General Theoretical Concerns in AM II


Examining the right hand side of the equation we find



We can therefore alter  voltage amplitude, phase or frequency. Unsurprisingly in amplitude modulation it is the voltage amplitude we vary. We do this by combining a modulating signal with the carrier wave. It produces a waveform such as the red one in fig 2 below, which we can then transmit.

fig2: typical AM waveform

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It can be clearly seen that the zeniths and nadirs of  successive cycles are no longer equal in amplitude but follow the alternations of the modulating signal, here shown in blue. This is the general principle of amplitude modulation: we take a low frequency audio signal which cannot radiate itself through an antenna and  heterodyne it to a high frequency carrier which can by  varying the total power in the wave.

It can probably be gathered from the graph that  a mathematical relationship exists between the modulating signal and the carrier wave. It is known as the modulating factor or the modulation index. It is given by the equation :

m= Em/Ec

where Em is the modulating voltage and Ec that of the carrier.

It can either be expressed as a  number or as a percentage, so for Em at 7V and Ec at 10V then the index would be 0.7, or multiplying by 100 gives 70%.

Any carrier should not undergo a modulation greater than 100% as this distorts the signal being transmitted. The BBC regards the best (i.e theoretically ideal) modulation as being  approximately 80%.

Why modulate?


Most of the power in a human voice is at  less than 1 kHz in frequency, although harmonics exist as high as 3kHz. This is what gives a voice a unique timbre. Any power  radiating through an antenna  will, on the alternate half of the cycle, attempt to fall back into the antenna. It is stopped from doing so by the next wave front, which repulses its predecessor  and causes dissipation through  the air- providing the next wave front arrives fast enough . At frequencies lesser than 15kHz this does not happen. We must modulate the low audio frequency onto the high radio frequency. This is why an early term for a modulating circuit was frequency changer.

Radio Principles