Trying to understand harmonics - Page 1
Forum section: electronics / beginners

author: reyntjensm
author_rank: Regular Contributor
timestamp: December 22, 2020, 10:06:58 pm
content: I have a 50Hz ac signal getting rectified with 1 diode. This results in a 50Hz pulsed sine wave. When i look at the FFT in LTspice i see my first harmonic at 100Hz, the second one is lower at 150Hz and the third harmonic is larger again at 200Hz. What i don't get is why there is still a peak at 50Hz? Am i understanding this whole harmonics thing wrong? Can somebody please help me to understand this....

author: coppice
author_rank: Super Contributor
timestamp: December 22, 2020, 10:09:30 pm
content: Maybe you could explain what you expect. The half wave rectified waveform is cycling 50 times a second. You might expect a large 50Hz component.

author: sibeen
author_rank: Frequent Contributor
timestamp: December 22, 2020, 10:22:04 pm
content: The fundamental frequency is at 50 Hz. The harmonic at 100 HZ is called the second harmonic, the third harmonic is at 150 Hz, the fourth at 200 Hz. Just getting your nomenclature correct so that we are on the same page.

author: reyntjensm
author_rank: Regular Contributor
timestamp: December 22, 2020, 10:33:29 pm
content: Attached is the same FFT display but without diode. Here is the fundamental frequency at 50 Hz(first harmonic?) and i thought the second harmonic is opposite or lower, here at 100Hz. The third harmonic is higher again at 150Hz. So there is a shift in harmonic count with or without diode?

author: coppice
author_rank: Super Contributor
timestamp: December 22, 2020, 10:38:28 pm
content: If you have a pure sine wave there is only one frequency present - the fundamental, or 1st harmonic. If you distort the waveform in a symmetrical way you get odd harmonics added to the fundamental - 3rd, 5th, 7th, etc. If you distort the waveform in an asymmetric way, like half wave rectifying it with a single diode, you get lots of even harmonics added to the fundamental - 2nd, 4th. 6th. etc. You have a lot of even harmonic content in your first spectrum for this reason. You have some odd harmonic content in your unprocessed signal because its not pure, but the distortion is symmetric.

author: reyntjensm
author_rank: Regular Contributor
timestamp: December 22, 2020, 10:51:34 pm
content: Quote from: coppice on December 22, 2020, 10:38:28 pmI see, and what about the size of the harmonics?

author: sibeen
author_rank: Frequent Contributor
timestamp: December 22, 2020, 10:52:01 pm
content: What you are seeing here is just the slight distortion on the mains waveform. You need to note the scale on each of your pictures taken. In the first, with the diode, you have a large second harmonic and then your third harmonic (150 Hz) is sitting at around -10 dB. In the FFT of just the mains the third harmonic is sitting at around -35 dB, that's about 300 times less.You really wont see any of the even harmonics when you are looking at a mains waveform as to have an even harmonic (2nd, 4th, 6th...) you need a DC component in the waveform. You have this in the diode circuit but not when measuring the mains waveform.

author: reyntjensm
author_rank: Regular Contributor
timestamp: December 22, 2020, 10:59:24 pm
content: Quote from: sibeen on December 22, 2020, 10:52:01 pmSo in the FFT with the diode the first harmonic is at 100Hz and not the fundamental frequency of 50Hz?

author: sibeen
author_rank: Frequent Contributor
timestamp: December 22, 2020, 11:22:11 pm
content: The fundamental frequency (50 HZ) is the first harmonic, although it is only rarely called that, and is just referred to as the fundamental. The harmonic at 100 Hz is the second harmonic as it is twice the value of the fundamental. The third harmonic is 3x the value, the fourth is 4x etc etc.

author: TimFox
author_rank: Super Contributor
timestamp: December 22, 2020, 11:43:21 pm
content: Fourier's original idea, the Fourier series, states that any periodic waveform, of frequencyf, can be expressed as a sum of sine and cosine waves of integer multiples (nxf) of that frequency, includingn= 1. The casen= 0 gives a DC component. In the special cases mentioned above, the amplitude of even or odd multiples (harmonics) may go to zero.In more general case of musical sounds, the sinusoids above the fundamental are called "overtones" (a mis-translation of the German "Obertöne" in Helmholtz' analysis of musical tones). In the case of a circular membrane (kettle drum), the overtones are not harmonic, since they are not integer multiples of the fundamental, and the resulting waveform is not simply periodic. One-dimensional oscillators (guitar string or organ pipe) produce almost harmonic overtones. The first overtone of the kettle drum is approximately 1.6 times the fundamental: the solution for the vibration involves Bessel functions. Similarly, since quartz crystals are three-dimensional, they show resonant modes at overtone frequencies that are close, but not equal, to odd-order harmonics of the fundamental mode.When a pure sine wave (of constant frequency for all time) goes through a non-linear distortion (rectifier, bad amplifier, etc.), the result is exactly periodic and the Fourier series discussed above is good.

author: donlisms
author_rank: Frequent Contributor
timestamp: December 24, 2020, 12:36:20 pm
content: One way to think of harmonics is that they reveal the amount of non-sine-ness of the waveform. They will all be 0 for a pure sine wave. Any departure from a pure sine wave (assuming a repeating wave form) is a matter of introducing harmonics.Consider this: starting with a 50Hz sine wave, if you add a 100Hz sine wave, it's going to be one cycle added to the first half of the fundamental, and another cycle added to the second half of the fundamental. Because the fundamental is positive on the first half and negative on the second, the impact is different -- an upward section of the harmonic will push the first half upward to become even higher, and an upward section of the harmonic will push the second half downward.The fourth harmonic will do the same thing to the second harmonic, and so on. If you add enough even harmonics, their initial "up-ness" gets earlier and earlier as the waves get faster, pushing the start of the waveform upward sharper and sharper, and their final "down-ness" gets later and later, pushing the last bit of the wave form more sharply downward. In the end, if you add enough even harmonics, you end up with a sawtooth.With odd harmonics, things line up differently, e.g. the upward first half of the fundamental is subjected to an "up down up", and the downward second half is subjected to a "down up down". So the first half of the fundemental has its leading and trailing sections pushed upward, and the middle pushed downard, making the whole thing a little more square-ish.I would suggest there is huge value in getting some graph paper and drawing some waveforms, and adding them up yourself, to really get a sense of how the whole thing works.

author: ratatax
author_rank: Regular Contributor
timestamp: December 24, 2020, 12:54:07 pm
content: Without diode, fs=50hz without any other harmonicsWith diode, fs=100hz and many harmonics due to the sine being broken in halfEverything else is noise and/or things related to imperfections of components and other real-world thingsWith some experience you can guess pretty accurately how much harmonics a waveform has just by looking at it or by listening to it.

author: BravoV
author_rank: Super Contributor
timestamp: December 24, 2020, 02:30:54 pm
content: I guess you have to know and understand what is called Fourier Transform.Forget about the math involves, this video should be give you a glance what are you experiencing.

author: innkeeper
author_rank: Unknown
timestamp: December 26, 2020, 11:17:29 pm
content: Quote from: reyntjensm on December 22, 2020, 10:59:24 pmexactly yes. lets see if i can make this easier to remember / explain as i can see how it can be confusing they way your looking at it.harmonics are my definition multiples of the fundamental frequency, so 50hz, in your example is not a harmonic, but the fundamental, and 100hz being the 1st harmonic of that fundamental frequency.the notation for the fundamental is F0making the first harmonic notation F1so another way this is looked at is the fundamental is harmonic 0 and the first harmonic is harmonic 1so in your caseF0=50hzF1=100hzI hope that helps make it click for you.

author: bdunham7
author_rank: Super Contributor
timestamp: December 26, 2020, 11:25:46 pm
content: Quote from: reyntjensm on December 22, 2020, 10:06:58 pmWhat circuit are you modeling in LTSpice?