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78 2. Tutorial
In[10]:= CircuitEquations[rlcfilter,
Formulation −> SparseTableau] // DisplayForm
Out[10]//DisplayForm=
1 1 1 0 0 0 0 0 0 0 0 0 V$V0
1 1 0 1 1 0 0 0 0 0 0 0 V$RA
1 1 0 1 0 1 0 0 0 0 0 0 V$C1
0 0 0 0 0 0 1 1 0 0 0 0 V$L1
0 0 0 0 0 0 0 1 1 1 0 0 V$C2
0 0 0 0 0 0 0 0 0 1 1 1 V$RB
.
1 0 0 0 0 0 0 0 0 0 0 0 I$V0
⩵⩵
0 1 0 0 0 0 0 RA 0 0 0 0 I$RA
0 0 C1 s 0 0 0 0 0 1 0 0 0 I$C1
0 0 0 1 0 0 0 0 0 L1 s 0 0 I$L1
0 0 0 0 C2 s 0 0 0 0 0 1 0
I$C2
0 0 0 0 0 1 0 0 0 0 0 RB I$RB
0
0
0
0
0
0
V0
0
0
0
0
0
Sparse Tableau Analysis: The Extended Formulation
Analog Insydes also supports an extended sparse tableau formulation in which the vector of
unknowns comprises the branch voltages v, the branch currents i, and the node voltages v n .
With I denoting an identity matrix of rank n and A T the transpose of the nodal incidence matrix A,
Kirchhoff’s voltage law is expressed indirectly in terms of the node voltages as I v A T v n ⩵ 0.
Therefore, the extended sparse tableau formulation does not require the calculation of a loop matrix,
though at the expense of a larger matrix size than that of the basic variant:
I 0 A
T v 0
0 A 0
I
⩵
0
Y Z 0 v n s
The extended variant is selected by the option setting Formulation −> ExtendedTableau: