How is information sent to a radio?

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The short answer to the question is that information is transmitted to a radio by modulating a carrier signal (by packaging the original information inside a sinusoidal signal). After this packed signal is received by the radio it is unpacked and the original info restored.

Suppose you have random signal to transmit `U=U(t)` that varies over time and a sinusoidal carrier `A_max*sin(omega_0*t)` . There are two ways of modulating this carrier with the original signal.

First way is to modulate the value of the amplitude of the carrier, i.e. to replace the constant value `A_max` with the signal `U(t)` . The signal obtained is of the form `U(t)*sin(omega_0*t)` . This is the so named **amplitude modulation**. After arriving at destination, using a tuned circuit on the angular frequency `omega_0` , the component `sin(omega_0*t)` is removed remaining only the original signal `U(t)` .

Second way is to modulate the value of the angular frequency of the carrier `omega =omega_0+U(t)` with the signal `U(t)` . The signal obtained is of the form `A_max*sin[(omega_0+U(t))*t]` . This is the so called **frequency modulation**. After arriving at destination, using a frequency locked circuit (the angular locking frequency is `omega_0` ) the original info signal `U(t)` is extracted from the modulated signal.

Observation:

Of course all these signal are electric, they generate a variable electric field, that in turns generate a variable magnetic field, and so on, (an electromagnetic wave) that propagate in space and thus cover the distance between the emitter and the receiver (radio).

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