Modulated amplitude

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amplitude modulation (AM) or amplitude modulation is a technique used in signal processing and electronic communication, most commonly for the transmission of information through a transversal television wave. Amplitude modulation (AM) works by varying the amplitude of the transmitted signal in relation to the information being sent. Contrast this with frequency modulation, in which the frequency is varied, and phase modulation, in which the phase is varied. In the mid-1870s, a form of amplitude modulation, initially called "ripple currents," was the first method of successfully sending audio over telephone lines in acceptable quality.

A signal (up) can be transported on an AM or FM wave.

Technological applications of AM

AM Radio

Signal Processing

AM has also been used in signal processing, particularly in the field of music production, to generate various sound effects. Probably the most popular of these is the tremolo (from English: tremolo), in which a single low-frequency carrier wave (generated by an LFO) and sustained usually at a fixed frequency less than 20 Hz, it is modulated by an input signal. This sound effect can be found in guitar amps, stompboxes, synthesizers, and plug-ins for digital audio workstations. Some examples in music are the song Bang, Bang (My Baby Shot Me Down) by Nancy Sinatra, Born on the Bayou by Creedence Clearwater Revival, or How Soon Is Now? by The Smiths.

Other sound effect units that also use amplitude modulation are:

The chopper (from English): cutteror slicer (from English): slicer), which usually forms occupying one or more tremolos, using square wave forms or pulse at different depth rates (usually extreme) and harmoniously synchronized repetition, which allows cut or slice the input signal to certain regular intervals and give it a more rhythmic feeling. An example of its use is found in the introduction of the song Boulevard of Broken Dreams Green Day.
The ring modulator (from English): Ring modulator) which, in its analogue origin, the circuit contains diodes in the form of a ring that participates in the modulation process. Its operation is very similar to that of the classic tremolo. However, unlike this, the frequency of the bearer wave is fast enough to be perceived by the human ear (i.e. greater than 20 Hz), so the resulting effect is the mixture of the two signals sounding to the unison, consisting of the sums and differences of the frequencies that make them, and that they may (or may not) be harmoniously linked. Given the non-linear nature of this processing, results are very common inarmonicswith a qualitatively described sound aggressive, metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metallic metal metal metallic metallic metallic metallic metal metal metal metal metal metal metal metallic metallic metallic metal metal metallic metallic metallic metal metal metal metal metal metal metal or artificial. This effect can be found in synthesizers and some effect pedals, usually to create bell-like bells or other sound sources that possess a spectrum of frequencies naturally. Inarmonic; so also, to generate various special effects or to modify the ringing of the voice, as can be exemplified with the daleks in Dr. Who.

It is worth mentioning that tremolo (amplitude modulated) should not be confused with vibrato (frequency modulated).

AM demodulation

There are two possibilities for the demodulation of a signal $f(t)$ modulated in AM. The first, the simplest, is only possible in case the following condition is fulfilled:

{big |}f_{n}(t){big |}leq m

In this case, the envelope of the modulated signal, this is $1+mcdot f_{n}(t)$ is always positive and to recover the modulator signal is sufficient with a receiver that captures such envelope. This is achieved with a simple grinding circuit with capacitive load. That's how the galena radio was working.

The other option for the demodulation of the modulated signal in AM is to use the same type of demodulation used in the other linear modulations. This is the coherent demodulator. To do so, it is necessary to know the frequency of the carrier $w_{p}$ and, sometimes, also the phase, which requires the use of a PLL (Phase Lock). In this other case, it is not necessary that the modulation index be less than the unit, or what is the same, it is not necessary that the envelope [1 + m·x(t)] be always positive.

The coherent demodulator uses the following mathematical property of the cosine function:

{displaystyle cos ^{2}(phi)={frac {1}{2}}+{frac {cos(2phi)}{2}}}

to multiply the function $S(t)$ by the carrier:

{displaystyle S_{D}(t)=S(t)cos(w_{c})={frac {1+mcdot f_{n}(t)}{2}}+{frac {cos(2w_{c})}{2}}}

From this, with a low step filter and a continuous suppressor, you get the signal $f(t)$ .

Power of the modulated signal

The maximum width of each lateral band is given by the expression: $m={frac {V_{m}}{V_{p}}}$ , being ${displaystyle V_{m}}$ the effective tension of the modulator signal and ${displaystyle V_{p}}$ the effective tension of the carrier. As the power is proportional to the square of the tension, the power of the modulated signal will result the sum of the power of the carrier signal plus the power of both lateral bands:

Pequiv V_{p}^{2}+left({frac {mV_{p}}{2}}right)^{2}+left({frac {mV_{p}}{2}}right)^{2}

Pequiv V_{p}^{2}+{frac {m^{2}V_{p}^{2}}{4}}+{frac {m^{2}V_{p}^{2}}{4}}

For equality to be possible we must take into account the powers instead of the voltages:

P=P_{p}+{frac {m^{2}}{4}}P_{p}+{frac {m^{2}}{4}}P_{p}

P=P_{p}+{frac {m^{2}}{2}}P_{p}

P=left(1+{frac {m^{2}}{2}}right)P_{p}

In case the modulation is 100%, then $m=1$ and therefore the power of the modulated signal will be:

P=left(1+{frac {1}{2}}right)P_{p}

P={frac {3}{2}}P_{p}

Or what is the same:

P_{p}={frac {2}{3}}P

From the latter it follows that the carrier wave will consume two thirds of the total power, leaving one third for both sidebands.

Modulation index

The AM modulation index is a measure of the variation of amplitude that surrounds an unmodulated carrier. As with other modulation indices, in AM this amount (also called "modulation depth") indicates the variation introduced by modulation regarding the level of the original signal. In AM, it refers to variations in the width of the carrier and is defined as: ${displaystyle h={frac {mathrm {valor m{acute {a}}ximo de } m(t)}{A}}={frac {M}{A}}}$ where $M$ and $A$ are the breadth of the message and the width of the carrier, respectively.

So yes $h=0,5$ , the width of the carrier varies by 50% above (and below) its original level; for $h=1,0$ The signal varies by 100%. To avoid distortion, the modulation depth should not exceed 100%. Transmission systems will typically incorporate a limiting circuit to ensure compliance with this requirement. However, AM demodulators can be designed to detect the phase investment that occurs when modulation exceeds 100%, and automatically corrects this defect. Below are some images in which you can see the modular results with different modulation indices.

Modulation Index.
In the diagram, the unmodulated signal has a width of 1.

AM Stereo

Amplitude Modulated Stereo modulates the amplitude in the stereo.

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