[fwiw] Capacitor Math doc

[gaussmarkov]

for some time, i have been working on a description of some of the math behind equations that we use for passive filters.  i do this kind of writing to check for my own understanding, but then i share it in the hope of finding my own mistakes and possibly helping others.  (yes, i know that can be contradictory ) 

so i'm putting out a draft for comment before integrating it into the non-math description of capacitors i already have in place on gaussmarkov.net (link: http://gaussmarkov.net/parts/capacitors.php).  there's an outline at the end of this post.  the draft is a pdf document that i have placed here: http://gaussmarkov.net/parts/capmath.pdf.

this is not intended for everyone.  to read it, you will need to know enough calculus to differentiate and integrate the exponential function and the sine function and enough trigonometry to have seen the angle sum forumula for the sine function.  i chose not to use phasor notation.  i think that sine functions are more concrete and better for learning this material the first time.

in the spirit of keeping things real (pun intended  ), i included some calculations for the discharging filter caps of an amp with a resistor and some illustrations using the BMP tone stack.

Capacitor Mathematics

• Summary
• Capacitor Behaviour
• Discharging and Charging
  
  
  
  • Differential Equation Solution
  • Discharging
• Discharging a Capacitor with a Resistor
• Alternating Current
• RC Filters
  
  
  
  • The Angle Sum Formula
    
    
    
    • Phase
    • Summing Sine Waves
  • Voltage of the Capacitor: Guess and Check
  • Current
  • Voltage of the Resistor
• High Pass Filter
• Low Pass Filter
• Cut-Off Frequency
• A Final Note

[alanlan]

Good stuff!
I'll print out a copy and have a read in slow time.

It is said that if you want to learn about a subject it's better to write a book rather than read a book.

[gaussmarkov]

great.  if you have any comments, positive or negative or inquisitive, i would appreciate hearing them.

[gaussmarkov]

in case you haven't seen this announcement and are interested ... bump

[jrc4558]

WOW!!!
What a good document!
Thank you very very much!

[gaussmarkov]

WOW!!!
What a good document!
Thank you very very much!

hey constantin, your are very welcome.   

[Arno van der Heijden]

Ah.... another LaTeX user.... 
I love LaTeX! 

[gaussmarkov]

Ah.... another LaTeX user.... 
I love LaTeX! 

and it seems we may also have povray in common, although it's been years since i used it.      i wonder if we are actually twins, separated at birth.