A transmitter radiates 9 kW without modulation and 10.125 kW afte
| A transmitter radiates 9 kW without modulation and 10.125 kW after modulation. Determine the modulation index.
A. 1
B. 0.7
C. 0.5
D. 0.8
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
Concept:
The total power transmitted for an AM signal is calculated as:
\({{\rm{P}}_{\rm{t}}} = {{\rm{P}}_{\rm{c}}}\left( {1 + \frac{{{{\rm{μ }}^2}}}{2}} \right)\)
Pc = Carrier Power
μ = Modulation Index
Calculation:
Given,
Pc (Carrier power) = 9 kW
Pt (Total modulated signal power) = 10.125 kW
\({{\rm{P}}_{\rm{t}}} = {{\rm{P}}_{\rm{c}}}\left( {1 + \frac{{{{\rm{μ }}^2}}}{2}} \right)\)
Rearranging the above, we get:
\({\rm{μ }} = \sqrt {2\left( {\frac{{{{\rm{P}}_{\rm{t}}}}}{{{{\rm{P}}_{\rm{c}}}}} - 1} \right)} \)
Putting the respective values:
\({\rm{μ }} = \sqrt {2\left( {\frac{{10.125}}{9} - 1} \right)}\)
\(\Rightarrow {\rm{μ }} = 0.5\)