Laplace transforms, Bode plots, transfer functions - Page 1
Forum section: electronics / beginners

author: lordvader88
author_rank: Frequent Contributor
timestamp: September 06, 2018, 08:29:11 am
content: I've done LT's before and I'm reviewing them. I'm new to BP's and transfer functions. I really want to learn them for what they call "type 2 compensators" , using the op-amp nature of a TL431 adjustable voltage reference.I have some design guide's on using them, and had to go back and refresh LT's and now LT's on ODE's. I've done most of the complex number stuff for this before, repeatedly, for different subjects.What else do they teach for Bode plots, transfer functions ?

author: Benta
author_rank: Super Contributor
timestamp: September 06, 2018, 10:47:04 am
content: Pole/Zero plots in the complex plane (stability analysis).

author: rstofer
author_rank: Super Contributor
timestamp: September 06, 2018, 02:18:31 pm
content: Quote from: Benta on September 06, 2018, 10:47:04 amWith the ever popular Spirule:http://www.nzeldes.com/HOC/Spirule.htmToday, I would use MATLAB for all of this stuff.

author: rstofer
author_rank: Super Contributor
timestamp: September 06, 2018, 02:22:47 pm
content: Quote from: lordvader88 on September 06, 2018, 08:29:11 amBesides the obvious use of Bode' plots to display phase and gain of things like filters, they are used for phase and gain margin to prove stability of closed loop systems by analyzing the open loop system.http://www.mit.edu/afs.new/athena/course/2/2.010/www_f00/psets/hw3_dir/tutor3_dir/tut3_g.html

author: Mattjd
author_rank: Regular Contributor
timestamp: September 06, 2018, 03:02:46 pm
content: Quote from: lordvader88 on September 06, 2018, 08:29:11 amSo you take your linear circuit and define the input and the output through some differential equations, you take the ratio of the two (input over output) and you have the transfer function. Taking the laplace transform of that function opens up an entire field of analysis called control theory, which deals with the stability of the system. This is the transient side of things i.e. how does your system act when turned on (an impulse), how does it react to a certain input, does it overshoot its target, undershoot? How fast does it respond, is that too fast or too slow? These are all questions that are answered with control theory, and can be tuned by adding the appropriate compensators using OP amps, this is known as PID control.If you wait for the transients to go away, you are now dealing with frequency analysis which is dealt with by fourier transform. Note that in the laplace transform, s = sigma + j*omega, where omega is the frequency and sigma is some dampening factor. If the laplace transform of the transfer function has an ROC (region of convergence) that contains the imaginary axis (j*omega axis) then assuming no transients (dampening factor i.e. sigma = 0) then you are now in the frequency domain, which is what you would get if you took the fourier transform of the transfer function to begin with. Hence, the fourier transform is a special case of the laplace transform, notably when there are no transients. This is known as steady state analysis.So for linear circuits you have steady state analysis, where you look at the system by the frequency, this used for filter. Then you have transient analysis, were you look at the frequency and the dampening factor, this is used for controls/stability.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: September 06, 2018, 07:17:19 pm
content: 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.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

author: lordvader88
author_rank: Frequent Contributor
timestamp: September 08, 2018, 10:25:59 pm
content: 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 yearsYup more to learn in order to understand where the 1st few eqn's in that TL431 design guide comes from.

author: Nitrousoxide
author_rank: Regular Contributor
timestamp: September 09, 2018, 01:59:49 am
content: 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.

author: rstofer
author_rank: Super Contributor
timestamp: September 09, 2018, 02:04:26 am
content: Quote from: lordvader88 on September 08, 2018, 10:25:59 pmKhan 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.

author: JugglingElectrons
author_rank: Contributor
timestamp: September 23, 2018, 05:45:04 am
content: 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.