Designing Filters with the Ti-84 plus (CE)

Explanation of how to design and redesign filters

Description

A method is shown to design electrical filters. Very useful for Electrical Engineering. As an example, we take a low pass filter consisting of a resistor of 1000 Ohm and a capacitor of 4,7 nF =0.00471uF. See the scheme.

The complex transfer function of this filter equals : Vout/Vin= 1/(1+i2πXR1C1) where X is the frequency (Hz) of the input Voltage. The value of R is stored in memory R, and the value of C is stored in memory C.

Using Y1 as the logarithmic absolute value of the transfer function for the Bode plot and Y2=-3 (dB) the Ti calculates the bandwidth (33782,44 Hz) by using the command intersect.

Formula of the transfer function of the RC filter

Output of the Analysis of the RC filter. Note the -3dB line for calulating the Bandwith

Calulating the Bandwidth of the low pass filter

Redesign

Next: Two examples are shown by using the numeric solver in the math menu to redesign the filter.

New bandwidth, 25000 Hz and capacitor 4.7nF results in a new resistor value of 1351.29 Ohm.

A bandwidth of 1000Hz and a resistor of 1000 Ohm results in a capacitor of 15.87nF.

Calculating new resistor value and Capacitor value for a new desired Bandwith

Input for the equation solver for new R value for a new bandwith of 25000 rad/sec

Result for new R value for a new desired bandwith of 25000 rad/sec000 rad/sec

A bandwidth of 1000Hz and a resistor of 1000 Ohm results in a capacitor of 15.87nF

Calculating new capacitor value for bandwidth of 25000 rad/sec and constant R value of 1000 Ohm