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Amplitude and Frequency

<^< Waveforms and Signals | Course Index | Examples: Amplitude and Frequency >^>

The amplitude (or peak value) of a waveform is a measure of the extent of its voltage or current excursion from the resting value (usually zero). The peak-to-peak value for a wave which is symmetrical about its resting value is twice its peak value.

The frequency of a repetitive waveform is the number of cycles of the waveform which occur in unit time. Frequency is expressed in Hertz (Hz). A frequency of 1Hz is equivalent to one cycle per second. Hence, if a voltage has a frequency of 400Hz, 400 cycles will occur in every second.

The periodic time of a waveform is the time taken for one complete cycle of the wave. The relationship between periodic time and frequency is thus:

t = 1/f or f = 1/t

where t is the periodic time, in seconds and f is the frequency, in Hz.

The equation for the sinusoidal voltage shown at a time, t, is:

v = V_max sin(ωt)

where v is the instantaneous voltage, V_max is the amplitude (or peak) voltage, and ω is the angular speed of the wave (in radians per second).

Since one complete rotation of the wave (i.e. 360º) is equivalent to 2π radians we can deduce that:

ω = 2πf

where f is the frequency of the wave in Hertz.

The images below allows you to see the relationship between waveform frequency, amplitude and the mathematical representation of the waveform.

v = 1sin(2πx100t) v = 1sin(2πx1000t) v = 1sin(2πx500t) v = 0.1sin(2πx500t)

v = 1sin(2πx100t) v = 1sin(2πx1000t) v = 1sin(2πx500t) v = 0.1sin(2πx500t)

<^< Waveforms and Signals | Course index | Examples: Amplitude and Frequency >^>