This imaginary line on the carrier waveform is known as the
envelope.
Because complex waveforms such as that shown in Fig. 3-1 are difi cult to draw,
they are often simplii ed by representing the high-frequency carrier wave as many equally
spaced vertical lines whose amplitudes vary in accordance with a modulating signal, as
in Fig. 3-2. This method of representation is used throughout this book.
The signals illustrated in Figs. 3-1 and 3-2 show the variation of the carrier amplitude
with respect to time and are said to be in the time domain. Time-domain signals—
voltage or current variations that occur over time—are displayed on the screen of an
oscilloscope.
Using trigonometric functions, we can express the sine wave carrier with the simple
expression
_c 5 Vc sin 2_fc t
In this expression, _c represents the instantaneous value of the carrier sine wave voltage
at some specii c time in the cycle; Vc represents the peak value of the constant unmodulated
carrier sine wave as measured between zero and the maximum amplitude of either
the positive-going or the negative-going alternations (Fig. 3-1); fc is the frequency of the
carrier sine wave; and t is a particular point in time during the carrier cycle.
A sine wave modulating signal can be expressed with a similar formula
_m 5 Vm sin 2_fmt
where _m 5 instantaneous value of information signal
Vm 5 peak amplitude of information signal
fm 5 frequency of modulating signal
Envelope