In WRspice, the following functions are implemented in such a way
that they are compatible with Newton iterations and convergence
testing. Logically, a separate random value is obtained at each point
of a grid in time that covers the simulation interval. The actual
random number used is interpolated from this grid at the present
simulation time. Thus, the ``random'' function becomes deterministic,
and simulations that include output from the random generator will
converge and iterate normally. This can be used to model Johnson
noise in the time domain, for example.
Each has an additional optional ``dt'' argument which if given
is taken as the time period of the random number grid. If not given,
the TStep from the running transient analysis is assumed. This
value has significance only in transient analysis. During other types
of analysis, calls to these functions will return a single random
value, generated on the first call.
Note that during transient analysis, the seed value should not change,
or non-convergence can result.
The following rules apply to these functions.
- All arguments to the system functions are real values, except
for seed (which is defined by $random). For the $rdist_exponential, $rdist_poisson, $rdist_chi_square, $rdist_t, and $rdist_erlang
functions, the arguments mean, dof, and k shall be
greater than zero (0).
- Each of these functions returns a pseudo-random number whose
characteristics are described by the function name, e.g., $rdist_uniform returns random numbers uniformly distributed in the
interval specified by its arguments.
- For each system function, the seed argument shall be an
integer. If it is an integer variable, then it is an inout argument;
that is, a value is passed to the function and a different value is
returned. The variable is initialized by the user and only updated by
the system function. This ensures the desired distribution is
achieved upon successive calls to the system function. If the seed argument is a parameter or constant, then the system function
does not update the value. This makes the system function useable for
parameter initialization. WRspice doesn't handle this.
- The system functions shall always return the same value given
the same seed. This facilitates debugging by making the operation of
the system repeatable. In order to get different random values when
the seed argument is a parameter, the user can override the
The two paragraphs above are difficult to follow. In WRspice, if
the same seed value is used for all calls, the sequence of values is
repeatable. A call with a different seed will reset the internal
random number generator and a different sequence would be returned.
The system functions never reset the seed. There is only one seed in
WRspice, so if any function call changes the seed, all subsequent
random number calls are affected.
- All functions return a real value.
- In $rdist_uniform, the start and end
arguments are real inputs which bound the values returned. The start value shall be smaller than the end value.
- The mean argument used by $rdist_normal, $rdist_exponential, $rdist_poisson, and $rdist_erlang is a real input which causes the average value
returned by the function to approach the value specified.
- The standard_deviation argument used by $rdist_normal is a real input, which helps determine the shape of
the density function. Using larger numbers for standard_deviation spreads the returned values over a wider range.
Using a mean of zero (0) and a standard deviation of one (1), $rdist_normal generates Gaussian distribution.
- The dof (degree of freedom) argument used by $rdist_chi_square and $rdist_t is a real input, which
helps determine the shape of the density function. Using larger
numbers for dof spreads the returned values over a wider range.