# modulation

Posted on Feb 5, 2014

As mentioned before, a reason to modulate a message signal is to match the communication`s channel frequency. The reason for this is that information to be send over the channel is often at a rather low frequency. For example, the sound of music range in frequency from about 100 to 15, 000 Hz. It is very difficult to send such low-frequency signals

over great distance. Low frequency signals will be interfered by other similar signals. There are many techniques for modulation. The technique that we will emphasis on is standard amplitude modulation. There are also many other modulations including methods using frequency and phase. In amplitude modulation, the circuit or the modulator combines the carrier wave (Fig 1) and the message signal (Fig 2) to form a modulated wave (Fig 3) that is a carrier wave with change in amplitude. The frequency that I choose for the figures is for examples only. In reality, the value of the frequency is higher. The message signal is a cosine wave or a sine wave. In another word, the message signal is a sinusoidal wave function. This is the same for a carrier wave except its frequency is very large when compare to the frequency of the message signal. Let us use mathematical terms to relate our signals. For the message signal in the above example, the following mathematical expression represents it. The constant Ka is the amplitude sensitivity of the modulator or the transmitter. The amplitude of equation 3 is called the envelope of the AM wave. We can represent that as a(t). The percentage of modulation will depend on the absolute value of Ka*m(t). If the absolute value of Ka*m(t) is less or equal to 1 for all t, then the percentage of modulation is less than or equal to 100%. However, if the absolute value of Ka*m(t) is greater than 1 for...

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