[SOLVED] What are Harmonics & How they are generated?

I am very confused with this term harmonics and when I read about them in different books they are all same not much explanation.
Can anyone explain me what harmonic exactly is and how they are generated in signals and why?

Harmonic Waves definition of Harmonic Waves in the Free Online Encyclopedia.

:wink:

Harmonics are nothing but multiples of fundamental frequency.

For suppose if u have a fundamental frequency of f1, harmonic contents are of 2f1,3f1,4f1,....

So, in case of power supply lines for a 50Hz signal they are at 100Hz, 150Hz, 220Hz and so on....
They are mainly caused due to phase effects....

But when we measure ac signal on Oscilloscope we only see a single ac signal , not other waves associated with it.

oscilloscope must have very high resolution to see that. for that purpose there are equipments like radio communication test set (RCTS) and spectrum analyser

Because in oscilliosccope you will be showing signal variation over a period of time......i.e., time domain
In instruemnts like Spectrum Analyzer we show variation of signal over frequency......i.e., frequeny domain

It is basically the horizontal vs vertical axis which we are representing.

In simple words it's the resolution... if resolution is high in oscillioscope u can observe harmonics as well.

Qote: In simple words it's the resolution... if resolution is high in oscillioscope u can observe harmonics as well.

This must be a an interesting measuring device, that can "observe harmonics" in the time domain.
On my oscilloscop I only can see the consequences of harmonics in the time domain (distortions).

An answer to tahir4awan: By displaying an ac signal you can see neither harmonics nor their influences on the signal, as "ac" per definition is a pure sinusoidal signal. For example, a squarewave or a triangular signal has a lot of harmonics (multiples of the fundamental sinusoidal with f=1/period).

It is effect of harmonics and not pure harmonics you will observe....
Infact, you will not be able to see the pure fundamental signal, because of the effect of harmonics which gives you a distorted view......
It means you can'tobserve a pure signal if harmonic content is high...
we may not be able to observe harmonics, but effect of harmonics can be seen.....

This example might be nice:
Radar Basics - Fourier Transformation

You see how a rectangular waveform is built from the fundamental sinewave with harmonics

But my question still exists that why do they generated. There must be some reason of harmonics generation.
It is said that square wave consists of multiple sine waves i.e harmonics but in 555 timers square wave is simply generated by switching then where do these harmonics (sine waves) come in.

Harmonics are generated in electrical A.c systems due to non-linear loads. There are even harmonics multiples 2,4.6 etc and odd harmonics multiples of 3,5,7 etc. There are current Harmonics as well as voltage Harmonics .These Harmonics will cause un necessary heating in the electrical equipments resulting the to fail prematurely.Bad effects of Harmonics are mitigated by harmonic filters ( Active or passive filters ). Active filters generates Harmonics of opposite polarity to system Harmonics to nullify the effects where passive filters give low impedance path for for Harmonics. ( Filter is nothing but combination of
capacitor and inductor to create least resistive path for Harmonics )

How they are generated.
1. **broken link removed**

the how's, and why's of harmonics

1. **broken link removed**

Ok pal, this is the way I understand it, it's written in my own words and I'm open to receive suggestions and corrections.

Well, as I see it there is a lot of theory about harmonics, yet if you have any doubt, any music tutorial will provide you with practical evidence of a main tone and the sound and frequency of it's harmonic tones, but the word "harmonic" is just a name, ok, to name the "bad" or "should be avoided" frequencies.

In all everyday industry, all respectable motors and machinery will work with 3-phase power systems, so what matters is knowing the causes and effects of harmonic frequencies in these power systems, which cost many thousands of dollars to install, maintain and repair; in order to keep 'em running smoothly.

The causes of harmonics are the fast switching solid-state power electronic devices used these days to drive machinery, because of their fast-switching nature and the fact that the load can shift the phase of the current forwards or backwards; of course, this happens all the time you might say, but the problem is when this occurs in a frequency that is harmonic to the fundamental frequency.

why?...

The effect: In school we learn that the neutral line of a 3-phase system has zero current, but in a system affected with harmonics, the phase currents no longer cancel themselves in the neutral, but they add. So you can have a lot of problems in your power systems as overheating wires, random tripping of protections and I think misreading power meters.

:grin:

tahir4awan said:

But my question still exists that why do they generated. There must be some reason of harmonics generation.
It is said that square wave consists of multiple sine waves i.e harmonics but in 555 timers square wave is simply generated by switching then where do these harmonics (sine waves) come in.

Click to expand...

I believe, the problem tahir4awan has, is much more simple - and I'll try to answer as follows.

Harmonics are NOT "generated". They are "only" results from applying mathematics to any periodic signal.
Take, for a example, a pure sinewave. If imposed on a non-linear transfer curve (diode or transistor) the resulting signal is not 100% sinusoidal anymore but distorted.
Now comes mathematics: FOURIER has shown that each periodic non-sinusoidal wave can be thought of a superposition of various 100% clean sinusoidal signals of different frequencies, amplitudes and (eventually) phases. And it turns out that these different frequencies all are related to a fundamental frequency by factors 2,3,4,.....
And these frequency components are called "harmonics".

As another example:
A squarewave can be generated either with a "squarewave generator" (timer, or any other circuitry) or via superposition of (theoretically) an infinite number of sinusoidal oscillators generating f, 3f, 5f, 7f....., all with amplitudes according to FOURIER series. In the first case, no harmonics are "generated" but it is something like "as if".....
(In the above example for an ideal squarewave no even harmonics are present)

Does this answer your question?

Harmonics are distorsion of signals due to nonlinear components. If you input a sine wave ( A*sin(2*pi*w*t + pangle) into a LTI system you will get a signal out that is of the same form but possibly different in amplitude or phase. Signal frequency components are only scaled or delayed in some manner. We can generalize this in the following manner.

Let's call a single frequency component of the input signal Xi such that Xi = A*cos (2*pi*i + p). A complete signal constitues a linear sum of all it's frequency components. (Input signal consisting af a 50hz cos superimposed on a 100hz cos both with the same phase with amplitudes 2 would mean our input signal is X50 + x100 = 2*cos(2*pi*50*t) + 2*cos(2*pi*100*t).

A LTI system will ouput a signal that is a sum of these same frequency components scaled and delayed in some manner. Y = sigma(i = 0 to infinity) (A'*Xi(t-delay)) where A' is the scaling each signal frequency aquires from the LTI system and delay is the delay applied by the system. The scaling and delay can be aquired from the LTI system's transfer function.

You see from the ouput relation that no new frequency components are generated in the system. The ouput consists of the same frequency components as the input. This is a general attribute of linear time invariant systems. This may be rather vaque but mathematicly the input signals are never put it any powers of themselfs other then 1. That is a term x^n other then n = 1 ever exists in the input ouput relationship since for example squaring the input signal (n=2) at any point destroys the linearity property of the system.

nonlinear systems however do not exhibit the linearity property. Somewhere in their input/output relation, mathematicly the input is squared or put in some power x^n (n>1). Let's say we have a nonlinear system which has the input output relation y = x^2.
If we take the signal A*cos(2*pi*f*t) and square it we get A^2*cos(2*pi*f*t)^2. The squared cos term can be expanded into the term 1/2 ( 1 + cos(2*pi*2*f).
Notice that now we have a output that is of frequency TWICE the input frequency. The nonlinearity of the systems has "generated" a new frequency. This is an example of what seperates LTI systems from non-linear ones.

Now, imagine a BJT transistor amplifier. BJT transistors are nonlinear devices. The current Ic is governed by a exponential relation. If we expand the exponential function via Taylor series we get something along the line of
e^x = 1 + x + (x^2)/2! + + (x^3)/3! + ..... and so on
As you see we have alot of x terms in increasing powers. We have nonlinearity and if you try puting cos input signals into this expression you will see a output relation constituing of a sum of the original signal frequency + infinite amount of signals which are at frequencies which are a intiger multiple of the input frequency. These latter terms are called "harmonics" because they show up at frequencies which are intiger multiplies of the input frequencies. If the components are operating in "regions" which are close to being "linear" these latter terms in some powers of n will be too small to notice. But if components are operating in regions which are highly nonlinear these terms can become dominant and greatly distort the input signals