This program simulates the response of a resonant filter to an input signal.
A resonant filter is a circuit composed of an inductor with inductance L, a resistor with resistance R, and a capacitor with capactiance C.
A known input voltage V_{in} is applied, and the response voltage V_{out} is measured.
The equation that governs the circuit can be determined by applying Kirchoff's Laws. Assume that the measuring device draws no current, and let the current that flows across the resistor, capacitor, and inductor be called I. Then
At the same time, we know that
Thus, if we substitute the second of these into the first, we obtain the following second order differential equation for the output voltage V_{out}
Entries marked with a ☼ can be expanded to give more information by clicking on them.
Inductance, Capacitance and Resistance ☼

Initial Data ☼


Input Signal ☼


Numerical Method ☼


End Time ☼


Preferred Frequency ☼

The input graph shows the input signal V_{in}. It is the sum of the three input signals that the user can control. 

The output graph shows the output signal V_{out.} 

The windows for the input signal and the output signal can be resized. 

The scale on the graphs can be changed by selecting the change scale item on the menu.

Aside from showing the solution to the second order differential equation that describes the resonant filter, there are two other useful demonstrations that this software can perform.
First, it is known that solutions of a second order differential equation with constant coefficients and a sinusoidal forcing term break up into two components a transient solution and a steady state solution. Simply sliding the bars for the initial data shows quite clearly the presence of a transient solution that depends on the initial data, and a steady state solution that is unaffected by changes in the initial data.
As a second demonstration, choose three different input signals of different frequencies. Set the resistance to a low value, and slide either the inductance or capacitance values so that the preferred frequency varies across the frequencies of your input signals. You will be able to visually pick out the frequencies that correspond to the initial frequencies. It is a nice demonstration of a primitive method for tuning a radio.
This demonstration was originally conceived as a student project in our class Scientific Modeling and Simulation, taught at Towson University. This is an interdisciplinary class which teaches mathematical modeling, numerical methods and computer programming using C++ and MFC.


This work, and the work of developing the course Scientific Modeling and Simulation has been supported by the National Science Foundation, through grand DUE9952625. 

This program is distributed with the source code. The program was written in C++ using MFC. Feel free to reuse the source code, but note that I am a mathematician by trade, not a computer programmer. If you find it useful, please let me know. 

This has been written by 

Comments and suggestions for improvement are especially welcome. 