By David Herres
A non-sinusoidal waveform is one that is not a sine wave and is also not sinusoidal (sine-like). This may sound like a minor distinction but actually there are some substantive implications.
A sine wave is the graph of the sine function, usually with time as the independent variable. A cosine wave is sinusoidal. It has the same form but it has been phase-shifted one-half π radians.
A non-sinusoidal waveform is typically a periodic oscillation but is neither of these. Some examples are triangle waves, rectangle waves, square waves, trapezoid waves and saw tooth waves. Typically, they do not arise in nature, where inertia of rest and conservation of angular momentum preclude the abrupt transitions that characterize non-sinusoidal phenomena.
Non-sinusoidal waveforms are prominent in the world of electronics and they are readily synthesized. A non-sinusoidal waveform can be constructed by adding two or more sine waves. The synthesis of a specific non-sinusoidal waveform is a matter of combining signals of the appropriate frequency, amplitude and phase. In this manner square waves and similar non-linear waveforms can be constructed and represented graphically.
Such waveforms, known as complex waves, consist of one fundamental frequency and one or more harmonic frequencies. By convention, the fundamental wave is the lowest frequency and generally the highest amplitude.
Harmonics are what give complex waves their characteristic shape. Harmonics are integer multiples of the fundamental frequency. The integer may be odd or even, i.e. divisible by two.
In an advanced oscilloscope, such as the Tektronix MDO3104, any waveform can be viewed in either the time or the frequency domain. In the time domain, amplitude displays along the Y axis and the passage of time is represented along the X axis. In the frequency domain, amplitude is also shown along the Y axis, but now in decibels as opposed to volts as in the more conventional time domain. So now rather than looking at a temporal view, we have a static snapshot of the function depicting its amplitude expressed as units of power rather than units of electromotive force.
Normally the greatest amount of power is in the fundamental. A square wave, to take one example of a non-sinusoidal waveform, has rapid rise and fall times which result in numerous high-order harmonics in its spectrum display. Even at low frequencies it has many high-frequency characteristics. For this reason, the harmonics contain a significant amount of power. The irregular traces along the bottoms of the frequency domain displays visible in the accompanying image are what is known as the noise floor, variously attributed to atomic motion in the oscilloscope circuitry and music of the spheres.