# Does not have any harmonics

Discussion in 'Electronic Basics' started by karthikbalaguru, Jan 1, 2008.

1. ### karthikbalaguruGuest

Hi,
Why does a sinusoidal waveform alone does not have any harmonics or
distortion ?

For example, (Reference -> http://en.wikipedia.org/wiki/Waveform),
Sawtooth wave of constant period contains odd and even harmonics
Square wave of constant period contains odd harmonics
Triangle wave, (an integral of square wave) contains odd harmonics

But, How is it possible that sinusoidal wave alone does not have any
harmonics or distortion ?
I searched the internet,but i did not find any link/pdf that talks in
Any ideas ?

Karthik Balaguru

2. ### JoergGuest

Just calculate the FFT of a sine wave

3. ### David WrightGuest

A continuous sinewave with infinite duration in an ideal distortionless
transmission medium would only have the fundamental in its spectrum.
However, real-world finite duration sinewaves in distorted transmission
system would have some harmonics. These harmonics would not be as
pronounced as those of an impulse waveform. However, by running the impulse
through an integrator circuit, the harmonics can be reduced. With a series
sinewave. Since most radio transmission are bandwidth limited with filters,
many of the higher harmonics are hopefully missing.

4. ### Mike WahlerGuest

As I understand it, a harmonic *is* a sine wave. So I suppose if
you consider something to contain itself, a sine wave contains a
(single) harmonic.

From http://www.ethnomusic.ucla.edu/systematic/definiti.htm :
Harmonic: Sine component of a complex signal. Thus, a complex
signal is composed of harmonics. Its frequency is obtained as
the integer multiple of the fundamental frequency

Also see:
http://www.its.bldrdoc.gov/fs-1037/dir-017/_2542.htm

-Mike

5. ### David WrightGuest

Mike is correct. A frequency spectrum consists of a positive and negative
mirror image of the waveform. This brings up all sorts of interesting
possibilities - such a SSB or single-sided sideband and DSB or double-sided
sideband.

6. ### Don BoweyGuest

(It's not nice to Top Post)

YOU are talking of modulation products, which is not what the OP was asking.

Whatever Mike had in mind, it is wrong WRT the OP's question.

It could have some distortion. It depends on the quality of the signal
generator. For practical purposes the distortion may not be significant,
but may be measurable.

Yes. Complex waveforms are constructed of various harmonics.

A single frequency sinewave is not a "harmonic" (it is NOT a multiple
frequency of itself)

See above.

7. ### EeyoreGuest

Because it doesn't. Read up 'simple harmonic motion'.

Graham

9. ### John FieldsGuest

---
Because it's a single pure tone.
---
---
Every waveform which isn't a perfect sine wave is made up of more
than one sine wave, and when they combine they result in the shape
of the final waveform.

10. ### Guest

You were badly brought up. My parents told me that fine dust particles
suspended in the air scattered my short wavelength light - blue light
- than longer-wavelength light - the other colours.

It didn't make much sense to me at the time - I was around four - but
at least I wasn't mis-informed.

In fact Eeyore has done a litttle better than your parents did -
"simple harmonic motion" as a search string does get you to this

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

which in turn points you to this

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

which gets you to

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

which is probably where the OP needs to go, though they may need a
fair bit of education before they can get much out of it.

11. ### John O'FlahertyGuest

Odd and even harmonics are themselves pure sine waves that are
frequency multiples of a fundamental sine wave. Distortion of a sine
wave produces odd and/or even harmonics. So, sine waves are
irreducible pure signals that other signals can be analyzed into.

12. ### john jardineGuest

It's a good question.
Myself I'd say a triangle waveform looks like it should be the one to have
no harmonics.
But it's all down to how smoothly the waveform voltage changes. The triangle
and square have significant 'shape' discontinuities during each cycle and
these have the effect of creating harmonics.
The sine wave although a horrible looking non linear waveform, is the one
with the absolutely smoothest rate of change over all its cycle.
(DC is even smoother but isn't a frequency

13. ### EeyoreGuest

Not QUITE correct.

Distortion as caused typically by non-linearities in a transfer
characteristic such as in an amplifier may be modelled and indeed measured
as harmonic distortion but the mechanism producing it is typically
producing a wide range of harmonic products of which typically only a few
may usually be considered of interest.

Graham,

14. ### EeyoreGuest

Uh ? With those rapid discontinuities ?

Exactly. Simple harmonic motion. As in a child's swing or a pendulum for
example.

Graham

15. ### Fred BartoliGuest

john jardine a écrit :
It's more a matter of definition. When you take the view of decomposing
a waveform on a sine waves base, it is not abnormal that a sine wave has
just one component on that base: itself. The contrary would be abnormal.

If you were to decompose a sine wave on a triagular waveforms base
(which is as valid as the sine waves case), it'd had lots of 'harmonics'
and a triangular waveform would have just the fundamental.

16. ### John O'FlahertyGuest

Sorry, but I think it's exactly correct.
That's a different question.

17. ### Phil AllisonGuest

"Fred Bartoli"

** No it is not - you posturing wanker.

** No it is not.

A sine wave uniquely has the property of no harmonics.

Unlike all other periodic waves, its shape is unaltered after passing
though any kind of filter.

........ Phil

18. ### EeyoreGuest

Phil's right too.

Graham

19. ### EeyoreGuest

The non-linearities that are/cause distortion *result* in the production of
harmonics. They don't actually *make* harmonics.

It's a subtle distinction.

Graham

20. ### Paul Hovnanian P.E.Guest

Fourier analysis (http://en.wikipedia.org/wiki/Fourier_analysis)
demonstrates that any periodic waveform can be expressed as the sum of a
series of sine waves. The relationship between the waves frequencies of
the series is that there is one, called the fundamental, which is a sine
wave of frequency equal to that of the periodic waveform. All of the
other waves of the series have frequencies that are integer multiples of
the fundamental. These are called harmonics.

If, for your periodic wave, you select a sine wave, then the fundamental
of the series emulates it exactly. No other harmonics are needed.
Distortion is a bit different. It is a broad term that refers to a
change in a waveform between the input and output of some system.

Used in the context you, it refers to the change in harmonic content
introduced when driving a system with a pure sinusoidal input.