#  Modulation of a signal in Amplitude

The amplitude modulation (A.M.) is a used technique to transmit LF signals (as the sound or the images) using another signal of greater frequency by physical means as the air or a cable.
In the case of the sound, when we spoke, we emitted a series of frequencies, that united gives rise to the sound in himself, but that could be disturbed in a series of components of frequencies. This is what phantom is called, and for it we are going to make one first activity in the classroom.
Activity:  Using the mobile, to lower some APP that treats the frequency spectrum that we perceived around to ours. For example, Spectroid is one of them. Very good other with more capacity of phantom is SPL spectrum analyzer Search some other if it is better. Once unloaded, to analyze the sound phantom. To prove how vari¡n the low frequencies and high based on some sounds. If it is possible, to lower some APP that arrives until the audible limit.

## Bandwidth.

The bandwidth of a signal, that we denominated B (x) is the representation of the frequencies obtained by the transformed one of Fourier.  Due to the properties of symmetry of the transformed one of Fourier, this bandwidth has an equal symmetry in the axis and, being the same for the negative frequencies We are going to have three signals that take part in this process, which they are:
• Moduladora signal, that we are going it to indicate as x (t). It is the signal that contains the information that interests to us to transmit, as an image or sound signal. We are going to assign to this signal a bandwidth B (x) that if we showed it in the domain of the frequencies, we obtain the signal that imagines in the image superior
•   Carrying signal. c (t). It is a sinusoidal signal of greater frequency coming from an oscillating intern, who has three parameters to emphasize, that they are, the amplitude of the signal, the frequency of the same and the phase angle (in which moment the signal takes place€). Of them, the carrier frequency, is the parameter that is going to us to interest but in this study and must be much greater to the bandwidth of the moduladora signal, that is f (c) >> B (x)
• Modulated signal. We denominated it s (t) and is the resulting signal of the modulation process. This signal, due to the modulation, has a certain bandwidth around the carrier frequency, as we see ahead but

We show of schematic form, these three signals

###  The result of the previous process we see it in the following image, where we see that the moduladora signal has modified the carrying signal in amplitude (the signal of down), giving the result of modulated signal (signal inferior) ## Commercial data on A.M.

In the commercial A.M., we mainly have of a signal of voice or musical comedy of low quality, with a 4 bandwidth of about kHz. The 526.5 the carrier frequencies are understood enters kHz the 1,606, 5 kHz.

### Because to use a signal of greater frequency when the signal can be emitted that interests to us?

To use modulation A.M. using signals of much greater frequency to the moduladora, has among others, the following advantages

1  To adapt the signals to propagation means.

For an effective electromagnetic radiation, we have a rule, that with certain shades comes near to consider the size of an antenna. This rule says that for a propagation of the signals electromagnetic good, the length of the antenna must be one tenth part the wavelength of the signal. If we consider the law that governs this aspect, that says to us:
The speed of the light is equal to the wavelength between the period: The wavelength for a signal of sound, applied directly to the antenna, would be of the order of: Applied the tenth part, we have about 7500 meters. It is understood that this, clearly is not viable
Nevertheless, for a signal already modulated, if the frequency is of the order of 1 Mhz, we have antenna is going it to have a dimension of about 30 meters. This already is another thing.
In the following image, we have a photography of this type of antennas of the Center National Radio transmitter of Spain in Majadahonda One more first higher antenna is seen, of 264 meters, that it emits to 585 KHZ, corresponding to RNE1, and with a power of emission of 600 KW.
2 lower antenna (130 meters) corresponds to RNE5, emitting in 657 KHz with 50 KW of power

2 Multiplexar several signals to transmit by the same means.
If we must send by the same antenna three signals of LF, we have the problem that the bandwidths are overlapped. This is solved when using carriers of different value and moving the bandwidth.
In the following image we have three signals A.M., with different carrier. Once in the receiver, it is possible to be discriminated the different signals by means of the use from step filters band centered in each one of the frequencies of the carrying signal.
This, represented in the domain of the frequencies, does not give a graph as: ## How we obtain the signals in our receiver?

The simplest system is uniting the functions of the band-pass filter next to the action of a system of load of a condenser. This is the principle of the receiver of Galena, where a band-pass filter, lets pass the carrier that interests to us, that it passes through a filter (a germanium diode, with threshold voltage of or, 2 volts) and a circuit of load of a Condenser. We will see the part where we already received the modulated signal (selected with a band-pass filter). The diode is in charge to pass only the positive half-cycles, signals of equal frequency but that they vary in the time (blue waves). Condenser C is loaded to the maximum value of the tips and unloading in the voltage drops of the same signal (line orange). It is necessary to consider that the value of R and C must be like: Where the f (c) is the frequency of the carrying signal.

If we completed the circuit, we have something as Activity.

Of voluntary way, but with extra note for the subject, to realise one radio soft A.M. of type, using some tutorial of Internet and with the precaution to use diode of germanium and some earpiece of high impedance. This is because the energy that we are going to catch by the antenna is very low and components are needed that do not prevent the current passage (case of the diode) and which they require loss intensity of operation (auricular of high impedance).

Bibliography. Notes of the Oberta University.   To see document in denominated DRIVE modulations A.M. and FM (Oberta University)