Indeed,just as "W Bahn"is a subset of "AAC Contributors",but it would not be normal to call you the latter term when referring directly to your goodself.

 

Ok,

So I have been studying Fourier analysis and transform videos on youtube.
I see that by adding a DC component the pulse may be made unipolar.
What I'm still not understanding is this.

How do you determine the impedance if the wave is made up of an infinite number of harmonics? If you add the sum of each one then you get infinite impedance???

 

Ever since Steinmetz (http://en.wikipedia.org/wiki/Charles_Proteus_Steinmetz) discovered that it's possible to solve AC circuits using just the algebra of complex numbers rather than setting up and solving the differential equation for the circuit, the word "impedance" is understood by engineers the world over to only apply when the currents and voltages are phasors--sinusoidal waveshapes.

If you want to apply a square wave of voltage to an inductor (call it e(t)) and measure the resulting current (call it i(t)) and take the ratio e(t)/i(t) to be a measure of the inductor's opposition to current, please don't call it "impedance". That leads to muddled thinking; invent another word for that ratio, perhaps "impediment".

Try this experiment: set a function generator to output a sine wave with some magnitude, perhaps 5V RMS. Apply that waveform to an inductor and switch the waveform to a triangle wave, then a square wave, then a trapezoid wave. Leave the voltage at 5V RMS. Measure the current in each case and calculate the ratio e(t)/i(t); it will be different in each case. What?? The opposition to current varies with the wave shape? This "impediment" varies with waveshape.

We would like to have a value for current opposition that doesn't vary with waveshape as is the case with resistors. But, if we can't do that, then let's use a definition for one waveshape only--sine waves. And, since phasors are always sinusoidal and can be used to solve networks, let's only use the word "impedance" for the ratio of voltage phasors to current phasors, and thus only with respect to sinusoidal waveshapes.

 

..........................

How do you determine the impedance if the wave is made up of an infinite number of harmonics? If you add the sum of each one then you get infinite impedance???

You are trying to determine an "impedance" where impedance has no real meaning or use. It's a nonsensical question, at least at the engineering level.

 

Ok,

So I have been studying Fourier analysis and transform videos on youtube.
I see that by adding a DC component the pulse may be made unipolar.
What I'm still not understanding is this.

How do you determine the impedance if the wave is made up of an infinite number of harmonics? If you add the sum of each one then you get infinite impedance???

Waves do not have impedances.

The impedance of an inductor is (jωL).

The waveform you are applying has many different frequencies. Each frequency sees a device having the impedance that the inductor has at that particular frequency.

 

Ok,

I must be asking a question that is beyond my knowledge.
So, where do I start to learn about Fourier and Laplace transforms and analysis? I have only been as far as high school algebra.
Where should I start?

 

The path to Lapalce and Fourier transforms leads directly through the Calculus: both differential and integral. The good news is that if you are comfortable with high school algebra, the rudimentary mechanics of calculus are not that difficult. A deep understanding of and the ability to prove theorems is more challenging.

 

Ok,
...
How do you determine the impedance if the wave is made up of an infinite number of harmonics? If you add the sum of each one then you get infinite impedance???

No you don't. It depends entirely on the relative magnitude of the terms. In the Calculus you might study sequences and series. One of the things that you find is that many infinite series add up to a finite value. There is even an online encyclopedia of sequences and series along with their sums.

https://oeis.org/

or check out the wiki on convergent and divergent series
http://en.wikipedia.org/wiki/Convergent_series

 

Because the V/L is your rate of current change over time then 100A/50uS is 5mA. This is how long the charge is flowing for before you turn it off. The longer the on time the higher the current. As long as the rise time is much much smaller than the pulse width then the above holds true doesn't it.
Adam

 

Because the V/L is your rate of current change over time then 100A/50uS is 5mA. This is how long the charge is flowing for before you turn it off. The longer the on time the higher the current. As long as the rise time is much much smaller than the pulse width then the above holds true doesn't it.
Adam

What rise time?

Before you turn what off? The voltage? If you turn the voltage off (i.e., force it to 0V), what happens to the current? It keeps flowing!

 

Ok,

I must be asking a question that is beyond my knowledge.
So, where do I start to learn about Fourier and Laplace transforms and analysis? I have only been as far as high school algebra.
Where should I start?

You probably start where the rest of us started - in a learning environment where that material is taught in a systematic manner. If that doesn't suit or is impractical then it will be a hard slog teaching yourself. Whilst a stong mathematical foundation is a great benefit the real challenge is grasping the physical truths.

 

Ok,

I must be asking a question that is beyond my knowledge.
So, where do I start to learn about Fourier and Laplace transforms and analysis? I have only been as far as high school algebra.
Where should I start?

Pretty much all learning involves asking (or being asked) questions that are beyond our knowledge. So don't let that bother you.

But you ARE trying to bite off a whole lot in one fell swoop. Laplace transforms are typically taught at the very end of a course in Differential Equations, which in turn typically follows three semesters of Calculus, which follows Trigonometry, which follows Geometry, which follows High School Algebra.

If ALL you want to know are Laplace and Fourier transforms, then you could probably tighten things up somewhat, but you still have a significant hill to climb.

The fundamental concepts of Calculus are actually quite easy to grasp -- but if you don't have solid algebra, trig, and geometry (and ideally analytic geometry) skills as your foundation, the mechanics of any practical application will quickly overwhelm you.

 

What rise time?

Before you turn what off? The voltage? If you turn the voltage off (i.e., force it to 0V), what happens to the current? It keeps flowing!

I think the original question was has the pulse width anything to do with the maximum current not what will happen to the current in time. The 50us pulse is what will give you the maximum current for that duration. Yes the current will carry on forever in an ideal inductor but it won't increase. If you increase the on time then you will increase the maximum current. I think that's what he means.
Sorry if I am missing something.
Thanks
Adam

 

Pretty much all learning involves asking (or being asked) questions that are beyond our knowledge. So don't let that bother you.

But you ARE trying to bite off a whole lot in one fell swoop. Laplace transforms are typically taught at the very end of a course in Differential Equations, which in turn typically follows three semesters of Calculus, which follows Trigonometry, which follows Geometry, which follows High School Algebra.

If ALL you want to know are Laplace and Fourier transforms, then you could probably tighten things up somewhat, but you still have a significant hill to climb.

The fundamental concepts of Calculus are actually quite easy to grasp -- but if you don't have solid algebra, trig, and geometry (and ideally analytic geometry) skills as your foundation, the mechanics of any practical application will quickly overwhelm you.

I don't have time for math - I would rather toast something ...

 

Ok,

I must be asking a question that is beyond my knowledge.
So, where do I start to learn about Fourier and Laplace transforms and analysis? I have only been as far as high school algebra.
Where should I start?

I have done analog design for all my career and have seldom used Fourier analysis or Laplace transforms. Most of what you need to do for circuit design and analysis can be done using algebra along with basic calculus and an understanding of complex numbers. So where you start depends upon what you really want to do.

For example, your question about the impedance of an inductor when driven by a square-wave is really not a question that has a simple answer as far as the understanding of the circuit operation. That's why you received a number of varied answers. Using Fourier analysis and Laplace transforms is a very complicated way to get that answer and ultimately not very useful from a practical standpoint. The answer to what current goes through the inductor from a square-wave or pulse is most easily determined by using time-domain analysis, not frequency-domain analysis.

So, to repeat, what will be the purpose/use of the knowledge you want to obtain? That will tell you where to start.