§ 17-6 Writing a set of normal form equations
1,Establish a normal tree.
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?
??
),(,)(c o t
),(,
RiLic h o r d sr e e
RCb r a n c h e st r e e
ds
ds ??
2,Assign voltage and current variables,Assign a voltage
(with polarity reference) to every capacitor and a
current (with arrow) to every inductor; there are the
state variables.Indicate the voltage across every tree
branch and the current through every link in terms of
the source voltages,source currents,and the state
variables,if possible; otherwise,assign a new voltage or
current variable to that resistive tree branch or link.
3,Write the C equations(KCL)--fundamental cutset.
4,Write the L equations(KVL)--fundamental loop.
5,Write the R equations(if necessary).
6,Write the normal form equations,Substitute the
expressions for each into the equations
obtained in steps 3 and 4,thus eliminating all resistor
variables.
RR iand?
The network contains a loop in which every element is a
capacitor or voltage source,the other occurs if there in a node or
supernode that is connected to the remainder of the circuit only by
inductors and current sources.
When either of these events occurs,we meet the challenge by
leaving a capacitor out of the tree in one case and omitting an
inductor from the cotree in the other.
2
2
8.13.0)3(3.0 '113.0 t
t
H teidt
eid ?? ?????
22 124)3(4 114 tt eiei ??? ?????
)(5)305.4(10 21'1 2 tutteiior t ????? ?
Solution:
0)(21248.13.01.0 21'1'1 22 ??????? ?? tuteiteii tt1i
23 te?
)3( 21 tei ??
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?
)(2 2 tut
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H1.0
Vtut )(2 2
Ae t23 ?
H3.0
4
Example:
1,Establish a normal tree.
?
?
?
?
??
),(,)(c o t
),(,
RiLic h o r d sr e e
RCb r a n c h e st r e e
ds
ds ??
2,Assign voltage and current variables,Assign a voltage
(with polarity reference) to every capacitor and a
current (with arrow) to every inductor; there are the
state variables.Indicate the voltage across every tree
branch and the current through every link in terms of
the source voltages,source currents,and the state
variables,if possible; otherwise,assign a new voltage or
current variable to that resistive tree branch or link.
3,Write the C equations(KCL)--fundamental cutset.
4,Write the L equations(KVL)--fundamental loop.
5,Write the R equations(if necessary).
6,Write the normal form equations,Substitute the
expressions for each into the equations
obtained in steps 3 and 4,thus eliminating all resistor
variables.
RR iand?
The network contains a loop in which every element is a
capacitor or voltage source,the other occurs if there in a node or
supernode that is connected to the remainder of the circuit only by
inductors and current sources.
When either of these events occurs,we meet the challenge by
leaving a capacitor out of the tree in one case and omitting an
inductor from the cotree in the other.
2
2
8.13.0)3(3.0 '113.0 t
t
H teidt
eid ?? ?????
22 124)3(4 114 tt eiei ??? ?????
)(5)305.4(10 21'1 2 tutteiior t ????? ?
Solution:
0)(21248.13.01.0 21'1'1 22 ??????? ?? tuteiteii tt1i
23 te?
)3( 21 tei ??
?
?
)(2 2 tut
?
?
H1.0
Vtut )(2 2
Ae t23 ?
H3.0
4
Example:
