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 :
63.28 W
Find the carrier power first, then scale it by the modulation factor.
Step 1 — the carrier power. The 150 V is a peak value, so the RMS value is \(150/\sqrt{2}\) and
\(P_{c}=\dfrac{V_{c}^{2}}{2R}=\dfrac{150^{2}}{2\times200}=\dfrac{22500}{400}=56.25\ \text{W}\)
The factor 2 in the denominator is exactly the squared \(\sqrt{2}\) of the peak-to-RMS conversion, and forgetting it doubles the answer — which is what option 4 nearly represents.
Step 2 — add the sideband power.
\(P_{t}=P_{c}\left(1+\dfrac{m^{2}}{2}\right)=56.25\left(1+\dfrac{0.5^{2}}{2}\right)\)
\(=56.25\left(1+0.125\right)=56.25\times1.125=63.28\ \text{W}\)
— option 3.
Where the m2/2 comes from. Each sideband has an amplitude of \(mV_{c}/2\), so each carries
\(P_{SB}=\dfrac{\left(mV_{c}/2\right)^{2}}{2R}=\dfrac{m^{2}}{4}P_{c}\)
and there are two of them, giving \(m^{2}P_{c}/2\) in total. Here that is 7.03 W of information-bearing power against 56.25 W of carrier.
| Component | Power | Share |
|---|---|---|
| Carrier | 56.25 W | 88.9 % |
| Both sidebands | 7.03 W | 11.1 % |
| Total | 63.28 W | 100 % |
What the numbers say about AM's efficiency. At \(m=0.5\) only 11 % of the transmitted power carries any information; the rest is spent on a carrier that conveys nothing. Even at full modulation, \(m=1\), the figure rises only to 33 %. That is the whole case for suppressed-carrier transmission — and the reason the carrier is nevertheless kept in broadcasting is that it allows a receiver to be built from a single diode.
A useful check on the result : the total can never be less than the carrier power alone, and for \(m\le1\) can never exceed \(1.5P_{c}=84.4\) W. Options 1 and 2 fall outside those bounds — 263.5 W is far too large and 45.23 W is below the carrier power — so both can be rejected before any arithmetic.
Hence, the total power is 63.28 W.
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.
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 :
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
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.
