Assertion (A) : In amplitude modulation technique the modulation index should be close to 1. Reason (R) : The power carried by message signal in the side bands increases with increase in modulation index.
Both (A) and (R) are correct and (R) is correct explanation of (A).
Both are true, and the reason states precisely why the assertion holds — option 1.
The quantitative link. Total transmitted power in an AM signal is
\(P_{t}=P_{c}\left(1+\dfrac{m^{2}}{2}\right)\)
of which the carrier carries \(P_{c}\) — and the carrier contains no information. Only the sidebands do, and their share is
\(\eta=\dfrac{m^{2}/2}{1+m^{2}/2}\)
| m | Power in sidebands |
|---|---|
| 0.3 | 4.3 % |
| 0.5 | 11.1 % |
| 1.0 | 33.3 % |
Even at full modulation two-thirds of the transmitted power is spent on the carrier; at m = 0.3 more than 95 % is wasted. Since the useful power rises monotonically with m, the index should be pushed as high as possible — which is the assertion.
Why the limit is exactly 1 and not more. The envelope of the modulated wave is \(A_{c}\left(1+m\cos\omega_{m}t\right)\). For \(m\gt1\) this quantity goes negative on the troughs, the envelope crosses zero and folds back, and a diode envelope detector — which follows the magnitude only — reproduces the folded shape. The recovered signal is distorted beyond repair. This is overmodulation, and it also splatters energy into adjacent channels through the sharp corners it creates.
So m = 1 is the optimum: the largest index that keeps the envelope faithful, giving maximum sideband power without distortion. In practice broadcasters keep peak modulation slightly below 100 % to allow for programme peaks, and use compressors and limiters to hold the average index high without ever crossing the line.
The obvious further step is to remove the carrier altogether, which is what DSB-SC does, putting 100 % of the power into the sidebands — at the cost of needing a coherent detector rather than a diode. The carrier's only virtue is that it makes the receiver cheap, and that is why AM broadcasting spends two-thirds of its power on it.
Hence, both (A) and (R) are correct and (R) explains (A).
Similar Questions
Read the statements :
i. DSB has two side bands and SSB has one
ii. DSB has carrier and two side bands and SSB has a carrier and a side band
iii. DSB has carrier and two side bands and SSB without carrier and two different side bands.Which statements are correct ?
Assertion (A) : Amplitude modulation is wastage of power.
Reason (R) : Amplitude modulation is wastage of bandwidth.
The peak carrier voltage is 150 V. If the resistor is 200 Ω and the modulation index is 0.5, the total power in the AM signal is :
The modulation index of an AM wave is given by :
Consider an AM (amplitude modulated) signal
\(s(t) = 20\left[1 + 0.9\cos 2\pi \times 10^4 t\right]\cos 2\pi \times 10^6 t\)
The power efficiency (η) in the AM signal is
In amplitude modulation:
A. Amplitude of carrier is varied by modulating signal
B. Modulation index is between 0 and 1
C. Bandwidth is infinite
D. Bandwidth is twice of minimum modulating frequency.
Choose the correct answer from the options given below:
Match List I with List II
LIST I LIST II A. Power of AM Wave I. \(P_c\left(\frac{m^{2}}{4}\right)\) B. Power of VSB II. \(\frac{m^{2}}{4}P_c+F\left(\frac{m^{2}}{4}P_c\right)\) C. Power of SSB III. \(\frac{m^{2}}{4}\left(\frac{V_c^{2}}{2R}\right)+\frac{m^{2}}{4}\left(\frac{V_c^{2}}{2R}\right)\) D. Power of DSBSC IV. \(\frac{V_{carr}^{2}}{R}+\frac{V_{LSB}^{2}}{R}+\frac{V_{USB}^{2}}{R}\) Choose the correct answer from the options given below:
If 1 MHz carrier is amplitude modulated with a 5 kHz audio signal, the Upper Side Band (USB) and Lower Side Band (LSB) frequencies are ________ respectively.
Which of the following is associated with single balanced modulator circuit :
Important Questions from Amplitude Modulation
The highest modulation frequency typically used in AM broadcast is
Which of the following is NOT the advantage of amplitude modulation?
Bandwidth requirement for Amplitude modulated wave is:
The frequency range of AM radio is:
In an amplitude modulated system, a sinusoidal carrier signal of 1 MHz is modulated by a 10 kHz sinusoidal signal. If the lower sideband and the carrier are suppressed and if the amplitude modulated signal is sampled for further processing, what should be the minimum sampling frequency for baseband sampling?
