Marko Rodin Coil -- 007 Device

[MileHigh]

To me,a pure square wave would mean just that-pure,and that would mean that the wave shape is pure--free from harmonic ripple.

Brad

Actually Brad, a pure square wave would mean.... That the wave shape is pure - including all of the harmonic ripple.  It must include all of the harmonic ripple to be a pure square wave.

So the team has probably tried around five times but unfortunately you got it backwards. 

I suppose the experts can try one more time to see if it will sink in.

[poynt99]

To me,a pure square wave would mean just that-pure,and that would mean that the wave shape is pure--free from harmonic ripple.

Brad,

A perfectly flat and square square-wave contains an infinite order of odd harmonic frequencies.

A perfectly flat, but not-so-square square-wave (where the edges have a finite rise time) will contain a limited order of odd harmonic frequencies.

[picowatt]

To me,a pure square wave would mean just that-pure,and that would mean that the wave shape is pure--free from harmonic ripple.

These are not just abstract mathematical concepts that don't exist in the real world...

Imagine you have a tunable bandpass filter with a narrow bandwidth in the passband.  You connect your function generator output to the filter's input and monitor the filter output on a scope.

With the FG set to output a 1kHz sine wave you tune the filter to 1kHz and you see a 1kHz sine wave on your scope.  As you increase the filter's frequency, the signal disappears from the scope and you see only noise.  If your sine wave was "perfect", you would not see any more signals at the filter output as you continue to tune upward.

But your sine wave is not perfect, so at 2kHz you see a very low amplitude signal and have to crank up the scope, but you do see that there is a low amplitude 2kHz sine wave being displayed.  That is the first of the sine wave's even order harmonic distortion (the 2nd harmonic).  As you continue to tune higher with the filter, you again see nothing but noise until you reach 3kHz, where once again you see a very small amplitude 3kHz sine wave which is the first of the sine wave's odd order harmonic distortion (the 3rd harmonic).  Which harmonics you see, and their amplitudes, is dependent on the design and specifications of your FG (how far the generated sine wave deviates from perfect).  Analog FG's typically had "not so great" THD values of around 1% to .5% (Total Harmonic Distortion being the sum of the harmonic amplitudes expressed as a percentage of the fundamental's amplitude).  Digital function generators (like yours) are likely better than this, perhaps less than .1%.  Some digital sine wave generation techniques can effectively remove all the lower order harmonics.  Signal generators purpose built for generating only low distortion sine waves can have very low THD.  For example, I have analog sine wave generators capable of around .00015% THD (out to the fifth harmonic).

(The point of course being that if the 1kHz sine wave was a perfect sine wave, it would contain no harmonics at all.  Only when the filter is tuned to 1kHz would you see any signal at the filter's output.)


OK, so now you repeat the above tests but switch your FG to produce a 1kHz square wave.  As you tune the filter to 1kHz you see a large 1kHz sine wave displayed on the scope.  This is the square wave's fundamental frequency of 1kHz.  As you tune the filter frequency upward, the signal on the scope disappears into the noise floor.  You pass 2kHz seeing nothing but noise until you reach 3kHz on the filter when suddenly a 3kHz sine wave appears on your scope.  The amplitude of this 3rd harmonic is fairly large, being about 2/3 of the amplitude of the 1kHz fundamental.  You continue tuning the filter frequency upward and again see nothing but noise until you reach 5kHz where again you see another sine wave appear on the scope.  This 5kHz sine wave, the 5th harmonic, has an amplitude about half that of the observed 3kHz sine wave.  As you continue to tune the filter upward, you note that you see a sine wave at every odd harmonic (3kHz, 5kHz, 7kHz, 9kHz, 11kHz, 13kHz, 15kHz, etc) with the amplitude decreasing with each higher harmonic.

In reality, if the duty cycle of the square wave is not perfectly 50%, you will see some low amplitude even order harmonics (2nd, 4th, etc) due to the square wave deviating from being "perfectly square" but the amplitude of these harmonics will be very low compared to the odd order harmonics (unless you adjust the duty cycle to be something other than 50%).

The FFT display on your scope can be used instead of a tunable filter.  The FFT can mathematically analyze the digitized waveform and output a graphic display of the various frequencies, and their amplitudes, contained in the waveform.

In the days before digital, using a tunable analog filter to determine frequency/harmonic content was quite common.  A tunable analog filter was the basis for most distortion and spectrum analyzers.  Today, converting analog signals to digital and using Fourier analysis is becoming more common.

PW

If you have an audio graphic equalizer available, connect your FG output to the equalizer's input and monitor the equalizer's output with your scope.  Feed a 1kHz sine wave into it and play around with the equalizer's boost/cut controls at the various frequency bands it covers (a rather boring exercise).  Then switch the FG's output to a 1kHz square wave and again play around with the equalizer's boost/cut controls.  What the equalizer does to the frequency content of the square wave, that is, the various shapes the square wave morphs into as you boost/cut various frequencies can be most informative (and a good way to test graphic equalizers...).

[tinman]

There is no "pure" anything,,

Pure, perfect,, ideal,,

No pure sine wave,, no pure square wave,, no perfect circles,, no perfect squares,, the Universe is not ideal, perfect or pure.

A pure anything would not have anything but what it is,, so to say anything other is nonsense,, the word pure takes care of anything else being present.

Ideals only work in an ideal experiment that is not carried out in the real world with real things.

I would have to agree Webby.
To be pure,is to have nothing but the stated.
As there is no such thing as pure in the real world,that can only mean we cannot have a pure wave form of any type-depending on how closely  you want to look at that wave form.

But as you say,in an ideal world,such purity could exist,and as MHs question uses an ideal voltage source,you would think the step from one  voltage value to another would be ideal,and result in a pure square wave shape without this harmonic ripple being present.

The real issue is-what difference dose it make in regards to the subject at hand ?


Brad

[poynt99]

Brad,

I'm curious if you read this and if you watched the animation?

Does it make sense?