Table 3.1 Units of periods and frequencies Unit Equivalent Unit EquivalentSeconds (s) 1s hertz (Hz) 1 HzMilliseconds (ms) 10–3 s kilohertz (KHz) 103 HzMicroseconds (ms) 10–6 s megahertz (MHz) 106 HzNanoseconds (ns) 10–9 s gigahertz (GHz) 109 HzPicoseconds (ps) 10–12 s terahertz (THz) 1012 Hz
Example 1Express a period of 100 ms in microseconds, and expressthe corresponding frequency in kilohertz.SolutionFrom Table 3.1 we find the equivalent of 1 ms.We makethe following substitutions:100 ms = 100 10-3 s = 100 10-3 10 s = 105 sNow we use the inverse relationship to find thefrequency, changing hertz to kilohertz100 ms = 100 10-3 s = 10-1 sf = 1/10-1 Hz = 10 10-3 KHz = 10-2 KHz
Note: Frequency is the rate of change withrespect to time. Change in a short span of time means high frequency. Change over a long span of time means low frequency.
Note: If a signal does not change at all, its frequency is zero. If a signal changesinstantaneously, its frequency is infinite.
Note:Phase describes the position of the waveform relative to time zero.
Figure 3.5 Relationships between different phases
Example 2A sine wave is offset one-sixth of a cycle with respect totime zero. What is its phase in degrees and radians?SolutionWe know that one complete cycle is 360 degrees.Therefore, 1/6 cycle is (1/6) 360 = 60 degrees = 60 x 2 /360 rad = 1.046 rad