \frac{{0.625 \times 4}}{{1.25 \times 0.36}} \simeq 5.56\;kW\)
Option (2) correct.
More information:
Modulation Technique 
Total power (P_{T}) 
Bandwidth (BW) 
Application 
AM 
P_{c} + P_{SB}

2ω_{m} 
Mediumwave Short wave 
DSBSC 
P_{SB} 
2ω_{m} 
 
VSBSC 
\(\frac{{{P_{SB}}}}{2} < {P_T} < {P_{SB}}\) 
ω_{m} < Bw < 2ω_{m} 
Picture signal in TV 
SSBSC 
\(\frac{{{P_{SB}}}}{2}\) 
ω_{m} 
Telephony 
Concept:
The generalized AM expression is represented as:
s(t) = Ac [1 + μa mn (t)] cos ωc t
The total transmitted power for an AM system is given by:
\({P_t} = {P_c}\left( {1 + \frac{{{μ^2}}}{2}} \right)\)
Pc = Carrier Power
μ = Modulation Index
The above expression can be expanded to get:
\({P_t} = {P_c} + P_c\frac{{{μ^2}}}{2}\)
The total power is the sum of the carrier power and the sideband power, i.e.
\({P_s} = P_c\frac{{{μ^2}}}{2}\)
The power in a single sideband will be:
\({P_s} = \frac{1}{2}\times P_c\frac{{{μ^2}}}{2}\)
With \(P_c=\frac{A^2}{2}\), the above can be written as:
\({P_s} = \frac{1}{2}\times \frac{A_c^2}{2}\frac{{{μ^2}}}{2}\)
\({P_s} = \frac{{{A_c^2μ^2}}}{8}\)
\(Power Saved=\frac{P_c}{P_{total}}\) (1)
Power Saved = Pc in DSB  SC
\(Power \ Saved=\frac{2}{2 \ + \ μ^2}\)
Analysis:
When μ = 1, the transmitted power will be:
\({P_t} = {P_c}\left( {1 + \frac{{{1^2}}}{2}} \right)=\frac{3}{2}P_c\)
\(Power Saved=\frac{P_c}{P_c(1 \ + \ \frac{μ^2}{2})}\)
As μ = 1
\(Power \ Saved=\frac{2}{2 \ + \ 1^2}\times 100\)
Power Saved = 66 %
Concept:
When a carrier is modulated by different waves having different modulation indexes, the effective (total) modulation index is given by:
\({{\rm{μ }}_{{\rm{eff}}}} = \sqrt {{\rm{μ }}_1^2 + {\rm{μ }}_2^2+μ_3^2+...}\)
Calculation:
With μ_{1} = 0.25, μ2 = 0.50, μ3 = 0.75, the effective modulation index will be:
\({{\rm{μ }}_{{\rm{eff}}}} = \sqrt {(0.25)^2 + (0.50)^2+(0.75)^2}\)
μ_{eff} = 0.935
Important Note:
The total power of the modulated signal for the given effective modulation index is given by:
\({P_t} = {P_c}\left( {1 + \frac{{{μ_{eff}^2}}}{2}} \right)\)
Pc = Carrier Power
μeff = Effective modulation Index