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Characteristic Parameters of Sinusoidal Signals

The instantaneous value u(t) of a sinusoidal alternating voltage is given by the equation.

characteristic-parameters-sinusoidal-signals.jpg

The diagram below shows the shape of such a signal.

characteristic-parameters-sinusoidal-signals1.jpg

u0 is termed the voltage's peak value; it represents the largest positive or negative voltage and is also called signal amplitude. The variable w is the angular frequency determined from the frequency of oscillation f using the equation.

characteristic-parameters-sinusoidal-signals2.jpg

The product of the angular frequency and time w·t gives the instantaneous value of the phase angle.

The time T taken to complete one oscillation is termed the period of oscillation. Its inverse is equal to the frequency f, i.e. the number of oscillations per second:

characteristic-parameters-sinusoidal-signals3.jpg

The unit of frequency is named Hertz (abbreviated to Hz ) after the German physicist. 1 Hz corresponds to one oscillation per second. The period in the example above is T = 0.02 s, i.e. the frequency is f = 1/T = 50 Hz. This is the figure for the mains frequency usually used in Europe. The mains frequency in the US and most other countries in the Americas is 60 Hz.

If, unlike the example above, the alternating voltage does not start at the coordinate origins but is instead displaced along the time axis, this displacement can be represented by adding a phase angle j to the argument of the sine function. The instantaneous voltage value is then determined by the equation.

characteristic-parameters-sinusoidal-signals4.jpg

All these equations apply in the same way to sinusoidal alternating current.

The following interactive animation can be used to visualise sinusoidal signals of different amplitudes, frequencies and phase angles. Use the slider controls to vary these characteristic parameters and observe the resulting display.

 

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