Way to solve a modulation problem

 

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You have several equations that you will become familiar with regarding analog modulation.

The "message" or "information" wave which contains the intelligence:  m(t) = Am cos(2πfmφ),

The "carrier" wave which is modulated by the "message" wave, which is a sinusoidal wave:  c(t)= Ac cos(2πfcφ),

You will note that both m(t) and c(t) are sinusoidal waves; however, your information wave is typically not a perfect sinusoid, since speech, music, video or data is never as predictable as a sine or cosine wave.  We use a simple sinusoidal wave for m(t) for demonstrative purposes only in order to see what happens during the modulation.

Our resultant, modulated "signal" wave (transmitted over guided or unguided medium), for AM techniques looks like this:  sAM(t) = Ac [1 + μAMcos(2πfmt)]cos(2πfct),  Modulation Index, μAM = AM/AC  ,

 So if given sAM(t) = 3 [1 + 4cos(2π10t)]cos(2π6000t), and comparing it to the signal equation above, we can discern the following:

 Ac (carrier wave amplitude in volts) = 3 v

μAM (AM modulation index) = 4

fm (frequency of the message wave) = 10 Hz

fc (frequency of the carrier wave) = 6 kHz

Am = μAM x A, therefore Am = 4 x 3 =  12 v

 We also know that since μAM = 4, it is not within the recommended 0 ≤ μAM ≤ 1, your signal will experience distortion

 The amplitude of our message wave is too large in comparison to the amplitude of the carrier wave.  As such, the message wave overwhelms the carrier wave leading to a distorted signal wave.

FM and PM modulation problems can be approached in a similar manner as the above.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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