Butterworth Filter Generator for the TI89

Notation: butterwr(n,R_L,R_S,mode,w,BW)

Where:

• N = order of the filter (1,2,3,4,…)
• R_L = load resistance in ohms
• R_S = source resistance in ohms
• mode = low-pass (1), band-pass (2) or high-pass (3)
• w = cut-off (-3dB) frequency in mode 1,3. Center frequency w₀ in mode 2. In radians/sec
• BW = -3dB bandwidth (mode 2) in radians/sec

Calculator modes: angle in RADIAN, display digits in FIX2, exp. format in SCIENTIFIC

Example

5th order Butterworth band-pass filter, center frequency 1000 rad/s, bandwidth 100 rad/s, load resistance is 50-ohm, source resistance is 25-ohm

1. Punch in: butterwr(5,50,25,2,1000,100)
2. The calculator will solve and display the L and C values for the normalized (w_C=1 rad/s and R_L=1-ohm) 5th order Butterworth filter, and then it will PAUSE.
3. Press ENTER. The calculator will scale the impedances so that R_L=50-ohm and display the new element values. The calculator will PAUSE.
4. Press ENTER. The calculator will perform the frequency transformation LP->BP and display the final values of the filter elements. The program ends here.
5. The displayed list can be translated in the following schematic and simulated in PSpice

Simulation Results:

Note that 1000 rad/s is equal to 159.15 Hz and the half-bandwidth is 7.9 Hz