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3.12 Nonlinear Simplification Techniques 411
Define netlist description
of a simple diode rectifier
circuit.
Set up the system of
symbolic time-domain
equations.
Show equation system.
Eliminate variables which
occur linear everywhere.
Show compressed equation
system.
Eliminate variables which
occur linear somewhere.
In[2]:= rectifier =
Circuit[
Netlist[
{V0, {1, 0}, Symbolic −> V0,
Value −> 2. Sin[10^6 Time]},
{R1, {2, 0}, Symbolic −> R1, Value −> 100.},
{C1, {2, 0}, Symbolic −> C1, Value −> 1.*^−7},
{D1, {1 −> A, 2 −> C},
Model −> "Diode", Selector −> "Spice"}
]
]
Out[2]= Circuit
In[3]:= rectifiereqs = CircuitEquations[rectifier,
AnalysisMode −> Transient,
ElementValues −> Symbolic] // UpdateDesignPoint
Out[3]= DAETransient, 4 4
In[4]:= DisplayForm[rectifiereqs]
Out[4]//DisplayForm=
I$AC$D1t I$V0t ⩵⩵ 0, I$AC$D1t
V$2t C1 V$2 ′ t ⩵⩵ 0,
R1
V$1t ⩵⩵ V0, I$AC$D1t ⩵⩵ AREA$D1
1
1. $q V$1tV$2t
TEMP
$k
IS$D1
TEMP 3.
TNOM
TEMP
1.11 1.
TNOM
$q
TEMP $k
GMIN V$1t V$2t,
V$1t, V$2t, I$V0t, I$AC$D1t, DesignPoint
V0 2. Sin1000000 t, R1 100., C1 1. 10 7 ,
AREA$D1 1., GMIN 1. 10 12 , IS$D1 1. 10 14 , TEMP 300.15,
TNOM 300.15, $k 1.38062 10 23 , $q 1.60219 10 19
In[5]:= rectifiercomp = CompressNonlinearEquations[rectifiereqs,
V$2[t], EliminateVariables −> Automatic]
Out[5]= DAETransient, 2 2
In[6]:= DisplayForm[rectifiercomp]
Out[6]//DisplayForm=
1. AREA$D1
TEMP
1.11 1.
TNOM
$q
TEMP $k
1.
1. $q V$1tV$2t
TEMP
$k
IS$D1
TEMP 3.
TNOM
1. GMIN V$1t 1. V$2t
V$2t C1 V$2 ′ t ⩵⩵ 0,
R1
V$1t ⩵⩵ V0, V$1t, V$2t, DesignPoint
V0 2. Sin1000000 t, R1 100., C1 1. 10 7 ,
AREA$D1 1., GMIN 1. 10 12 , IS$D1 1. 10 14 , TEMP 300.15,
TNOM 300.15, $k 1.38062 10 23 , $q 1.60219 10 19
In[7]:= rectifiercomp = CompressNonlinearEquations[rectifiereqs,
V$2[t], EliminateVariables −> All]
Out[7]= DAETransient, 1 1