Skip to content

Verilog-A System Functions Analysis

Analysis of $ system functions used in OpenVAF and VACASK .va files, and how they are handled in the JAX and OSDI paths.

Reference: This document summarizes system functions per the Verilog-AMS Language Reference Manual (VAMS-LRM-2023), Section 9.

Summary Statistics

From 135 .va files analyzed:

Function Count Category Description
$param_given 1891 Device Check if param was explicitly set
$strobe 1434 Debug Print at end of timestep
$simparam 481 Simulation Simulator parameters
$temperature 274 Simulation Device temperature in K
$limit 270 Device Limiting function for convergence
$write 251 Debug Print immediately
$warning 212 Debug Issue warning message
$mfactor 191 Simulation Device multiplier
$finish 92 Debug End simulation
$fatal 64 Debug Fatal error, stop simulation
$port_connected 57 Device Check if port is connected
$discontinuity 42 Device Notify simulator of discontinuity
$vt 28 Simulation Thermal voltage kT/q
$display 11 Debug Print with newline
$abstime 5 Simulation Absolute simulation time

Simulation-Critical Functions

These must be handled correctly for accurate simulation results.

$temperature (274 uses)

Returns the circuit ambient temperature in Kelvin (LRM 9.15).

LRM Definition: $temperature returns the ambient temperature as a real value in Kelvin.

Path Handling
JAX Param with kind='temperature' → uses temperature argument from translate_init()/translate_eval()
OSDI OsdiSimInfo.temperature field

$simparam (481 uses)

Queries simulator parameters (LRM 9.15). Usage pattern: $simparam("name", default)

LRM Definition: $simparam() queries the simulator for a real-valued simulation parameter named param_name. If param_name is not known and no default is supplied, an error is generated.

Standard Parameters (LRM Table 9-27)

Parameter Units LRM Description
gdev 1/Ohms Additional conductance for conductance homotopy convergence
gmin 1/Ohms Minimum conductance placed in parallel with nonlinear branches
imax Amps Branch current threshold above which constitutive relation should be linearized
imelt Amps Branch current threshold indicating device failure
iteration - Iteration number of the analog solver
scale - Scale factor for device instance geometry parameters
shrink - Optical linear shrink factor
simulatorSubversion - The simulator sub-version
simulatorVersion - The simulator version
sourceScaleFactor - Multiplicative factor for independent sources (source stepping homotopy)
tnom Celsius Default temperature at which model parameters were extracted
timeUnit s Time unit as specified in 'timescale
timePrecision s Time precision as specified in 'timescale

Usage in Vendored Models

Parameter Default Count Notes
gmin 1e-12 88 Standard LRM parameter
tnom 27 74 Standard LRM parameter
scale 1 41 Standard LRM parameter
iteration 10 36 Standard LRM parameter
iniLim -1 36 Non-standard (SPICE-specific)
oldlimit 0 34 Non-standard (SPICE-specific)
defl 1e-4 30 Non-standard (SPICE default L)
defw 1e-4 30 Non-standard (SPICE default W)
defas 0 30 Non-standard (SPICE default AS)
defad 0 30 Non-standard (SPICE default AD)
reltol 1e-3 10 Non-standard (SPICE tolerance)
epsmin 1e-28 10 Non-standard
abstol 1e-12 6 Non-standard (SPICE tolerance)
vntol 1e-6 6 Non-standard (SPICE voltage tolerance)
Path Handling
JAX Only gmin handled → inputs[-1]. Others return 0.0 or default.
OSDI OsdiSimParas struct with names[] and vals[] arrays

Gap: JAX only handles gmin. Models using scale, tnom, or iteration-dependent behavior may differ.

$mfactor (191 uses)

Shunt multiplicity factor (LRM 9.18).

LRM Definition: $mfactor is the shunt multiplicity factor of the instance, that is, the number of identical devices that should be combined in parallel and modeled. The value is computed by multiplying values from the top of the hierarchy down to the instance.

Hierarchy Combination: $mfactor = $mfactor_specified * $mfactor_hier

Top-level value: 1.0

Path Handling
JAX Param with kind='sysfun' → uses mfactor argument (default 1.0)
OSDI Instance parameter in OSDI descriptor

$vt (28 uses)

Thermal voltage kT/q (LRM 9.15).

LRM Definition: $vt can optionally have temperature (in Kelvin units) as an input argument and returns the thermal voltage (kT/q) at the given temperature. $vt without the optional input temperature argument returns the thermal voltage using $temperature.

Formula: $vt(T) = k * T / q where k = Boltzmann constant, q = electron charge

Usage patterns found: - $vt or $vt() - 21 uses - thermal voltage at simulation temperature - $vt($temperature) - 4 uses - explicit simulation temperature - $vt(Tnom) - 1 use - thermal voltage at nominal temperature - $vt(DevTemp) - 1 use - thermal voltage at device temperature

Path Handling
JAX Computed inline as k * T / q where T comes from temperature param
OSDI Computed inline

$abstime (5 uses)

Absolute simulation time (LRM Table 9-7). Only relevant for transient analysis.

LRM Definition: $abstime returns the absolute time as a real number in seconds. The absolute time at the beginning of a simulation is typically zero.

Path Handling
JAX Param with kind='abstime' → defaults to 0.0. For transient, caller updates the input.
OSDI OsdiSimInfo.abstime field

Note: For DC analysis, abstime=0.0 is correct. For transient analysis, the simulator must provide the current time value.

Device Behavior Functions

$param_given (1891 uses)

Checks if a parameter was explicitly provided vs using default (LRM 9.19).

LRM Definition: The $param_given() function can be used to determine whether a parameter value was obtained from the default value in its declaration statement or if that value was overridden. The return value shall be one (1) if the parameter was overridden, either by a defparam statement or by a module instance parameter value assignment, and zero (0) otherwise.

Note: The return value is constant during simulation (fixed at elaboration). This allows use in genvar expressions controlling conditional/looping behavior of analog operators.

if ($param_given(VTH0)) begin
    // Use provided VTH0
end else begin
    // Calculate VTH0 from other params
end
Path Handling
JAX Param with kind='param_given' → 1.0 if param in user dict, else 0.0
OSDI Tracked per-parameter in OSDI descriptor

$limit (270 uses)

Convergence limiting functions (LRM 9.17.3).

LRM Definition: The $limit() function is a special-purpose system function whose purpose, like that of limexp(), is to provide the simulator with help in managing convergence problems. $limit() has internal state containing information about the argument from iteration to iteration. It internally limits the change of the output from iteration to iteration in order to improve convergence.

Built-in limiting algorithms: - pnjlim - Limiting arguments to exponentials (PN junction) - Additional args: vte (step size), vcrit (critical voltage) - fetlim - Limiting potential across MOS oxide - Additional arg: vto (threshold voltage) - User-defined functions can also be used

Common patterns: - $limit(V(g, ...), "fetlim", ...) - 76 uses - $limit(V(b, ...), "pnjlim", ...) - 72 uses - $limit(V(d_int, ...), ...) - 40 uses

Path Handling
JAX Translated to JAX limiting functions
OSDI Native OSDI limiting support

$port_connected (57 uses)

Checks if an optional port is connected (LRM 9.19).

LRM Definition: The $port_connected() function can be used to determine whether a connection was specified for a port. The return value shall be one (1) if the port was connected to a net (by order or by name) when the module was instantiated, and zero (0) otherwise. Note that the port may be connected to a net that has no other connections, but $port_connected() shall still return one.

Note: The return value is constant during simulation (fixed at elaboration).

if ($port_connected(bulk)) begin
    // 4-terminal device
end else begin
    // 3-terminal device (bulk tied internally)
end
Path Handling
JAX Assumed all ports connected (returns true)
OSDI Proper port connection checking

Gap: Models with optional ports may behave differently.

$discontinuity (42 uses)

Notifies simulator of a discontinuity for timestep control (LRM 9.17.1).

LRM Definition: The $discontinuity task is used to give hints to the simulator about the behavior of the module so the simulator can control its simulation algorithms to properly handle the discontinuity. $discontinuity(i) implies a discontinuity in the i'th derivative of the constitutive equation. $discontinuity(0) indicates a discontinuity in the equation, $discontinuity(1) indicates a discontinuity in slope, etc.

Special case: $discontinuity(-1) is used with the $limit() function.

$discontinuity(-1);  // Always notify (42 uses found)
Path Handling
JAX Ignored (DC analysis only currently)
OSDI Passed to simulator for timestep control

Debug Functions (Ignored)

These functions are for debugging/output and are safely ignored during simulation.

Function Count Purpose
$strobe 1434 Print at end of timestep
$write 251 Print immediately
$warning 212 Issue warning message
$finish 92 End simulation
$fatal 64 Fatal error
$display 11 Print with newline
$debug 4 Debug output
$fopen 2 Open file
$fdisplay 2 Write to file

Gap Analysis

Currently Missing in JAX Path

  1. $simparam parameters beyond gmin
  2. tnom - May affect temperature-dependent calculations
  3. scale - Layout scaling (41 uses)
  4. iteration - Iteration-dependent limiting (36 uses)

  5. Tolerance values - May affect limiting behavior

  6. $port_connected - Always returns true

  7. Risk: Models with optional ports (bulk, substrate) may behave differently

  8. $vt(T) with explicit temperature

  9. Need to verify correct handling of $vt(Tnom) vs $vt($temperature)

Recommendations

  1. Add tnom simparam support - Used in 74 places for temperature normalization
  2. Add scale simparam support - Used in 41 places for geometry scaling
  3. Consider $port_connected - May explain differences in some models
  4. Verify $vt temperature handling - Ensure consistency with OSDI

Implementation Details

JAX Parameter Handling

Parameters are handled by kind in _build_param_inputs():

Kind Handling
param User-provided or OSDI default
voltage Placeholder 0.0 (set at runtime)
temperature Uses temperature argument
sysfun (mfactor) Uses mfactor argument
param_given 1.0 if param in user dict, else 0.0
port_connected Always 1.0 (all ports assumed connected)
abstime Defaults to 0.0 (DC); caller updates for transient
hidden_state Placeholder 0.0 (filled by init)
current Placeholder 0.0

Special Input Array Indices

For codegen, special values accessed via negative indices: 

inputs[-1]  →  gmin (from $simparam("gmin"))
inputs[-2]  →  analysis_type (for analysis() function)

OpenVAF Compile-Time Handling

Some system functions are evaluated at compile time by OpenVAF: - $simparam("name", default) with default → default value inlined - $discontinuity → Simulator hint, stripped during optimization - $vt → Computed inline as k * T / q

This means warnings for unknown $simparam only appear if OpenVAF preserves the call.

OSDI Structures

typedef struct OsdiSimParas {
    char** names;      // Array of simparam names
    double* vals;      // Array of simparam values
} OsdiSimParas;

typedef struct OsdiSimInfo {
    double temperature;  // Simulation temperature (K)
    double abstime;      // Absolute time (s)
    // ... other fields
} OsdiSimInfo;

References

LRM Section References

Section Content
9.15 Analog kernel parameter functions ($temperature, $vt, $simparam, $simparam$str)
9.17 Analog kernel control functions ($discontinuity, $bound_step, $limit)
9.18 Hierarchical parameter functions ($mfactor, $xposition, $yposition, $angle, $hflip, $vflip)
9.19 Explicit binding detection ($param_given, $port_connected)
Table 9-27 Standard $simparam parameter names
Table 9-28 Standard $simparam$str parameter names