Question

An AM transmitter is coupled to an aerial. The input current is found to be \(5\ \text{A}\). With modulation, the current value increases to \(5.9\ \text{A}\). The depth of modulation is:

• A. \(83.4\%\)
• B. \(88.6\%\)
• C. \(78.2\%\)
• D. \(62.6\%\)

Hint:

Use \(I_t = I_c\sqrt{1+m^2/2}\) and solve for \(m\) from the current ratio.

Answer 1

The Correct Option is B

Step 1: When a carrier of antenna current \(I_c\) is amplitude modulated to depth \(m\), the total antenna current rises to \[I_t = I_c\sqrt{1 + \frac{m^{2}}{2}}.\]
Step 2: Take the ratio of the currents: \[\frac{I_t}{I_c} = \frac{5.9}{5} = 1.18.\]
Step 3: Square both sides: \[1 + \frac{m^{2}}{2} = (1.18)^{2} = 1.3924.\]
Step 4: Solve for \(m^2\): \[\frac{m^{2}}{2} = 0.3924 \;\Rightarrow\; m^{2} = 0.7848 \;\Rightarrow\; m = 0.886.\]
Step 5: As a percentage the depth of modulation is about \(88.6\%\), option (B). \[\boxed{m \approx 88.6\%}\]