Amplitude modulation and demodulation:

With sinusoidal modulation, the positive and negative peak modulations will be the same, but, in general, this is not the case. When the degree of modulation is unity, the wave is said to be completely modulated.

It will be note that the degree of modulation can never exceed unity on the negative peaks, since the envelope amplitude can never be less than zero. The modulation can, however, exceed unity on the positive peaks, a condition referred to as overmodulation.

Analysis of Modulation Wave. In the case of simple sinusoidal modulation, the equation of the modulation wave can be written as

℮ = E₀(1+ m sin 2πf_st) sin 2πft

Where ℮ = instantaneous amplitude of the wave

E₀ = average amplitude of the wave

m = degree of modulation

f₀ = modulating (or carrier ) frequency.

℮ = E₀ sin 2πft + cos2π(f- f_s)t - cos2π(f+ f_s)t

The first component of the modulation wave is termed the carrier, and is the same irrespective of the degree of modulation or the modulation frequency. The second and the third components are termed side-band frequency, and are the part of the modulated wave that represents the intelligence.

In the general case of nonsinusoidal, the modulation envelope can be expressed as either a Fourier series or a Fourier integral, according to whether the modulation envelope is a periodic or nonpeiodic function of time. In either case, there is a carrier for each frequency components in modulation envelope. Each side-band component has an amplitude that is one-half the amplitude of the corresponding frequency contained in the equation of the modulation envelope, and the frequencies of the pair are greater and less than the carrier frequency by the corresponding modulation frequency component.

The power of a modulated wave is divided between the carrier and the side-band components. The carrier power remains constant, whereas the side-band power varies in accordance with the character and degree of modulation. In the extreme case of complete sinusoidal modulation, the side-band power varies in accordance with the character and degree of modulation. In the extreme case of complete sinusoidal modulation, the side-band power is 50 percent of the carrier power, and in other cases is usually less.

Speech of quality corresponding to that commonly existing on long-distance telephone circuits can be obtained by reproducing modulation frequencies from 250 to 2,750 cycles. Speech and music having a quality corresponding to that realized under typical broadcast receiving conditions can be obtained by reproducing modulation frequencies from 100 to 4,500 cycles, while practically perfect reproduction of audible sounds requires a frequency band of approximately 40 to 15,000 cycles. In picture transmission (including television), the maximum modulation frequency required to realize full definition is approximately

Maximum frequency that must be transmitted = n²N

Where w and h represent the ratio of width to height, n represents the number of lines, and N equals the number of pictures transmitted per second.

Controlled-carrier systems of Modulation. In controlled-carrier arrangements, the amplitude of the carrier wave is automatically varied in accordance with the degree of modulation as averaged over a short interval of time. When the modulation is small or zero, the carrier is made small, but as the modulating voltage is increased to a large value, then carrier is increased accordingly.

The use of a controlled-carrier system reduces the average power of the modulated wave, and hence the average power loss in the modulation tubes. Also, when such a wave is applied to a conventional linear amplifier, it is possible to obtain approximately twice as much peak power in typical case with the same average plate dissipation as would be obtained with an ordinary modulated wave. Controlled carrier has the disadvantage, however, that there is distortion when the modulating voltage suddenly increases in amplitude, since the carrier amplitude cannot be changed instantly. Furthermore, it is necessary that the receiver used in the reception of a controlled carrier wave be provided with automatic-volume-control circuits having time constants suitably related to those the transmitter. Otherwise violent distortion will occur when the carrier fluctuates in amplitude.

DETECTION: Diode Detection of Amplitude-modulation Waves. Detection, which is also sometimes referred to as demodulation, is the process of recovering from a wave the intelligence that was originally modulated upon it. In the cases of amplitude modulation, detection accordingly means deriving from the modulated wave a voltage that varies in accordance with the modulation envelope. In all practical cases, this is accomplished by rectification of the modulated wave.

Efficiency of Rectification. The ratio of d-c voltage developed across the output of a diode to the peak amplitude of the applied carrier is termed the efficiency of rectification of the carrier.