- How does the modulated amplitude work?
- Radio transmissions
- Signal reception
- Tune in to the radio and listen to the music
- Worked example
- Solution
The amplitude modulated AM (amplitude modulation) is a signal transmission technique in which an electromagnetic wave sinusoidal carrier frequency f c, responsible for transmitting a message frequency f s << f c varies (i.e., modulates) the amplitude according to the amplitude of the signal.
Both signals travel as one, a total signal (AM signal) that combines both: the carrier wave (carrier signal) and the wave (information signal) that contains the message, as shown in the following figure:
Figure 1. Amplitude modulation. Source: Wikimedia Commons.
It is noted that the information travels contained in the form that surrounds the AM signal, which is called an envelope.
Through this technique, a signal can be transmitted over long distances, hence this type of modulation is widely used by commercial radio and the civil band, although the procedure can be carried out with any type of signal.
To obtain the information, a receiver is needed, in which a process called demodulation is carried out by means of an envelope detector.
The envelope detector is nothing more than a very simple circuit, called a rectifier. The procedure is simple and inexpensive, but power losses always occur in the transmission process.
How does the modulated amplitude work?
To transmit the message together with the carrier signal, it is not enough to simply add the two signals.
It is a non-linear process, in which the transmission in the manner described above is achieved by multiplying the message signal by the carrier signal, both cosine. And to the result of this add the carrier signal.
The mathematical form that results from this procedure is a variable signal in time E (t), whose form is:
Where the amplitude E c is the amplitude of the carrier and m is the modulation index, given by:
Thus: E s = mE c
The amplitude of the message is small compared to the amplitude of the carrier, therefore:
Otherwise the envelope of the AM signal would not have the precise shape of the message to be transmitted. The equation for m can be expressed as a percentage of modulation:
We know that sinusoidal and cosine signals are characterized by having a certain frequency and wavelength.
When a signal is modulated, its frequency distribution (spectrum) is translated, which happens to occupy a certain region around the frequency of the carrier signal f c (which is not altered at all during the modulation process), called width band.
As they are electromagnetic waves, their speed in vacuum is that of light, which is related to wavelength and frequency by:
In this way, the information to be transmitted from, say, a radio station travels very quickly to the receivers.
Radio transmissions
The radio station must transform words and music, all of which are sound signals, into an electrical signal of the same frequency, for example using microphones.
This electrical signal is called the auditory frequency signal FA, because it is in the range of 20 to 20,000 Hz, which is the audible spectrum (the frequencies that humans hear).
Figure 2. Many radio stations broadcast in AM. Source: Pixabay.
This signal must be electronically amplified. In the early days of radio it was made with vacuum tubes, which were later replaced by much more efficient transistors.
The amplified signal is then combined with the radio frequency signal FR by AM modulator circuits, so as to result in a specific frequency for each radio station. This is the carrier frequency f c mentioned above.
The carrier frequencies of AM radio stations are between 530 Hz and 1600 Hz, but stations that use modulated frequency or FM have higher frequency carriers: 88-108 MHz.
The next step is to amplify the combined signal again and send it to the antenna so that it can be emitted as a radio wave. In this way it can spread through space until it reaches the receivers.
Signal reception
A radio receiver has an antenna to pick up the electromagnetic waves coming from the station.
An antenna consists of a conductive material that in turn has free electrons. The electromagnetic field exerts force on these electrons, which immediately vibrate at the same frequency as the waves, producing an electric current.
Another option is that the receiving antenna contains a coil of wire and the electromagnetic field of radio waves induces an electric current in it. In either case, this stream contains the information that comes from all the radio stations that have been captured.
What follows now is that the radio receiver is able to distinguish each radio station, that is, to tune in to the one that is preferred.
Tune in to the radio and listen to the music
Choosing between the various signals is accomplished by a resonant LC circuit or LC oscillator. This is a very simple circuit that contains a variable inductor L and capacitor C placed in series.
To tune the radio station, the values of L and C are adjusted so that the resonant frequency of the circuit coincides with the frequency of the signal to be tuned, which is none other than the carrier frequency of the radio station: f c.
Once the station is tuned in, the demodulator circuit mentioned at the beginning comes into action. He is the one in charge of deciphering, so to speak, the message broadcast by the radio station. It does this by separating the carrier signal and the message signal, using a diode, and an RC circuit called a low-pass filter.
Figure 3. On the left LC oscillator circuit. On the right a demodulator circuit. Source: F. Zapata.
The already separated signal goes through an amplification process again and from there it goes to the speakers or headphones so that we can hear it.
The process is outlined here, because there are actually more stages and it is much more complex. But it gives us a good idea of how amplitude modulation happens and how it reaches the receiver's ears.
Worked example
A carrier wave has amplitude E c = 2 V (RMS) and frequency f c = 1.5 MHz. It is modulated by a signal of frequency fs = 500 Hz and amplitude E s = 1 V (RMS). What is the equation of the AM signal?
Solution
Substitute the appropriate values into the equation for the modulated signal:
However, it is important to note that the equation includes the peak amplitudes, which in this case are voltages. Therefore it is necessary to pass the RMS voltages to peak multiplying by √2:
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