Analysis and Simulation of Low Pass and High Filters


Filters are used to extract different frequency components from input signals. A low pass filter extracts the low frequency components from a given signal while a high pass filters outputs the high frequency ones. A first order filter has a single pole in its transfer function. A simple example of a first order filter is a circuit consisting of a resistor and a capacitor in series, commonly known as an RC circuit.

RC circuit - Low and High Pass filter

This tool simulates first order high and low pass filters. Both time domain and frequency domain responses are calculated by this tool. It allows different signals to be simulated and the filter constant adjusted using a slider control. The Bode plots show the frequency response. The response upto the bandwidth is shown as a solid line.

Analysis and Simulation of first order filters



.xlsx file

How to Use

To change the input signal, key in the function using 't' (time) as the variable name with an equal to sign in front. The download file has a square wave input function already entered in. More examples are shown below:

Input Signal

Sine wave input

Change the maximum plot time for the time domain by setting the maximum time value. The range for the Bode plots can be set using the min and max values of the angular frequency in radians/second. 1 radian/second is 1/2π (approximately 0.159155) Hertz.

Use the slider to adjust the filter setting. For an RC circuit, this sets the value of the product R x C.

How it works

A data table under cell C45 is used to evaluate the function at 100 points between t = 0 and the max plot time. This is similar to the function evaluation in the Graphing Calculator Tool.

The Bode plots are generated in a manner similar to the method used in the Bode Plot Generator. Defined formulae are used for all the calculations for the frequency response.

As the first order low pass filter is the same as exponential smoothing, the exponential smoothing formula is used to calculate the low pass filter output. This is subtracted from the input signal to obtain the high pass filter output.

Also See:

Bode Plot Generator

PID Loop Simulator

Nyquist Plot Generator

Nyquist plot