Behavioral modeling

# Chapter 4 Behavioral modeling

Gnucap behavioral modeling is in a state of transition, so this is subject to change in a future release.
Basically, all simple components can have a behavioral description, with syntax designed as an extension of the Spice time dependent sources. They are not necessarily physically realizeable. Some only work on particular types of analysis, or over a small range of values. Some can be used together, some cannot.
In general, all simple components are considered to have simple transformations. A function returns one parameter as a function of one other, as an extension of their linear behavior.
Linear behavior:

`Capacitor`
  q = C v
`Inductor`
  ϕ = L i
`Resistor`
  v = I r
`Admittance`
  i = Y v
`VCVS`
  vo = E vi
`VCCS`
  io = G vi
`CCVS`
  vo = E ii
`CCCS`
  io = G ii

Sources are defined as functions of time:

`Voltage source`
  v = f(t)
`Current source`
  i = f(t)

For behavioral modeling / nonlinear values, replace the constant times input by an arbitrary function:

`Capacitor`
  q = f(v)
`Inductor`
  ϕ = f(i)
`Resistor`
  v = f(r)
`Admittance`
  i = f(v)
`VCVS`
  vo = f(vi)
`VCCS`
  io = f(vi)
`CCVS`
  vo = f(ii)
`CCCS`
  io = f(ii)

### Conditionals

`AC`
  AC analysis only.
`DC`
  DC (steady state) value.
`OP`
  OP analysis.
`TRAN`
  Transient analysis.
`FOUR`
  Fourier analysis only.
`ELSE`
  Anything not listed.
`ALL`
  All modes.

### Functions

`COMPLEX`
  Complex (re, im) value.
`EXP`
  Spice Exp source. (time dependent value).
`FIT`
  Fit a curve with splines.
`GENERATOR`
  Value from Generator command.
`POLY`
  Polynomial (Spice style).
`POSY`
  Posynomial (Like poly, non-integer powers).
`PULSE`
  Spice Pulse source. (time dependent value).
`PWL`
  Piece-wise linear.
`SFFM`
  Spice Frequency Modulation (time dependent value).
`SIN`
  Spice Sin source. (time dependent value).
`TANH`
  Hyperbolic tangent xfer function.

### Model Functions

`TABLE`
  Fit a curve with splines.
`Cap`
  Spice semiconductor “capacitor” model.
`Res`
  Spice semiconductor “resistor” model.

- Conditionals
- Functions
- `COMPLEX`: Complex value
- `EXP`: Exponential time dependent value
- `FIT`: Fit a curve
- `GENERATOR`: Signal Generator time dependent value
- `POLY`: Polynomial nonlinear transfer function
- `POSY`: Polynomial with non-integer powers
- `PULSE`: Pulsed time dependent value
- `PWL`: Piecewise linear function
- `SFFM`: Frequency Modulation time dependent value
- `SIN`: Sinusoidal time dependent value
- `TANH`: Hyperbolic tangent transfer function
- .model `TABLE`: Fit a curve