2.6.2 Defining Behavioral Models

The Argument Sequence of the Model Command for ABM Definitions

Behavioral models are defined using the Model command, just like subcircuits (see Section 2.3.2). Analog Insydes recognizes a request to define a behavioral model by the presence of the named parameter Variables and the absence of a subcircuit Netlist on the right-hand side of the Definition argument in a Model call. The full syntax for an ABM definition is shown below. Again, slanted typewriter font denotes optional arguments.

Model[

Name -> subcircuit class name,

Selector -> selector,

Scope -> scope,

Ports -> port nodes,

Parameters -> parameters,

Symbolic -> symbolic parameters,

Defaults -> defaults,

InitialConditions -> initial conditions,

InitialGuess -> initial guess,

Translation -> parameter translation rules,

Variables -> variables,

Definition -> Equations[equations]

]

Except for the additional arguments and the keyword Definition, all other named arguments of the Model function have the same meaning as for subcircuit definitions. Following, we discuss the two arguments Definition and Variables.

Example: A Diode

Let's illustrate the steps which are necessary to define a behavioral model by implementing a nonlinear device model for a junction diode.

Figure 6.1: Junction diode

The diode shown in Figure 6.1 has two terminals, the anode and the cathode, denoted by the node identifiers A and C, respectively. The branch voltage and the branch current satisfy the device equation

where denotes the reverse-bias saturation current and the thermal voltage. Typical values for are . is given by where denotes Boltzmann's constant (). is the absolute temperature (in Kelvin), and is the charge of an electron ().

In[1]:= <<AnalogInsydes`

In[2]:= ThermalVoltage[T_] := 1.381*10^-23 * T / (1.602*10^-19)

At a temperature of (), is approximately :

In[3]:= ThermalVoltage[300.]

Out[3]=

Since the thermal voltage is only defined in terms of constants and the global quantity temperature, is a global parameter. Thus, we have a local parameter of the diode device equation which is , and a global parameter which is . Note that a global parameter param is defined by setting Global[param] in the Parameters argument. Assuming Scope -> Local and no Translation rules, the first half of the Model definition is thus given by

Model[

Name -> Diode,

Selector -> DC,

Ports -> {A, C},

Parameters -> {Is, Global[Vt]},



]

The Definition Argument

For behavioral model definitions, the Definition parameter must be of the form

Definition -> Equations[, , ]

where , , denote the symbolic device equations. (For compatibility reasons the right hand side of the Definition parameter may also be a list of equations.) When specifying an arbitrary set of equations we must tell Analog Insydes how the unknowns of the equations relate to the port currents and voltages of a model object.

Figure 6.2: Voltage and current identifiers at a model port branch

Ports of behavioral models are defined in terms of electrical port branches. Every unique pair of node identifiers [node+, node-] introduces an electrical port branch in between the model port nodes node+ and node-. For the associated port voltage and current the positive reference direction is defined to be oriented from node+ to node-, which is illustrated in Figure 6.2.

Port variables in behavioral model equations can be referred to by means of two special keywords which are recognized by Analog Insydes and replaced by the corresponding global current or voltage identifiers during model instantiation and expansion. The keywords provided to make references to port currents and voltages are, respectively:

Current[node+, node-]

Voltage[node+, node-]

Note that the above definition of positive reference directions implies that Current[nodeA, nodeB] and Current[nodeB, nodeA] are two different quantities and refer to different port branches. Similarly, Current[nodeA, nodeB] and Voltage[nodeB, nodeA] do not refer to the same port branch.

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. , is thus designated by Current[A, C] and the port voltage, i.e. , 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)]

]