Sine waves quantities

Properties of a Sine Wave

Key Properties

  • Peak Value: The maximum amplitude of the wave.

  • Peak to Peak Value: The difference between the maximum positive and maximum negative values; for a peak amplitude of 10V, peak to peak is 20V.

  • Periodic Time: The time required to complete one cycle of the wave.

  • Frequency: The number of cycles completed per second; measured in Hertz (Hz).

  • RMS (Root Mean Square): A measure which gives the effective value of the waveform.

  • Average Value: Represents the average level over one cycle.

Definition

  • A sine wave is a sinusoidal waveshape that represents one cycle of alternating voltage or current.

    • Horizontal Axis: Time

    • Vertical Axis: Voltage

Amplitude

  • Represents alternating voltage signal.

  • For example, peak amplitude = 10V, peak to peak amplitude = 20V.

  • Can also represent a current waveshape.

Mean Value

  • The mean value is the average of the wave's values over a half cycle.

  • Calculated as:

    • Mean Value = (Area above the line) = (Area below the line)

  • Quick method:

    • Mean value = Peak value x 0.636 (64% of peak value).

RMS Value

  • RMS: Defined as the square root of the mean of the squared values.

    • RMS Value of a pure sine wave = 70.7% (0.707) of peak value.

  • Example: For a sine wave with a peak value of 10V, RMS = 0.707 × 10 = 7.07V.

  • Significance: This RMS value produces the same heating effect as an equivalent DC voltage.

Periodic Time

  • Example: One complete cycle takes 8ms; therefore, periodic time = 8ms.

Frequency

  • Defined as the number of cycles per second.

    • Example: A wave completing 1000 cycles per second has a frequency of 1000 Hz (1kHz).

  • Relationship: Frequency = 1 / t (where t = periodic time).

    • For a periodic time of 8ms = 0.008s, Frequency = 1 / 0.008 = 125Hz.

Summary

  • A sine wave represents one cycle of alternating voltage or current with key properties such as peak value, peak to peak value, periodic time, frequency, RMS, and average.

  • Key formulas:

    • Peak Value = Half of Peak to Peak Value

    • Periodic Time = t = 1 / f

    • RMS = Peak x 0.707

    • Average = Peak x 0.636