What modulation AM?

The general meaning of the verb “modulate” is “change, regular, to vary” and that captures the essence of modulation even in the specialized field of wireless communication. Modular is simply a signal change it intentionally, but obviously this change is done in a very specific way because the goal of the modulation is the transfer of data.

More specifically, we need a language compatible with high-frequency sinusoidal signals, since these signals constitute the only practical means for “to carry” the information in a typical RF system.

This high-frequency sine wave that is used to carry information carrier is called. It is a useful name because it reminds us that the purpose of an RF system is not to generate and transmit a sine wave high frequency. Rather, the aim is to transfer information (Low frequency), and the carrier is simply the means that we have to use this information to move from an RF transmitter to an RF receiver.

Modulation schemes

In verbal communication, The human body generates sound waves and change or modulated to produce a wide variety of vowels and consonants. Intelligent use of these vowels and consonants is reflected in the transfer of information by the speaker to the listener. The system by which the sound waves are modulated is called a language.

In RF communication, the situation is very similar. A device modulates electric waves according to a predefined system called modulation scheme (or modulation technique). Just as there are many human languages, There are many ways in which a vector can be modulated.

Sophisticated modulation schemes help modern RF systems to achieve greater reach and better immunity to interference.

It is possible that certain human languages are particularly effective in transmitting certain kinds of information; for example from the ancient world, perhaps the greek was better for philosophy and Latin was best to codify laws. There is no doubt, however, that reliable communication is possible with any language properly developed, provided that both the speaker and listener know it. The same goes for RF systems. Each modulation scheme has its advantages and disadvantages, but all can provide excellent wireless communication if the basic requirement is satisfied, that is, the receiver must be able to understand what he is saying the transmitter.

width, frequency, phase

A basic sine wave is a simple thing. If we ignore the DC offset, It can be fully characterized with only two parameters: amplitude and frequency. We also stage, that comes into play when we consider the initial state of the sinusoid, or when changes in the behavior of the waves allow us to compare a portion of the sinusoid with an earlier portion. The stage is also relevant when comparing two sinusoids; this aspect of the sinusoidal phase has become very important due to the widespread use of quadrature signals (O “IQ”) nei sistemi RF.

Modulation is a change, and we can only change what is already there. The sine waves have amplitude, frequency and phase, so it should come as no surprise that the modulation schemes are classified as amplitude modulation, frequency modulation or phase modulation. (In reality, it is possible to connect these categories by combining the amplitude modulation with the frequency or phase modulation.) Within each category there are two subcategories: Analog and digital modulation modulation.

Amplitude modulation (AM)

The analog AM consists in multiplying a sinusoidal carrier that varies continuously and by an offset version of a variable information in continuous signal (ie baseband). With “offset version” I mean that the amplitude of the signal in base band is always greater than or equal to zero.

Suppose we have a carrier 10 MHz and a waveform in the baseband by 1 MHz:

If we multiply these two signals, we obtain the following waveform (errata):

You can clearly see the relationship between the baseband signal (rosso) and the amplitude of the carrier (blu).

But we have a problem: if only observe the amplitude of the carrier, how can you determine if the value of the baseband is positive or negative? It is not possible, and consequently, the amplitude demodulation will not extract the baseband signal from the modulated carrier.

The solution is to move the base band signal so that from various 0 a 2 instead of -1 a 1:

If we multiply the baseband signal shifted, we have the following:

Now the amplitude of the carrier can be mapped directly to the base band signal behavior.

The simplest form of digital AM applies the same mathematical relationship to a baseband signal whose amplitude is 0 O 1. The result is referred to as “on-off keying” (ALSO): when the information signal is logic zero, the amplitude is zero (= “off”); when the information signal is a logic, the carrier is at full amplitude (= “on”).

In mathematics

The mathematical relationship for the amplitude modulation is simple and intuitive: It multiplies the carrier by the baseband signal. The frequency of the carrier itself is not altered, but the amplitude varies continuously according to the value of the base band. (However, as we shall see, the amplitude variations introduce new frequency characteristics.) The only subtle detail here is the need to move the base-band signal; we discussed just above. If we have a waveform baseband ranging between -1 e +1, the mathematical relationship can be expressed as follows:

XAM is where the waveform amplitude modulated, xC is the carrier and xbb is the baseband signal. We can make a step further if we consider the vector as an infinite sine wave, at a constant amplitude, a fixed frequency. If we assume that the amplitude of the carrier is 1, we can replace sin with xC (ωCt).

So far, so good, but there is a problem with this report: there is no intensity modulation control. In other words, the report change baseband-transmission-carrier-amplitude is fixed For example, we can not design the system so that a small change in the value of the baseband create a big change in amplitude of the carrier. To overcome this limitation, introduce m, known as modulation index.

Now, ranging m we can control the intensity of the signal of the baseband amplitude of the carrier. Note, however, that m It is multiplied by the original baseband signal, not for the baseband moved. Then, if xbb extends from -1 a +1, any value of m greater than 1 will cause (1 + mxBB) to extend in the negative part of the axis y, but that's exactly what we were trying to avoid moving it up in the first place. Then, remember, if a modulation index is used, the signal must be shifted on the basis of the maximum amplitude of mxBB, not xbb.

The time domain

We examined the waveforms in the time domain AM on the previous page. Here is the ultimate storyline (baseband in rosso, AM waveform in blue):

Now examine the index modulation effect. Here is a similar display, but this time I moved the baseband signal by adding 3 rather than 1 (the original range is yet to be -1 a +1).

Now we will incorporate a modulation index. The following chart is with m = 3.

The amplitude of the carrier is now “more sensitive” to the variable value of the signal in base band. The baseband moved does not enter the negative side of the y why I chose the DC offset by index modulation.

One might ask something: how can we choose the correct DC offset without knowing the exact amplitude characteristics of the baseband signal? In other words, how do we ensure that the negative swing of the waveform in the baseband extends exactly zero? Answer: it is not necessary. The previous two graphics waveforms AM equally valid; the baseband signal is faithfully transferred in both cases. Any DC offset that remains after the demodulation is easily removed by a series capacitor.

The frequency domain

The development of radio frequency analysis makes extensive use of the frequency domain. We can inspect and evaluate a signal modulated in real life by measuring it with a spectrum analyzer, but this means that we must know how it should look the spectrum.

We begin with the representation of the frequency domain of a carrier signal:

This is exactly what we expect for the carrier unmodulated: a single peak at 10 Mhz. We observe now the spectrum of a signal created amplitude modulating the carrier with a sine wave from 1 MHz at constant frequency.

Here you see the standard features of a waveform amplitude modulated: the baseband signal has been shifted according to the frequency of the carrier. You could also think of this as “to add” the baseband frequencies to the carrier signal, which it is effectively what we are doing when we use the amplitude modulation – the carrier frequency remains, as you can see in the waveforms in the time domain, but the amplitude variations constitute a new frequency content that corresponds to the spectral characteristics of the baseband signal.

If we look more closely the modulated spectrum, we can see that two new peaks 1 MHz (ie the frequency of the baseband) above and 1 MHz below the carrier frequency:

(In case you were wondering, the asymmetry is an artifact of the calculation process: These graphs were generated using real data, with limited resolution. An idealized spectrum would be symmetrical.)

negative frequencies

To sum up, then, the amplitude modulation translates the spectrum in base band in a frequency band centered around the carrier frequency. There is something that we have to explain, But: because there are two peaks, one at a carrier frequency over the frequency in the base band and another at the carrier frequency minus the frequency baseband? The answer becomes clear if we simply remember that a Fourier spectrum is symmetrical with respect to the y axis; although often we visualize only positive frequencies, the negative part of the x-axis contains the corresponding negative frequencies. These negative frequencies are easily ignored when we deal with the original spectrum, but it is essential to include the negative frequencies when we move the spectrum.

The following diagram should clarify this situation.

As you can see, the spectrum in base band and the carrier spectrum are symmetrical with respect to the y axis. For the baseband signal, this translates into a spectrum which extends in a continuous manner by the positive portion of the x-axis to the negative part; for the carrier, we simply have two peaks, one + ωC e uno a -ωC. And the AM spectrum is, Once again, symmetrical: the spectrum of the baseband translated appears in the positive portion and the negative part of the axis x.

And here's another thing to keep in mind: the modulation increases the bandwidth by a factor 2. We measure the bandwidth using only positive frequencies, then the baseband bandwidth is simply BωBB (see diagram below). But after translating the entire spectrum (positive and negative frequencies), all original frequencies become positive, in such a way that the bandwidth modulated both 2BωBB.