| Electronics > Beginners |
| Laplace transforms, Bode plots, transfer functions |
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| lordvader88:
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 ? |
| Benta:
Pole/Zero plots in the complex plane (stability analysis). |
| rstofer:
--- Quote from: Benta on September 06, 2018, 10:47:04 am ---Pole/Zero plots in the complex plane (stability analysis). --- End quote --- With the ever popular Spirule: http://www.nzeldes.com/HOC/Spirule.htm Today, I would use MATLAB for all of this stuff. |
| rstofer:
--- Quote from: lordvader88 on September 06, 2018, 08:29:11 am ---What else do they teach for Bode plots, transfer functions ? --- End quote --- Besides 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 |
| Mattjd:
--- Quote from: lordvader88 on September 06, 2018, 08:29:11 am ---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 ? --- End quote --- So 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. |
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