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2.6 Modeling and Analysis of Nonlinear Circuits 95
In the case of the diode we have two port nodes A and C, which are connected by an electrical port
branch [A, C]. The port current, i.e. i D , is thus designated by Current[A, C] and the port voltage,
i.e. v D , is designated by Voltage[A, C]. Hence, the model equation must be written as
Definition −>
Equations[Current[A, C] == Is (Exp[Voltage[A, C]/Vt] − 1)]
In this example, the Definition contains only one single equation, but there is no limit to the
number of equations. We will discuss some more advanced examples in which this will become
apparent later in this chapter.
A note on interfacing: Some numerical circuit simulators with behavioral model simulation capabilities use the
currents into the pins (port nodes) of a model object and the node voltages at the pins as symbolic quantities
by which the model equations are interfaced with the exterior circuit. This approach is not well suited for other
analysis methods than modified nodal analysis. Using port branches with associated currents and voltages
facilitates setting up other formulations which involve loop equations, such as the sparse tableau.
The Variables Argument
The Variables argument serves to specify the symbols which are unknowns of the model equations.
The diode equation contains two unknowns, Current[A, C] and Voltage[A, C], so the Variables
argument is
Variables −> {Current[A, C], Voltage[A, C]}
The need for the Variables specification may not be entirely obvious here. One might argue that
Analog Insydes should know that port current and voltage identifiers are unknowns. However,
port currents and voltages are not always the only variables of a set of model equations. Similarly
to a subcircuit which may have internal nodes, a behavioral model may also contain internal
variables which are not of the form Voltage[node+, node−] or Current[node+, node−]. Without the
Variables argument, Analog Insydes would not be able to distinguish between internal variables
and global parameters, such as Vt in the diode equation. So, by convention, you must specify all
identifiers in a set of model equations which are neither local nor global parameters, including the
port branch quantities. The complete ABM definition for the diode is then given by
Model[
Name −> Diode,
Selector −> DC,
Ports −> {A, C},
Parameters −> {Is, Global[Vt]},
Variables −> {Current[A, C], Voltage[A, C]},
Definition −>
Equations[Current[A, C] == Is (Exp[Voltage[A, C]/Vt] − 1)]
]