Solving A Large System Of Complex Equations - HP -15C Advanced Functions Handbook

128 Section 4: Using Matrix Operations
Solving a Large System of Complex Equations
Example: Find the output voltage at a radian frequency of
u> = 15 X 10
3
rad/s for the filter network shown below.
V= 10 volts
R! = 100 ohms
R
2
= 10
6
ohms
# = 10
5
ohms
L = 10"
2
henry
Ci = 25 X 10"
8
farad
C
2
= 25 X 10'
6
farad
Describe the circuit using loop currents:
0
(-•R
2
)
/a>C
2
+ia
-M)
0
0
>L) (-iwL)
(Rz+inL-i/uCz)
h
h
Is
It
V
0
0
0
Solve this complex system for 7
1;
7
2
, ^3, ^
n
d I\. Then VQ = (R^I^.
Because this system is too large to solve using the standard method
for a system of complex equations, this alternate method (described
in the owner's handbook) is used. First, enter the system matrix
into matrix A in complex form and calculate its inverse. Note that
wL = 150,1/wCi = 800/3, and l/a>C
2
= 8/3.
Keystrokes Display
000-
Program mode.
Clears program memory.