how non linear device can generate harmonics

Thread Starter

cdennis414

Joined Dec 19, 2012
15
Hi i need some help please
One of the question on my assignment is
Describe how a non liner devise can generate harmonics? and I need to describe two devices.
My first choice is a diode.
I know what the harmonics are
I can build the circuit in Multisim
I know that they are produce because voltage is disproportional to current....
But i don't know HOW ARE THEY PRODUCED
And i don't know what to chose as second device
Any help would be much appreciated..
Thaks...
 

Brownout

Joined Jan 10, 2012
2,390
Harmonics are frequecies that are integer multiples of the frequency of the original signal. If you have a sine wave of, say 1KHz, you can have harmonics of 2KHz, 3KHz, 4Khz, etc. Nonlinear circuits generate harmonics when fed a signal. For example, a BJT amplifier produces harmonics due to its exponential forward transfer characteristics. A MOSFET produces harmonics due to its "square" transfer characteristics. Basically, the output slope is multiplied by the nonlinear function, producing the harmonics. As an experiment, draw the slope of a sine wave form, say -∏/2 to +∏/2. Then draw an expontial curve which would be output from a transistor amplifier, using the sine wave as the input. Using the graphing functions of Excel is helpful here ( or any graphing program or graphing calculator ) Notice the faster rise of the exponential vs the sine wave. That's the harmonics.
 

crutschow

Joined Mar 14, 2008
34,285
It's related to the frequencies in a particular waveform as defined in its Fourier transform. Any waveform, other than a pure sinewave, is composed of harmonics. For example, a square wave-wave contains many harmonics of its fundamental frequency. So any time you distort a sinewave with a non-linear circuit you will generate harmonics of that fundamental frequency.
 

Papabravo

Joined Feb 24, 2006
21,159
It is non-linear operations on a pair of input signals that produce frequencies, including harmonics, that are not found in the original signals. For a mild brain bender study the trigonometric identity where two cosine waves of different frequencies are multiplied together and the output contains components at brand new frequencies.
 

Brownout

Joined Jan 10, 2012
2,390
Pairs of signals aren't needed for harmonics to be produced by a nonlinear operation. Harmonics are procuded on a single input signal ( see frequency doubler, tripler ) To see this is so, do a Taylor series expansion on a nonlinear function, say an exponential. Then subsitute a time-periodic signal for the variable, and apply trig identities for the higher order terms.
 

Papabravo

Joined Feb 24, 2006
21,159
So how much of the output is at the fundamental and how much is at the 2nd harmonic. In the case of a mixer, two input frequencies in, give four frequencies out. Does a doubler behave the same way, or is the fundamental attenuated by some significant amount amount?
 

Brownout

Joined Jan 10, 2012
2,390
It totally depends on the kind of circuit being used. A doubler would be designed to maximize the harmonics, and an amplifier would be designed to minimize them. In either case, the calculations would be the same. The output would be a fraction of the fundamental, at least down to 1/4 in the 2nd harmonic, by virtue of the 1/2 factor in the taylor series expansion ( in the case of the exponential ) and the 1/2 factor that comes from the cos^2 identity.
 

Thread Starter

cdennis414

Joined Dec 19, 2012
15
Thank you all very much for your replies, it's cleared things up a bit, but I am still not quite sure I understand it completely.....So far how I understand it : The input voltage creates distorted output current because non liner relation but what happened to output voltage does it get distorted according to Ohm,s Law ? are there any equations for it?
Thanks..
 

KL7AJ

Joined Nov 4, 2008
2,229
A diode DOES follow Ohm's Law, but you have two variables, one being the resistance itself, which is somewhat inversely proportional to the applied voltage. This is why (over a small region) the "output" of a diode voltage foillows the square law.

Eric
 

Brownout

Joined Jan 10, 2012
2,390
The input voltage creates distorted output current because non liner relation but what happened to output voltage does it get distorted according to Ohm,s Law ?
It has nothing to do with Ohm's law. It's due soley to the non-linear relationship between input votage or current and output voltage or current. If the output current is distorted, then so will be the voltage.

there any equations for it?
Thanks..
You can caluculate the harmonics, usually by using a Taylor series.
 

DickCappels

Joined Aug 21, 2008
10,152
@crutschow susuccinctly explained how nonlinear components cause the generation of harmonics in post #3.

It's related to the frequencies in a particular waveform as defined in its Fourier transform. Any waveform, other than a pure sinewave, is composed of harmonics. For example, a square wave-wave contains many harmonics of its fundamental frequency. So any time you distort a sinewave with a non-linear circuit you will generate harmonics of that fundamental frequency.

 

MrAl

Joined Jun 17, 2014
11,396
It was asked What creates harmonics here. I answered it;
Harmonics are not produced when the current is disproportionate to the voltage. You don't see harmonics coming out of RLC circuits do you? That totally dispels this myth, but to answer your question (8 years later, sorry about that).
Harmonics are not really caused by distortion. Distortion causes a sine wave (distortion impacts all waves, but it's easier to talk here about sine waves) to be distorted, and a distorted wave cannot exist without harmonics. Harmonics create the distorted wave, not the other way around, as you can see here:

4_pcnt_dist_animation copy.gif


This is a Bullard Plot, invented by yours truly. In the foreground you see the distorted wave in black, and behind it you can see the harmonics that make it up. These harmonics and the phases they are in are extracted from an FFT of the wave shown in each frame. Starting at the top is the fundamental, harmonic #1, and you will notice that this wave (in blue because it's odd) changes very little over the span of this animation. Below that is the 2nd harmonic, in red because it's an even harmonic. Below that is the 3rd harmonic in blue because it's odd, and so on all the way down to the 36th harmonic. Got the color code?
OK, as the fixed size distortion makes its way from the positive peak to the zero crossing, you can see how the harmonics conspire to create the distortion in the black wave. Again, this distortion is always the same size in the transfer function but because as the distortion moves through the transfer function, it changes the area because of the way a sine wave works. A sine wave spends a lot of time at the peaks, and so when you distort just 4% of the transfer function, a very large portion of the peak gets distorted. But if you move it down, the peak is not impacted, and it just makes a smallish triangle in the wave. As the distortion moves downward, the triangle gets smaller and smaller, until at the zero crossing you have a hard time making out the distortion. I explain this in full detail in chapter 4 of my book Distortion. Now, with this graphic it's easy to see how the distortion is created by the harmonics, but strictly speaking, the distoriton didn't make the harmonics.
Now, why do we color code the odd and even harmonics? All of this action happens on the positive peak of the sine wave, but why don't those distortions happen on the negative side? Think about it. Do you see that the even harmonics counter the odd harmonics in the right half of the wave, but the they accentuate the effects of the odd harmonics on the left side. Except for one frame. When the distortion hits the zero crossing, suddenly all the even harmonics go dead flat. Why? Because we are distorting both the upper half cycle and the lower half cycle exactly the same amount, with the same exact area, so we don't need the even harmonics, which server only one purpose: They prevent the distortion from being duplicated on the opposite half cycle. But they don't actually go away, they are simply cancelled out by even harmonics in the exact opposite phase. Because of the way harmonics work, only four phases are allowed relative to a sine wave input. Watch the animation, you will see only four phases for each and every harmonic, no matter where the distortion occurs. 0°, 90°, 180 and 270°. That is a law, Bullard Laws of Harmonics #5. I discovered this law, so I claim it. Because the harmonics are stuck with only four phases, how do the harmonics create the plethora of waves that can be created by distortion? The only other axis of freedom is amplitude. Notice as the animation runs that some harmonics go dead flat, then come back to life as the distortion moves on to the next location along the transfer function. That's not an accident. The Harmonic Signature depends on the angle at which the sine wave impacts the distortion. That's Bullard Laws of Harmonics #2. As you can see with this spectrum, the "nulls" in the spectrum depend on the angle at which the sine wave impacts the distortion.

clipped_wave_angle_fd copy.gif


Now to answer your question: If you apply say, a 1 volt peak sine wave to a diode, what will impact the harmonics? Obviously the forward voltage will determine the angle at which the diode starts to conduct, and that will determine the harmonic signature.
I've written a bunch on my five laws of harmonics and most of them are accessible on LinkedIn. (Promotional link removed by moderator)
Hi,

Interesting, but it is also interesting that the God Of Harmonics is certainly not the God Of Uploading Images. Perhaps try again so we can see your images.

I think this main issue can be explained in a multitude of ways.
For example, harmonics occur when a device causes a change in the assumed pure sine wave input that is not exactly and perfectly synchronous except in phase and amplitude with the assumed pure sine input. So in other words, harmonics result from any deviation from a sine wave (obviously of the same frequency) caused by a device.
 

MrAl

Joined Jun 17, 2014
11,396
The tools here on this site are rudimentary to say the least. The gatekeeper deleted my post, and when I tried to repost it, they removed my images. I posted pretty much the same thing on Quora, but I finally did get the article posted here: https://forum.allaboutcircuits.com/threads/how-are-harmonics-created.167681/#post-1484167
If you can't see the images on that one, it's your problem, not mine.
Your answer is way too simple. There are definite laws to harmonics created by distortion, and I discovered five laws after fighting with a guy with an MSEE degree who is a complete idiot. For example: Can DC offset change the harmonics created by a sine wave applied to a non-linear device? He says no, I say absolutely it can! Watch the video that started it all. I don't use simulation there, I use a real Analog Devices AD7671 A to D converter. and an Applicos ATX7006.
Hi,

First thanks for the reply. Your stuff sounds interesting but i am not sure what you are trying to get at.

Are you actually stating that distortion creates harmonics?
If so, then where did the distortion come from?

Also, any argument about what harmonics any wave contains should be easy to settle by using a Fourier Transform. I dont see a need for an actual experiment unless you are trying to prove that there are other effects that come into play because of the limits of the implementations available to us at the current date and time.

You said my statement was too simple but what i was getting at was that the harmonics come from the physical attributes of the device that caused them.

Comments welcome.
 

bogosort

Joined Sep 24, 2011
696
@crutschow susuccinctly explained how nonlinear components cause the generation of harmonics in post #3.
Actually, Brownout had the correct answer. Harmonic distortion is a consequence of the way sinusoids multiply.

Given a nonlinear system f(t), its output y(t) is a function of the input x(t): y(t) = f(x(t)). For most physically realizable systems, we can model f(t) with a Taylor series expansion, which makes y(t) a polynomial in x(t). That is, y(t) will be a sum of integer powers of x(t).

Let x(t) be a simple sinusoid of frequency w. Then, y(t) will be some function of the form
\[ y(t) = a_0 + a_1 \sin(\omega t) + a_2 \sin^2(\omega t) + a_3 \sin^3(\omega t) + \cdots \]
And since squares, cubics, quartics, etc. of sine are always a sum of sinusoids of integer multiples of w, y(t) will be comprised entirely of integer multiples of w, aka, harmonic distortion.

It's important to note that, in general, most waveform shapes are a mix of harmonic and inharmonic distortion. But, if you put a single sinusoid through a memoryless nonlinearity, you get strictly harmonic distortion because of the way sines multiply.
 
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