Electronics > Beginners
Laplace transforms, Bode plots, transfer functions
T3sl4co1l:
Incidentally, if you start with the differential form -- some function for input, plus derivatives of the output -- you can plug in a function and get a result directly. Well, with the small cost of still having to solve the differential equation. :P But, that can be done one small step at a time, if nothing else.
Which is precisely what SPICE does in the transient analysis mode: implicit integration, to solve the differential equation, given stimuli (arbitrary sources) and some system (the circuit and model you've entered). :)
When you do AC analysis, it's a small signal steady state analysis. That is, nonlinearities are approximated as various linear gains between points. Everything is set based on the DC operating point analysis, so if you've set up the circuit for the wrong operating point. (This can happen, where in transient mode, there's a big spike in the first few time steps (microseconds, picoseconds, who knows..) as the circuit settles from an incorrectly calculated DC operating point, to its correct instantaneous level.)
The AC analysis transfer function need not be straightforward, but it can still be approximated with poles and zeroes; this is what the Transfer Function analysis does (I never found it too useful, myself; it's too hard to spot the dominant poles and zeroes.)
Tim
lordvader88:
Ok I looked up a bit more, thanks, but not much, it's the weekend.
So far when I've done LT, I've only considered the s-variable as real, thats how they usually start when teaching it/books. I haven't really done much formal stuff from a book on algebra or calc. w/ complex numbers.
And no signal theory really either. A lot of "log stuff" I'm ok at math-wise but don't know all the physics relations that go with that. I need to do a crash course, lots of utube videos for that I'm sure.
I've started FT a few times, now it's time to learn/remember the main stuff.
Doing math/sci as a hobby over the years means I often never learn/practice or remember stuff like in real school, too bad I won't live billions of years
Yup more to learn in order to understand where the 1st few eqn's in that TL431 design guide comes from.
Nitrousoxide:
These topics are covered in detail by many control systems textbooks. A good one to start with is Norman S. Nise, "Control Systems Engineering".
It covers differential equation, laplace domain, compensator design by bode plot, root locus plots, lead/lad compensators and many forms of stability criterion (routh hurwitz) and many more topics.
rstofer:
--- Quote from: lordvader88 on September 08, 2018, 10:25:59 pm ---Doing math/sci as a hobby over the years means I often never learn/practice or remember stuff like in real school, too bad I won't live billions of years
Yup more to learn in order to understand where the 1st few eqn's in that TL431 design guide comes from.
--- End quote ---
Khan Academy has an Electrical Engineering track. It doesn't go as far as I would like but the Math track does have Laplace Transforms and Fourier Transforms. These Math topics are from a math point of view, not necessarily an EE view. Still Khan Academy is really good.
If you're up for paying for education, CalcWorkshop.com goes from Algebra up through Laplace Transforms. I didn't see Fourier Transforms right off the bat, it may be in there somewhere. The nice thing about this program is that it follows the sequence taught at our Community College using the text by Stewart. For Calc 2, the sequence is nearly a dead match to the college lecture sequence.
I paid for the first year and my grandson got an 'A' in Calc I. Yup, I'll buy the 2d year. And all the rest for that matter. In fact, I spend quite a bit of time there refreshing what I have forgotten decades ago.
BTW, if you want a sample of the CalcWorkshop courses, the one on "Limits" is free. As "Limits" are the underlying concept for Calculus, this is where all the excitement starts.
JugglingElectrons:
One of the things I find fascinating is the bridge between classic Phasor calculations (popularised by Charles Proteus Steinmetz) and the Laplace Transformed circuits.
With Phasors you solve the steady state output of an AC circuit with a pure sinusoidal input voltage. Laplace transforms and transfer functions allow you to not only get the steady state, but the transient On/Off periods and it extends the inputs beyond sinusoids to exponentials, etc. In other words Phasors are more like a special case and the Laplace Transformations are extending it to the general case.
Essentially you take the circuit in the time domain and transform it to the frequency domain. After you have the transfer function, Vout(s)/Vin(s), in the s domain (s = jw complex frequency), you multiply by the input voltage in the s domain to get the output voltage in the s domain. Then you can take the inverse Laplace transform to get the output voltage in the time domain!
I do really like Bode Plots as well. Being able to see how a circuit performs over its frequency range at a glance is a wonderful thing. Filters and Bode Plots go hand in hand so anyone wanting to study some cool amplifier and audio circuits should be familiar with them.
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