TI-84 Plus CE: Bode Plots of Transfer Functions
Introduction
The problem BODEPLOT (2021) plots the Bode plot of a transfer function in the form:
f(s) = ( (s - z1) (s - z2) (s - z3) * ... ) / ( (s - p1) (s - p2) (s - p3) * ... )
where:
z_i = zeros of the transfer function
p_i = pole of the transfer function
s = jw
j = i = √-1
w = frequency
The plot uses a linlog plotting where each x is replaced with 10^x. The y axis represents the conversion y = 20 log_10 ( abs f( 10^x * j) ).
Lists used:
L1: list of zeros
L2: list of poles
L3: x
L4: 20 log_10 ( abs f( 10^x * j) )
You can review the zeros and poles after each entry. Erasing zeros and poles will erase the latest entry.
TI-84 Plus CE Program: BODEPLOT
Version 5.3 and above
"EWS 2021-05-02"
ClrHome
Disp "TRANSFER FUNCTION","F(S)=(S-ZERO).../(S-POLE)","S=JW 10^(W),20log(abs())"
Pause
a+bi
0→A
0→B
0→Z
Lbl 0
toString(A)+" ZEROS, "+toString(B)+" POLES"
Menu(Ans,"ADD ZERO",1,"ADD POLE",2,"ERASE LAST ZERO",3,"ERASE LAST POLE",4,"REVIEW",5,"PLOT",6)
Lbl 1
Input "ZERO? ",S
If A=0
{S}→L1
If A>0
augment(L1,{S})→L1
A+1→A
Goto 0
Lbl 2
Input "POLE? ",S
If B=0
{S}→L2
If B>0
augment(L2,{S})→L2
B+1→B
Goto 0
Lbl 3
If A>1
Then
A-1→A
A→dim(L1)
Else
0→A
DelVar L1
End
Goto 0
Lbl 4
If B>0
Then
B-1→B
B→dim(L2)
Else
0→B
DelVar L2
End
Goto 0
Lbl 5
ClrHome
If A>0
Then
Disp "ZEROS:"
Pause L1
End
If B>0
Then
Disp "POLES:"
Pause L2
End
Goto 0
Lbl 6
For(I,-6,6)
1→N
If A>0
prod(i*10^(I)-L1)→N
1→D
If B>0
prod(i*10^(I)-L2)→D
If Z=0
Then
{I}→L3
{20log(abs(N/D))}→L4
1→Z
Else
augment(L3,{I})→L3
augment(L4,{20log(abs(N/D))})→L4
End
End
FnOff
PlotsOff
-7→Xmin
7→Xmax
1→Xscl
min(L4)-.5→Ymin
max(L4)+.5→Ymax
10→Yscl
Plot1(xyLine,L3,L4)
PlotsOn 1
DispGraph
You can download the zip file here.
Examples
f(s) = 1/(s-3)
Poles: { 3 }
f(s) = s-0.5
Zeros: { 0.5 }
f(s) = ((s+2)(s-2))/((s-1)(s-3))
Zeros: { -2, 2 }
Poles: { 1, 3}
f(s) = (s-4)/((s+1)(s-3))
Zeros: { 4 }
Poles: { -1, 3 }
Eddie
All original content copyright, © 2011-2021. Edward Shore. Unauthorized use and/or unauthorized distribution for commercial purposes without express and written permission from the author is strictly prohibited. This blog entry may be distributed for noncommercial purposes, provided that full credit is given to the author.
