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Final 3

This document presents equations modeling the behavior of an electrical circuit containing inductors and capacitors. It first derives differential equations describing the current in two inductors over time based on the circuit components. It then expresses the voltage across the inductors and capacitors in terms of the circuit currents and components. Finally, it derives additional differential equations for the rate of change of current in the inductors using a loop equation approach.

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Butta Rajasekhar
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51 views1 page

Final 3

This document presents equations modeling the behavior of an electrical circuit containing inductors and capacitors. It first derives differential equations describing the current in two inductors over time based on the circuit components. It then expresses the voltage across the inductors and capacitors in terms of the circuit currents and components. Finally, it derives additional differential equations for the rate of change of current in the inductors using a loop equation approach.

Uploaded by

Butta Rajasekhar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
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 iL1RL1  vC1   v0  0

RL1 di R R
iL1 RL1  vL1  v0  L1 L1  iL1 L1 L11  v0
RL1  RL11 dt RL1  RL11
diL1
 L1  iL1 K 5   iL1  iL 2  K1  vC 2 K 2 
dt
diL1
L1  iL1  K 5  K1   iL 2 K1  vC 2 K 2
dt
diL1    K1  K 5     K1   K2 
 iL1    iL1    vC 2  
dt  L1   L1   L1 
diL 2    K1  K 2     K1   K2 
similarly  iL11    iL 2    vC 2  
dt  L11   L11   L11 
Mode  3
from Mode  2 we had v0  iLx  iL1  iL11 
RRC 2 R
v0  (iLx  iL 2 )  vC 2
R  RC 2 R  RC 2
from Mode  3We have
vL1  iL1RL1  (vL11  iL11RL11 )  v0
vL1  v0  iL1RL1
RRC 2 R
 (iL1  iL11  iL 2)  vC 2  iL1RL1
R  RC 2 R  RC 2
Similarly
RRC 2 R
vL11  (iL11  iL11  iL 2)  vC 2  iL11RL11
R  RC 2 R  RC 2
(OR )
from Loop equation we have
vL1  iL1RL1  iL11RL11  vL11  0
diL1 1
  iL1RL1  iL11RL11    (1)
dt 2 L1
diL 2 1
 [iL1RL1  iL11RL11]    (2)
dt 2 L11
from Mode  (2) we have

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