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Amplitude Modulation in detail
In this article, I will explain Amplitude Modulation in detail. In this I have explained the process of amplitude modulation along with the amplitude modulator and mathematical expression with necessary diagram in detail.

Each modulation method shifts the baseband, the actual information in a higher frequency range defined. Each baseband to be transmitted is modulated on a separate carrier. Only then later recovery and separation into the individual information is possible. With amplitude modulation, AM can be many different information sequentially in the same transmission medium to transmit simultaneously. The sequence of the items of information on the frequency axis corresponding to a frequency division multiplexing method. In radio engineering the atmosphere is the ether, in the nearEarth region, the transmission medium. The transmission can be wired as well be in the pipeline network. The receiver filters the desired transmit signal and recovers the actual information returned by a demodulation. This chapter describes important aspects of normal AM.
Amplitude Modulation Amplitude modulation from a mathematical perspective The AM by selective transistor amplifier
In the AM modulation signal, a low frequency information signal, the amplitude of the high frequency carrier signal affected. The AM has long been the most important signal processing method to spread a lot of different information simultaneously on the radio. The method is easy to handle circuitry in the transmitter and receiver. The carrier signal of the transmitter is a sinusoidal highfrequency vibration. It contains no information, but is a necessary auxiliary signal. The information here speech and music, changed from the three possible carrier parameters, only the amplitude. The frequency and phase of the carrier are not affected.
The modulator Multiplying equation of the function of the support in the peak value u 0 with a greater or lesser factor, changes only the amplitude of the carrier. If the factor is not constant, but is itself a sinusoidal function at a lower frequency, the carrier frequency varies in the rhythm information of the lower frequency. Mathematically, the modulation of the carrier multiplication function with the information function. The module to which this computing operation is performed, is called modulator and is sometimes also referred to as English mixer as a mixer. There are ready integrated circuits, socalled fullor fourquadrant multiplier, at the two inputs of the support and information signal is applied. The output shows as a result of the modulation. The two signals are additively superimposed before the traditional modulation. This can be done in a passive resistance matrix. Active resistors have a linear characteristic, the modulation can not occur. the beat signal can be completely separated, therefore, appropriate filters in the two original signals.
After the addition, the sum signal is supplied to a fourpole network with a nonlinear characteristic curve. Very suitable is a diode array, such as the baseemitter input of a transistor amplifier. Where the modulation takes place, with more new frequencies arise that were not present in the input signal.
The current flow of a pn junction in a semiconductor diode is not linear to an exponential function. The following figure shows the good agreement of a diode characteristic curve (blue) with the parabolic function (green). The adjacent mathematical relationships to describe the diode current waveform in the passband show that the exponential of the higher powers of the yellow marked quadratic term has the greatest impact.
Controls the signal overlay information carrier and the baseemitter voltage of a transistor stage input of the nonlinear region, so the control circuit changes according to the number of potential. The output signal is distorted.
The potentiation corresponds to a multiple multiplication, recognizable by the example y 2 = y · y, where y is the time function of the overlay. During exponentiation of two superimposed sinusoidal or cosinusoidal oscillations at frequencies f 1 and f 2, give new oscillations at frequencies f m = ± n · f 1 · f 2. Therein, m and n are integers and their sum is equal to the exponent.
Amplitude modulation from a mathematical perspective The modulation signal is held at a curved characteristic here. In the exponential representation of the diode characteristic curve shown above, the quadratic term has a significant influence on the total signal. When the amplitude of the AM carrier signal is to be multiplied by the instantaneous values ??of the lower frequency signal. The operating point of the modulator is placed so that no negative amplitude values ??occur. This operating point corresponds to an additional DC voltage around which the modulation takes place. For optimal modulation, the carrier voltage has to be greater than the signal voltage. The operating point is the information or modulation signal S u (t) and the carrier signal u T (t) is multiplied. For simplicity, it is agreed that the signals are present as cosine function with the same phase. Mathematical relationships between trigonometric functions that can be useful in the calculation are the section Mathematics  trigonometric functions explained.
In purely formal terms, the following equations can be set up, and it always comes to the multiplication between the carrier and the information signal: (Carrier + DC) = carrier signal · · · + DC signal and signal (signal + DC) = carrier signal · · · + DC carrier carrier The second formula approach is executed with DC = 1 in more detail below.
After the modulation, the modulation signal is filtered with a tuned resonant circuit at the carrier frequency of sufficient bandwidth. The frequency spectrum of the AM signal then contains only the two symmetrically arranged to the carrier signal sideband signals. The amplitude of the modulation signal is distributed to 50% on the two side signals.

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