Gaussian Random

- General Form:
`gauss(`*stddev**mean**lattice*[*interp*])

- Examples:
`v1 1 0 gauss(.5, 2, 100n, 1)`

v2 1 0 gauss(.1, 0, 0)

This function can be called as `tgauss` to avoid possible conflict
with the `gauss` math function.

parameterdescriptiondefault valueunitsstddevstandard deviation none meanmean value none latticesample period seconds interpinterpolation 0 none

The `gauss` function can be used to generate correlated random
output. This function takes three or four arguments.

The parameter *lattice* is for use in transient analysis. A new
random value is computed at each time increment of *lattice*. If
*lattice* is 0, then no lattice is used, and an uncorrelated
random value is returned for each call. The *interp* parameter,
used when *lattice* is nonzero, can have value 1 or 0. If *interp* is nonzero, the value returned by the function is the (first
order) interpolation of the random values at the lattice points which
frame the time variable. If *interp* is 0, the function returns
the lattice cell's value for any time within the lattice cell, i.e., a
random step with an amplitude change at every lattice point.

The first example above provides a random signal with standard deviation of .5V and mean of 2V, based on random samples taken every 100nS.

The *lattice* value should be on the order of the user print
increment `tstep` in the transient analysis. It should not be
less than the maximum internal time step, since the past history is
not stored, and a rejected time point may back up the time across more
than one lattice cell, thus destroying the correlation.

This function applies only to transient analysis, where time is the running variable. The argument count is used to distinguish this function from the math function of the same name.

One important application of this function is to provide time-domain noise generation for noise modeling[15]. For example, below is a circuit which simulates the thermal noise generated in a resistor at 4.2K.

*** noise demo*@define noise(r,t,dt,n) gauss(sqrt(2*boltz*t/(r*dt)), 0, dt, n)

r1 1 0 1.0

ir1 1 0 noise(1.0, 4.2, 0.5p, 1)

c1 1 0 1p

.control

tran 1p 1n

plot v(1)

.endc

The second line defines a function named ``noise'' that takes four
arguments: the resistance, temperature in Kelvin, the lattice time
increment, and the interpolation method. This is simply a wrapper
around a `gauss` call, incorporating the standard noise equation
for current through a resistor at a given temperature, and taking the
inherent bandwidth to be one half of the reciprocal of the lattice
time increment (per Nyquist). The noise function is used in the
specification for current source `ir1`. In a more complicated
case, each resistor in a circuit may have an associated noise current
source similarly defined. It may be possible to demonstrate errors
due to thermal noise when simulating the circuit.