The term phase describes the position of the waveform relative to time zero. If we think of the wave as something that can be shifted backward or forward along the time axis, phase describes the amount of that shift. It indicates the status of the first cycle.
Phase is measured in degrees or radians (360 degrees is 2n radians). A phase shift of 360 degrees corresponds to a shift of a complete period; a phase shift of 180 degrees corresponds to a shift of half a period; and a phase shift of 90 degrees corresponds to a shift of a quarter of a period (see Figure 3.3-2).
A visual comparison of amplitude, frequency, and phase provides a reference useful for understanding their functions. Changes in all three attributes can be introduced into a signal and controlled electronically. Such control provides the basis for all telecommunications and will be discussed in Chapter 4 (see Figure 3.3-3, Figure 3.3-4, and Figure 3.3-5).
c. ISO degree phase change d_ 270 degree phase change
Fig. 3.3-5 Phase change c. ISO degree phase change d_ 270 degree phase change
Fig. 3.3-5 Phase change
Frequency, therefore, though described in cycles per second (Hz), is a general measurement of the rate of change of a signal with respect to time.
Since frequency is rate of change of a signal with respect to time, therefore, if the value of a signal changes over a very short span of time, its frequency is high; if it changes over a long span of time, its frequency is low.
Two Extremes What if a signal does not change at all? What if it maintains a constant voltage level the entire time it is active? In such a case, its frequency is zero. Conceptually, this idea is a simple one. If a signal does not change at all, it never completes a cycle, so its frequency is 0 Hz. But what if a signal changes instantaneously? What if it jumps from one level to another in no time? Then its frequency is infinite. In other words, when a signal changes instantaneously, its period is zero; since frequency is the inverse of period, then in this case, the frequency is l/0, or infinity.
Remember that if a signal does not change at all, its frequency is zero; if a signal changes instantaneously, its frequency is infinity.
Time versus Frequency Domain A sine wave is comprehensively defined by its amplitude, frequency, and phase. We have been showing a sine wave using what is called a time-domain plot. The time-domain plot shows changes in signal amplitude with respect to time (it is an amplitude versus time plot). Phase and frequency are not explicitly measured on a time-domain plot.
To show the relationship between the three characteristics (amplitude, frequency, and phase), we can use what is called a frequency-domain plot. There are two types of frequency-domain plots: maximum amplitude versus frequency and phase versus frequency. The first type of frequency-domain plot (maximum amplitude versus frequency) is more common in data communications than the second (phase versus frequency). Figure 3.3-6 compares the time domain (instantaneous amplitude with respect to time) and the frequency domain (maximum amplitude with respect to frequency).
Figure 3.3-7 gives examples of both the time-domain and frequency-domain plots of three signals with varying frequencies and amplitudes. Compare the models within each pair to see which sort of information each is best suited to convey.
Remember that a low-frequency signal in the frequency domain corresponds to a signal with a long period in the time domain and vice versa. A signal that changes rapidly in the time domain corresponds to high frequencies in the frequency domain.
a. Time domain b. Frequency domain Fig. 3.3-6 Time and frequency domains
Figure 3.3-7 gives examples of both the time-domain and frequency-domain plots of three signals with varying frequencies and amplitudes. Compare the models within each pair to see which sort of information each is best suited to convey.
Remember that a low-frequency signal in the frequency domain corresponds to a signal with a long period in the time domain and vice versa. A signal that changes rapidly in the time domain corresponds to high frequencies in the frequency domain.
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