Pi Filter

A pi filter is used to attenuate noise in power and signal lines. This Demonstration shows the output voltage from a DC power supply with a pi filter, which consists of an inductor (choke) between a pair of capacitors, as shown in the schematic in the upper-left corner. You can vary all the component values, including load resistance and internal resistances of the rectifier/input supply and the choke.


  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


The plotted output voltage is computed by solving the system of three differential equations from applying Kirchhoff’s voltage law to each of the three loops of the circuit. We have in mind the high-voltage, low-current application in vacuum-tube audio amplifiers.
The voltage-current characteristic of the rectifier (the function in the program) is typical of a solid-state diode; however, the parameter allows the inclusion of significant internal resistance typical of a vacuum-tube rectifier. The rectifier provides half-wave rectification; we can mimic full-wave rectification by using a full-wave rectified input voltage.
Ripple amplitude (rms) is computed and reported as a percentage of the mean output voltage. This is done by sampling over the last several computed cycles. For large inductance values, transient low-frequency "ringing" causes difficulties in the computation of the ripple amplitude. We attempt to remove the ringing using the Fourier transform. While this improves matters considerably, one should increase the parameter in order to obtain more accurate ripple amplitude calculation for large inductance values. (Unfortunately, the additional computation will cause the controls to become less responsive.)
An input amplitude control is provided for convenience. Input amplitude is 1/2 peak-to-peak, or rms.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+