Advertisements
Advertisements
Question
Identify the mathematical expression for amplitude modulated wave ______.
Options
Ac sin [{ωc + k1vm (t)}t + φ].
Ac sin {ωct + φ + k2 vm (t)}.
(Ac + k2 vm (t)) sin (ωct + φ).
Ac vm (t) sin (ωct + φ).
Advertisements
Solution
Identify the mathematical expression for amplitude modulated wave `underline((A_c + k_2 v_m (t)) sin (ω_ct + φ))`.
ω
Modulating signal m(t) = Am sin ωct
Carrier signal c(t) = Ac sin ωct
Modulated signal
`c_m (t) = (A_c + A_m sin ω_m t) sin ωt`
`c_m (t) = A_c [1 + A_m/A_c sin ω_m t] sin ω_mt`
`c_m (t) = (A_c + muA_c sin ω_ct)` as `k = muA_c`
`c_m (t) = (A_c + ksin ω_m t) sin ω_mt`
APPEARS IN
RELATED QUESTIONS
Explain any two factors that justify the need of modulating a low-frequency signal.
A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. What are the frequencies of the side bands produced?
How is amplitude modulation achieved?
Define the term 'amplitude modulation'
Explain any two factors which justify the need for modulating a low frequency base-band signal.
Draw a schematic sketch showing how amplitude modulated signal is obtained by superposing a modulating signal over a sinusoidal carrier wave.
Write two advantages of frequency modulation over amplitude modulation.
Write three important factors which justify the need of modulating a message signal. Show diagrammatically how an amplitude modulated wave is obtained when a modulating signal is superimposed on a carrier wave.
Solve the following question.
A message signal of frequency 20 kHz and peak voltage 10 V is used to modulate a carrier of frequency 2 MHz and peak voltage of 15 V. Calculate the modulation index. Why the modulation index is generally kept less than one?
Define amplitude modulation in a communication system.
In amplitude modulation, the modulation index m, is kept less than or equal to 1 because ______.
- m > 1, will result in interference between carrier frequency and message frequency, resulting into distortion.
- m > 1 will result in overlapping of both side bands resulting into loss of information.
- m > 1 will result in change in phase between carrier signal and message signal.
- m > 1 indicates amplitude of message signal greater than amplitude of carrier signal resulting into distortion.
An amplitude modulated wave is as shown in figure. Calculate
- the percentage modulation
- peak carrier voltage and
- peak value of information voltage.
Draw the plot of amplitude versus ‘ω’ for an amplitude modulated wave whose carrier wave (ωc) is carrying two modulating signals, ω1 and ω2 (ω2 > ω1).
- Is the plot symmetrical about ωc? Comment especially about plot in region ω < ωc.
- Extrapolate and predict the problems one can expect if more waves are to be modulated.
- Suggest solutions to the above problem. In the process can one understand another advantage of modulation in terms of bandwidth?
An audio signal vm = 20sin2π(1500t) amplitude modulates a carrier vc = 80 sin 2π (100,000t). The value of percent modulation is ______.
An amplitude-modulated wave is represented by Cm(t) = 10(1 + 0.2 cos 12560t) × sin (111 × 104t) volts. The modulating frequency in kHz will be ______.
A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal are ______.
