Capacitors: Math

by 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 my own understanding, and then I share it in the hope of finding my own mistakes and possibly helping others.

I have put everything into a single pdf document here: 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. Here’s an outline of the whole document:

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

If you have any comments, please post them!

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2 Responses to “Capacitors: Math”

  1. software development london said:

    Humm… interesting,

    I read your document and it seems write to me don’t worry you are teh best

    Keep up the good work

    Posted 18.08.2009 at 3:30 am

  2. Abhishek said:

    It is verry usefull,

    a request:

    send electronics ebook to my email

    Posted 01.10.2010 at 7:45 am