A 2KW carrier is to be modulated to a 90% level. The total transmitted power would be__________.
Calculating Total Transmitted Power in AM
The total transmitted power ($P_T$) in Amplitude Modulation (AM) is determined by the carrier power ($P_C$) and the modulation index ($m$). The formula used is:
$ P_T = P_C \left( 1 + \frac{m^2}{2} \right) $
Applying the Formula
Given values:
- Carrier Power ($P_C$) = 2 KW
- Modulation Index ($m$) = 90% = 0.9
Substitute these values into the formula:
$ P_T = 2 \text{ KW} \left( 1 + \frac{(0.9)^2}{2} \right) $
First, calculate the square of the modulation index:
$ (0.9)^2 = 0.81 $
Next, divide this by 2:
$ \frac{0.81}{2} = 0.405 $
Now, add 1 to this value:
$ 1 + 0.405 = 1.405 $
Finally, multiply by the carrier power:
$ P_T = 2 \text{ KW} \times 1.405 $
$ P_T = 2.81 \text{ KW} $
Therefore, the total transmitted power is 2.81 KW.
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.
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 :
