Modulation

A sinusoidal waveform does not carry any information on its own. In order to transmitany information, in our case voice, we need to make one parameter of a sinusoiddependent on this information.

In electronics, the information must of course be converted into an electrical signal, avoltage or a current, first. For example, a microphone converts sound into a voltage,which we first amplify and then use as information signal, vm(t). This signal is again atime varying signal, which can be represented as a linear combination of sinusoids.The frequency band of this signal, however, is not suitable for transmission in air, as itis. This frequency band is rather low for transmission and it is calledbase-band . Theinformation signal occupying this band is referred to asbase-band signal. Convertingthe information-carrying signal to a form suitable for (electromagnetic) transmissionis calledmodulation.

There are three parameters that we can play with in a sinusoid: amplitude, frequencyand phase. We must mount the information signal vm(t) on a sinusoid of appropriatehigh frequency, so that it can becarried on air at that radio frequency. We call thisoperation, modulation. In TRC-10 we useamplitude modulation (AM), which meansthat we make the amplitude of a sinusoid dependent on vm(t). Note that thefrequencies of sinusoids that are present in a voice signal is within few kHz, while wewish to transmit this voice signal at 30 MHz. Let us assume that vm(t) is a simple signal, Vmcos(ωmt). In order to modulate the amplitude of acarrier signal, Vccos(ωct),we construct the signal,

vm(t) is called themodulating signal. In AM, the maximum peak variation of |vm(t)| must always be less than Vc, otherwise it cannot bedemodulated by simpleenvelopedetector circuits which can be used with this modulation scheme, and vm(t) cannot berecovered. Vc[1 + (Vm/Vc)cos(ωmt)] part in AM signal is called theenvelope. An AMsignal is depicted in Figure(b).



Thedepth of modulationis determined by the maximum value of the normalizedmodulation signal

AM signal is said to have100% modulation, or modulation index is one. Similarly, if this maximum is, for example, 0.5, then the modulation index is 0.5 and the AMsignal has 50% modulation.

A special case of AM isdouble side-band suppressed carrier AM (DSBSC AM ). In this scheme a different demodulation must be used. A DSBSC AM waveform isshown in Figure(c).

Other parameters that can be modulated in a sinusoid are frequency and phase. Inanalog communication systems different forms of amplitude modulation andfrequency modulation (FM) are used. In FM, we construct the following signal.

Here we change the frequency of the carrier signal around the carrier frequency,ωc,according to the variation of modulating (information) signal. An FM modulatedsignal is shown in Figure(d).

Long wave and middle wave radio broadcasting is done by AM, and radiobroadcasting in 88-108 MHz band is done by FM. Analog terrestrial televisionbroadcasting employs a version of AM (calledvestigial side-band AM ) for image andFM for sound.