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76 2. Tutorial
2.4.3 Circuit Equation Formulations
Modified Nodal Analysis
The modified nodal analysis method (MNA) has already been introduced as the default formulation
by which Analog Insydes sets up circuit equations. The MNA formulation is general, yields
relatively compact systems of equations, and is easy to implement on a computer. These and a
few other favorable properties have made it the most widely used analysis method in electrical
circuit simulators, including Analog Insydes.
There are a number of user-settable options which have an influence on the way Analog Insydes
sets up MNA equations. You have already encountered the netlist option Pattern which specifies
explicitly whether to use the impedance or admittance fill-in pattern for an immittance element, i.e.
a two-terminal admittance or impedance. This option allows, for instance, to prevent the implicit
conversion of an impedance to an admittance, thereby augmenting the MNA system by the branch
current of the impedance. However, the Pattern option pertains only to the element in whose
value field it is given. To prevent implicit impedance conversion globally you can set the value
of the CircuitEquations option ConvertImmittances to False, either permanently by modifying
Options[CircuitEquations] using the SetOptions directive, or temporarily by passing the option
ConvertImmittances −> False to the function CircuitEquations:
In[8]:= CircuitEquations[rlcfilter,
ConvertImmittances −> False] // DisplayForm
Out[8]//DisplayForm=
0 0 0 1 1 0 0 V$1
0 C1 s 0 0 1 1 0 V$2
0 0 C2 s 0 0 1 1 V$3
1 0 0 0 0 0 0 . I$V0 ⩵⩵
1 1 0 0 RA 0 0 I$RA
0 1 1 0 0 L1 s 0
I$L1
0 0 1 0 0 0 RB
I$RB
0
0
0
V0
0
0
0
The Formulation Option
With modified nodal analysis being the default analysis method there is usually no need to request
this formulation explicitly. However, if you have changed the default settings in
Options[CircuitEquations] or if you wish to use one of the analysis methods to be discussed in
the following subsections you need to specify the formulation as an option to CircuitEquations.
The option keyword is Formulation, and the option value can be either
ModifiedNodal, SparseTableau, or ExtendedTableau. Hence, modified nodal analysis can be
explicitly selected by this command: