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160 2. Tutorial
In[27]:= twoportmna = CircuitEquations[twoport];
DisplayForm[twoportmna]
Out[28]//DisplayForm=
1
RB
CM s CM s 1 0 V$1 0
1
gm CM s
RO
CM s 0 1 V$2 0
. ⩵⩵
1 0 0 0 I$V1 V1
0 1 0 0 I$V2 V2
In[29]:= ypar = Solve[twoportmna, {I$V1, I$V2}]
V1 CM RB s V1 CM RB s V2
Out[29]= I$V1
,
RB
I$V2 gm CM s V1
1 CM s V2
RO
The Y-parameters of the two-port circuit are given by the coefficients of V1 and V2 on the right-hand
sides of the solutions.
In[30]:= yrhs = {I$V1, I$V2} /. First[ypar];
MatrixForm[yrhs]
V1CM RB s V1CM RB s V2
Out[31]//MatrixForm=
RB
gm CM s V1
1 CM s V2
To set up the Y-matrix we must extract the coefficient matrix from these two linear expressions, for
example by computing the Jacobian with respect to V1 and V2.
In[32]:= JacobianMatrix[eqs_, vars_] := Outer[D, eqs, vars]
In[33]:= ymatrix = JacobianMatrix[yrhs, {V1, V2}];
MatrixForm[ymatrix]
RO
1CM RB s
Out[34]//MatrixForm=
RB
gm CM s
1
RO
CM s
CM s
2.9.6 Advanced Transistor Modeling
Implementation of MOS Models with Inline Design-Point Information
By using the value-field keywords Value and Symbolic we can provide design-point information
in subcircuit or model definitions. However, directly specifying numerical values in the netlist definition
of a model object hardly makes sense because, in general, different model instances have
different sets of design-point values. Therefore, instead of treating these values as global quantities
we must pass individual parameter sets to every model instance.
The techniques for passing parameters to subcircuit instances have already been dealt with in
Chapter 2.3, and the same approaches can be used to handle instance-specific design-point information.
Here, we just have to observe the additional requirement that every element in a model netlist now
needs two symbolic parameters: one that represents the symbolic value of the element and one that
is replaced by the associated numerical value during subcircuit expansion.