OBSERVATIONS FROM SCOTLAND                            10 October 2007                                GM1SXX

Harmonics or Overtones. What's the difference?

What's in the can.

Radio amateurs tend to use the terms harmonic and overtone synonymously. In many instances, and in overtone oscillators and multiplier stages in particular, they are NOT the same thing.

Even the word harmonic has multiple meanings, but the common one is generally taken to mean an 'integer multiple' of the fundamental.  A Middle A at 440Hz having a second harmonic of 880Hz *could* be an example.  The reality is rather different! For many musical instruments as with quartz overtone oscillators this is not quite the reality. (See stretched Octave)

SO an overtone is usually a different thing from a harmonic. It doesn't have to have to bear an integer relationship to the fundamental and so is a bit different from an 'integer harmonic'.

Frequency control crystals below 30MHz are generally specified as fundamental  types. Above 30MHz they are generally specified as third, fifth or seventh overtones.  Overtones occur only at odd multiples. So, it is important to know if your oscillator is intended to operate in fundamental or overtone mode. An overtone is similar  to a harmonic, except that crystal oscillation overtones are not exact integer multiples of the fundamental. Selection of overtone is based on using the lowest possible overtone that will result in a crystal's fundamental frequency being below 30MHz.  So it's important when ordering to specify the type of operation you need.  Third, fifth or seventh overtone and if the circuit is designed for series operation (usual with overtone oscillators),  or not.  If not, you need to specify the load capacitance although it's normal for overtone crystals to operate in series mode.   If you plan to use a crystal heater... say so!

Crystal manufacturers sell overtone crystals because the quartz material becomes thinner and thinner as frequency increases. Crystals between 15MHz to 30MHz are generally specified in either a fundamental or 3rd overtone. Starting at about 30MHz, the quartz becomes so thin that it is hard to handle during the manufacturing process, and the crystal makers don't like handling thin quartz.  It costs more and the end result is inferior.

This business of overtones being different from harmonics is readily demonstrated in oscillator-multiplier strips that use overtone crystals.  At home I have several different exciter strips that all use  Colpitts oscillators followed by *2, *3 and *2 frequency multiplier stages.  ALL of the standard overtone crystals I've tried in these different strips end up being about 4Khz low in frequency at the output.  My 96.00000 Mhz rocks  produce RF at 1151.996Mhz.   I tried two different 96Mhz crystals in different oscillator circuits and both were low by 4Khz. Now 4Khz in 1152Mhz is a very small error, but it's real and easily measured.  Since a 5th overtone oscillator crystal doesn't actually operate at it's marked frequency but at around a fifth of that,  the actual error is really small..... about 66.7Hz.  My error measured 4Khz at the output which represents about 333Hz low at the oscillator output. Since the oscillator is a 5th OVT type, it's clear that the quartz slab operates at about 66.6667Hz lower in frequency than I'd like!  Not much, but it means a 4Khz error at the exciter output.

There seems to be two ways around this 'problem'.

#1 specify the crystal 333Hz high in frequency (333*12 is 4Khz near enough)

or

#2 get fussy with my suppliers, giving them ALL the details of the circuit you are using.

#1 might be easier but of these, no 2 is the better option.

You might wonder why a crystal overtone is not the same as an integer multiple. The reasons are largely mechanical, to do with the way an oscillating mechanical structure such as a crystal (or piano string) vibrates. Such structures do not produce harmonics in the sense of being 'integer harmonics'.  You'll notice the crystal manufacturers use the term overtone a great deal.  There is a sound reason for that.  They *are* overtones and not harmonics. If you make use of crystal controlled multiplier stages, be aware that harmonics and overtones are different things and plan accordingly.

It's certainly possible to 'pull' crystals by loading them with L or C, but for the cleanest performance, this is not really a good option. Best to take a lot of care in selecting the correct crystals to start with.

Some useful references.

http://en.wikipedia.org/wiki/Quartz_Oscillator#Crystals_and_frequency

http://en.wikipedia.org/wiki/Overtone
 http://en.wikipedia.org/wiki/Harmonic
 http://en.wikipedia.org/wiki/Harmonic_series_%28music%29
 http://en.wikipedia.org/wiki/Equal_temperament
 http://en.wikipedia.org/wiki/Just_intonation
http://en.wikipedia.org/wiki/Harmonic_oscillator

http://en.wikipedia.org/wiki/Stretched_octave

73 AL.
GM1SXX