INTRODUCTION TO VHDL-AMS
69
reference node linearly depends on the equations for the other nodes. Thus, it
will not be part of the system of network equations. Kirchhoff's Voltage Law
(KVL) requires that the sum of branch voltages of a mesh with respect to
their orientation equals zero. The equations which result from Kirchhoff's
laws can be automatically established on the base of the network graph. That
means they only depend on the network topology (see Figure 6-7 for the
example).
Furthermore, the voltage-current constitutive relations of the branches
must be fulfilled. These equations define further restrictions to branch
voltages and currents (see Figure 6-8 for the example). They must be
independent of the equations given by Kirchhoff's laws.
R1
v
R1
i
R1
v
in
(t)
i
q
v
q
C
i
D
i
C
v
D
v
C
voltage source =>
0
)
(t
v
v
in
q
resistor R1 =>
1
1
1
R
R
i
R
v
diode =>
,...)
(
D
D
v
f
i
capacitor =>
dt
dv
C
i
C
C
Figure 6-8.
Symbols to describe the constitutive relations of branches
Conclusions
All these conditions (KCL, KVL, constitutive relations) must be fulfilled
by the branch voltages and currents that solve the network analysis problem.
A differential algebraic system of equations has to be evaluated:
0
)
,
,
,
(
t
p
dt
dx
x
F
with
n
R
x
)
,
0
[
:
(time
)
,
0
[
x
and fixed parameters
m
R
p
)
Summary :
A differential algebraic system of equations has to be evaluated: 0 ) , , , ( t p dt dx x F with n R x ) , 0 [ : (time ) , 0 [ x and fixed parameters m R p )
Tags :
equations,network,relations,figure,kirchhoffs,constitutie,branch,oltages,example,see,laws,system,branches