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Deriving transfer equations of active filters with Wolfram Language

POSTED BY: Isaac Ayala Lozano
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Issac have you seen these built-in filters: Linear and Nonlinear Filters and specifically LowpassFilter ? I still think you work has educational value as you derive things from scratch. Perhaps it would also be interesting to compare your filters to built-in ones.

POSTED BY: Sam Carrettie

Hi Sam, I did not know about the existence of those functions. I'll play around with them later.

I still think you work has educational value as you derive things from scratch

I'm glad the point got accross, I made the post with the intention of showing how Mathematica can be integrated at an introductory level for Electronics. And sure, the automated functions are always faster to implement in code; my focus was to test development from the physical implementation perspective with limited values available for components (standard capacitor and resistor values).

The next step with the code is to set a Manipulate[] function which could solve the system of equations for the missing quantities and compare that to the standard equations used in Electronics to define resistor and capacitor values.
POSTED BY: Isaac Ayala Lozano

enter image description here - Congratulations! This post is now a Staff Pick as distinguished on your profile! Thank you, keep it coming! In future it is a good idea to add some meaningful outputs (as we did for formulas in your post) and possibly attach the notebook. We could not understand if meant this as a valid Wolfram Language syntax:

H(s) = Voutput / Vinput (* Transfer function equation in control theory*)
LP = vout/vin /. {solutionLP} (* Transfer function for the Low Pass Filter *)
POSTED BY: EDITORIAL BOARD

Isaac,

Nice presentation.

You may also be interested in Wolfram SystemModeler. It will derive the equations from the circuit diagram. For more complicated circuits it is a big time saver. Also, it is well integrated with Mathematica so you can do Mathematica analysis on the equations, optimize parameters, etc. Some things are easier in Mathematica and some things are easier in SystemModeler so it is good that they are well integrated.

Regards
POSTED BY: Neil Singer

Hi Neil,

I do agree with the simplicity that SystemModeler offers, and have enjoyed using it since June. I may make a comparison for higher order filters as a followup post just to show the benefits of the object representation.

I made the example with Mathematica because it's readily available at my university (Site license) and I am preparing a proper presentation to distribute to engineering students later in the year to aid their courses which will include both products. Hope to share it with all of you soon!
POSTED BY: Isaac Ayala Lozano
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