Normal variation¶

Variations describe the healthy population: how the parameters of good circuits differ. They are not faults. A fault is injected into a circuit already drawn from this population.

from spicefault.variation import NormalVariation, VariationSet, tolerances

population = tolerances(circuit, {"R": 0.01, "C": 0.05})   # by component kind
population = VariationSet([NormalVariation("R1", 10000, 500), NormalVariation("R2", 10000, 500)])
tighter = population.scaled(0.2)   # same random numbers, a fifth of the spread

instance_tolerances gives every instance of a subcircuit the same spread in its parameters, relative or, for a parameter that is nominally zero, absolute:

from spicefault.variation import instance_tolerances

amplifiers = instance_tolerances(circuit, "opamp", {"vos": (0.5e-3, "absolute"), "aol": 0.5})

A normal variation is not a fault: variations describe the healthy population, and a fault is injected into a circuit already drawn from it. scaled multiplies every spread while using the same random numbers, so a study of detectability against tolerance compares the same circuits at each tolerance level.

Every variation except the custom, joint and catalogue ones also has a quantile function, variation.quantile(u, nominal): the value at probability u. Sampling does not use it; the designs that choose their uniform numbers jointly do.

Parameters that are not independent¶

Independent tolerances overstate the spread of a ratio and understate that of a sum. Two variations describe the common cases without a function, so a dataset rebuilds them from its record:

from spicefault.variation import CorrelatedVariation, LotVariation, ToleranceVariation

# two resistors from the same reel: each within 1 %, tracking each other
CorrelatedVariation([ToleranceVariation("R1", 0.01), ToleranceVariation("R2", 0.01)],
                    correlation=0.9)

# a whole group shifted by its lot (4 %), each part 1 % around it
LotVariation(("R1", "R2", "R3"), lot=0.04, within=0.01)

CorrelatedVariation keeps the distribution of each parameter and joins them with a Gaussian copula. correlation, one number or the full matrix, is that of the underlying normals: the correlation of the values equals it only for normal variations, and their rank correlation is (6/π) asin(correlation/2) for any. Each variation it joins needs a quantile function. LotVariation draws one deviation for the group and one of each component, and records the first as a label.

JointVariation draws several parameters together: the parameters of a part whose type is drawn first, two resistors from the same reel, or a netlist parameter computed from two drawn quantities. It can also record labels, such as the type that was drawn. See the custom example.

When the dependence is a part that comes in several types, CatalogueVariation needs no function: the type is drawn first, with the given weights, and each parameter is the median of that type times a factor between 1/spread and spread. The type is recorded as a label, and the variation is rebuilt from the record of a dataset.

from spicefault.variation import CatalogueVariation

CatalogueVariation(
    "Xelectrode",
    options={"gel": {"r": 2e3, "c": 50e-9}, "steel": {"r": 2e5, "c": 5e-9}},
    weights=(3, 1), spread=2.0, label="electrode_kind",
)

Functions given to CustomVariation and JointVariation must be defined at module level, so that worker processes can import them. A record cannot store a function: a dataset keeps the name of the function, and the experiment has to be passed again to simulate its samples anew.