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
28.82%
Step 1 — read the modulation index from the equation. Compare the given signal with the standard AM form:
\(s(t)=A_c\left[1+\mu\cos\omega_m t\right]\cos\omega_c t\)
Matching term by term with \(s(t)=20\left[1+0.9\cos 2\pi\times10^{4}t\right]\cos 2\pi\times10^{6}t\) gives carrier amplitude Ac = 20 V, modulating frequency fm = 10 kHz, carrier frequency fc = 1 MHz, and modulation index
\(\mu = 0.9\)
Step 2 — what power efficiency means. In conventional AM (DSB-FC) the carrier itself carries no information; only the two sidebands do. Efficiency is therefore the fraction of total transmitted power that lies in the sidebands:
\(\eta = \dfrac{P_{SB}}{P_t} = \dfrac{\mu^{2}}{2+\mu^{2}}\)
This comes from \(P_t = P_c\left(1+\dfrac{\mu^{2}}{2}\right)\) and \(P_{SB} = P_c\dfrac{\mu^{2}}{2}\).
Step 3 — substitute μ = 0.9.
\(\eta = \dfrac{(0.9)^{2}}{2+(0.9)^{2}} = \dfrac{0.81}{2.81}\)
\(\eta = 0.2882 = 28.82\%\)
Interpretation. Even at 90 % modulation, under 29 % of the transmitted power does useful work — the rest is spent on the carrier. Efficiency peaks at only 33.3 % for μ = 1 (full modulation), and driving μ > 1 causes over-modulation and envelope distortion rather than any gain. This poor efficiency is exactly why DSB-SC and SSB were developed: suppressing the carrier raises efficiency to 100 %, at the cost of needing a coherent detector instead of a simple diode envelope detector.
Useful check with actual powers (for a 1 Ω reference): \(P_c = A_c^{2}/2 = 200\ \text{W}\), \(P_{SB}=P_c\mu^{2}/2 = 81\ \text{W}\), \(P_t = 281\ \text{W}\), so \(\eta = 81/281 = 28.82\%\) ✓.
Hence, the power efficiency of the AM signal is 28.82 %.
Similar Questions
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.
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 :
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 :
The modulation index of an AM wave is given by :
Important Questions from Amplitude Modulation
- An amplitude modulated voltage signal $x(t)$ drives a load of $1\ \Omega$. $$x(t) = K \cos(300\pi t) + L \cos(240\pi t) + L \cos(360\pi t).$$ If the efficiency is $60\%$, and the carrier power is $50\text{ W}$, the value of $L$ is ______ V.
A 2KW carrier is to be modulated to a 90% level. The total transmitted power would be__________.
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.
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.
