Communication Theory - Peak Envelope Power

[satchmo05]

Homework Statement

Peak envelope detector defined as A²_MAX, which is the square of AM signal's envelope. AM radio transmitter rated for 4[kW] peak envelope power. Find max value of modulation index (mu) for tone modulation when average transmitted power (P_T) is 1[kW].

Homework Equations

- Since this is a tone modulation problem, I know that z(t) is a sinusoid with efficiency, e = (mu²)/(2+mu²).

- mu = (A_max - A_min)/(A_max + A_min)

- I have found an equation, mu = sqrt(P_X/P_Z) - 1
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|--> I am curious if this will give me the answer I am looking for.

The Attempt at a Solution

Using the last equation above, the fact that Px = 4[kW], Pz = 1[kW] --> mu = 1? Seems like a trivial result where I don't even use Amax to find... Thank you for help!

 

[KataKoniK]

Your approach is correct, but there are a few things to consider. First, the equation you mentioned, mu = sqrt(Px/Pz) - 1, is only valid for a single tone modulation. In this case, we are dealing with a tone modulation, so it is applicable. However, for more complex modulation schemes, this equation may not give the correct result.

Secondly, the equation assumes that the modulation index is less than or equal to 1. If the modulation index exceeds 1, then the signal will be overmodulated and distortion will occur. Therefore, the maximum value of mu in this case would be 1.

Finally, the equation also assumes that the power in the sidebands is negligible compared to the carrier power. This may not always be the case, especially for large modulation indices. In those cases, a more accurate equation would need to be used.

In summary, for this specific problem, your approach is correct and the maximum value of mu would be 1. However, for more complex modulation schemes or when the assumptions of the equation do not hold, a different approach may be necessary. I hope this helps!