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
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?
Draw a block diagram of a detector for AM signal and show, using necessary processes and the waveforms, how the original message signal is detected from the input AM wave.
Explain the process of amplitude modulation.
A modulating signal is a square wave, as shown
The carrier wave is given by `c(t) = 2 sin (8pit) "volts"`
(i) Sketch the amplitude modulated waveform
(ii) What is the modulation index?
For an amplitude modulated wave, the maximum amplitude is found to be 10 V while the minimum amplitude is found to be 2 V. Determine the modulation index μ. What would be the value of μ if the minimum amplitude is zero volt?
Define the term 'amplitude modulation'
Explain any two factors which justify the need for modulating a low frequency base-band signal.
Answer the following question.
If A and B represent the maximum and minimum amplitudes of an amplitude-modulated wave, write the expression for the modulation index in terms of A and B.
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?
A message signal of frequency ωm is superposed on a carrier wave of frequency ωc to get an amplitude modulated wave (AM). The frequency of the AM wave will be ______.
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.
The maximum amplitude of an A.M. wave is found to be 15 V while its minimum amplitude is found to be 3 V. What is the modulation index?
On radiating (sending out) an AM modulated signal, the total radiated power is due to energy carried by ωc, ωc – ωm and ωc + ωm. Suggest ways to minimise cost of radiation without compromising on information.
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?
The maximum and minimum voltage of an amplitude modulated signal are 60 V and 20 V respectively. The percentage modulation index will be ______.
The maximum amplitude for an amplitude modulated wave is found to be 12V while the minimum amplitude is found to be 3V. The modulation index is 0.6x where x is ______.
A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal are ______.
