Harmonics and Heterodyning

[Guest guest]

Here is a short article that provides a basic

explanation of harmonics and heterodyning.

I added it to the " Bioelectronics/Frequencies and

Anecdotes " section of my website. -- turf

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A perfectly symmetrical square wave produces major

odd harmonics, that is, AC frequencies at

1,3,5,7,9... times its frequency. The power

available in those harmonics decreases as the

multiplication factor increases. For example, a

100Hz signal produces harmonics (AC frequencies)

at 100, 300, 500, 700, 900, ... but at strengths

of 1, 1/3, 1/5, 1/7, 1/9 ... of the original.

These harmonics extend to the radio frequency

range and beyond, to infinity,

theoretically. Frequencies also exhibit a

heterodyning effect. This is explained by an

excerpt from a web site:

From http://www.taralabs.com/papers/ism.htm

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[...] consider a sound wave of 264 cycles (middle

C on the Scale of Just Intonation). In order for

this tone to be perceived as both accurate and

natural, one must be able to hear not just the 264

cycle tone itself, but the higher order harmonics

which extend well up into the frequency range

vulnerable to RF modulation. This intermodulation

creates an effect called heterodyning, where

additive and subtractive tones, known as beat

frequencies, are created. For example, mixing two

frequencies of 100 KHz and 1 KHz results in the

following frequencies being created:

100 KHz

1 KHz

101 KHz

99 KHz

These frequencies will also combine to produce

beat frequencies of their own. Add in a

multiplicity of RF signals and it is easy to

imagine the degree to which RF alters and distorts

the musical signal. The effect is especially

evident in the higher frequency bands.

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Since square waves are used, this is not just

mixing two frequencies. It is mixing all the odd

harmonics. Instead of producing 100 and 1, we are

producing 100, 300, 500, 700, and all the

additions and subtractions. Now, combine the

effects of harmonics with heterodyning with this

example: Consider a 10Hz square wave. It is

producing a strong third harmonic at 30Hz (at 2/3

less power). Heterodyning means it is also

producing 30 - 10 = 20Hz and 30 + 10 = 40Hz. The

5th harmonic is 50. 50-10 = 40Hz. This means

that 40 gets a " boost " since it is produced in

these two ways, among others. While this process

goes up the scale with infinitely more numbers it

produces a huge range of frequencies of varying

intensities (all at less than the power at the

base frequency.)