Texas Instruments TI-89 Tip List page 139

w 0 s
G ( s ) =
w 0
s 2 +
Q
This is the general transfer function for a 2nd-order bandpass filter, with unity gain at the center
frequency. In general
s = jw j = −1
where
(Electrical engineers use j for the complex unit, but the TI-89/92+ use i).
In the frequency domain, we work with frequencies in radians/second, not Hz, so first we convert the
frequencies of interest:
10 Hz = 62.83 rad/sec
100 Hz = 628.3 rad/sec
1000 Hz = 6283 rad/sec
Substituting the values in the transfer function we have
62.83s
G ( s )
s 2 +57.12s+394761
At the calculator command line, we define this function by entering
(62.82*s)/(s^2+57.12*s+394761)→g(s)
Make sure that Exact/Approx mode is set to Approx, the angle mode is set to Radian, and the Complex
Format is set to Rectangular.
Create the logarithmic frequency list using loglist() from tip 3.22. We will plot 50 points between the
frequencies of 62 and 6300. Since I have loglist() stored in the \util folder, the command is
util\loglist(62,6300,50)→flist
and the list is stored in flist. flist looks like this: {62, 68, 74.6, 81.8, .... 4774, 5237, 6300}
To create the list of transfer function magnitudes at each frequency, use
20*log(abs(g(i*w)))|w=flist→mag
The expression 20*log() converts the magnitudes to decibels, which are typically used to express
transfer function gain. The built-in abs() function is used to find the magnitude of the complex result of
the transfer function, and i is the complex unit, not the letter "i". The magnitudes are stored in the list
mag.
To create the list of transfer function phase angles, use
angle(g(i*w))*(180/Œ)|w=flist→phase
*(180/Œ)|
The expression
want to plot the phase angle in radians. The resulting list is stored in the variable phase.
s+w 0 2
is used to convert the phase angles from radians to degrees. Omit it if you
where w = 100 Hz and Q = 11
0
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