# Modulation Index Dilemma - DSB-LC AM Modulation

1. May 14, 2013

### hmph

1. The problem statement, all variables and given/known data

A given DSB-LC AM transmitter develops an unmodulated power output of 1kW across a 50 ohm resistive load. When a sinusoidal test tone of 5V is applied to the input of the modulator, it is found that the spectral line for each sideband carrier in the magnitude spectrum is 40% of the output of the carrier line.

2. Relevant equations

The output signal of the modulator is (mA cos (w_mt) + A) cos (w_c t)
Where m is the modulation index, A is the carrier amplitude and w_m is the modulating frequency and w_c is the carrier frequency

3. The attempt at a solution

The "40% of the output carrier line" corresponds to a modulation index (m) of 0.8. (which is in the solution - I am not interested in the solution here really).

But since the "unmodulated power output is 1 kW across a 50 ohm resistive load), it means that A = √ (2RP_c) = √(2*50*1000) = 316.67. (This is also indirectly in the solution)

If the carrier amplitude is 316 V, and the input is 5V, is the modulation index not 5/316 ? Is the modulation index not the ratio of the input amplitude to the carrier amplitude?

The questions that follow on this make perfect sense to me if I ignore the fact that the input is a 5V sinusoid

2. May 14, 2013

### rude man

And the question is .... ?