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Speed and Accuracy
Integral Equation Method (IEM) Algorithm
Integral Equation Method (IEM) Algorithm
IEM is a unique algorithm to Eldo. It is useful when very high accuracy is desired and/or when
NR shows stability issues. Some components cannot be formulated in a way that is compatible
with IEM, thus it is also less general than NR.
Caution
The IEM algorithm only works well using simple models. Models are now quite
complicated due to latest process technology nodes. They require a more flexible interface,
GUDM, where you can specify any number of nodes as required. They are not supported by
IEM. This applies to almost all the newer families of models, including: BSIM4, BSIM5,
MM11, PSP, TFT, HISIM, HICUM, VBIC and MEXTRAM. Eldo built-in analog macromodels
and Verilog-A user-defined models are also not supported by IEM.
With IEM, the differential system is first transformed into a system of integral equations, which
is then transformed into an algebraic system by series expansion. The truncation error results
from the finite number of terms in the series. In all cases, truncation error is also a function of
the time step size.
Once the non-linear algebraic system is obtained, it is solved by an iteration loop. IEM targets
improvements of the accuracy of the solution (compared to Newton); it does not specifically
target large circuits, so it is mostly used for cell or macro-block simulations where accuracy is
critical.
IEM is of interest for cases where high accuracy is required and/or when the default Newton
method runs into numerical stability issues due to the integration methods (trapezoidal ringing
for example). IEM however does not support all devices, macro-models, and so on, that Newton
supports. Some devices cannot be efficiently formulated in a way that is compatible with the
IEM algorithm. Thus the applicability of IEM is somewhat limited, and it is mostly used for cell
characterization applications.
• Integration Method
When using IEM, the notion of integration method, such as BE, TRAP, or GEAR, is
irrelevant. The equations are cast to an integral form prior to the resolution. Thus there
are no choices about a numerical integration method to use.
• Time Step Control
When using IEM, the time step control algorithm uses local truncation error (LTE)
control. Only the LVLTIM=2 and LVLTIM=3 methods are selectable together with
IEM. The other methods are not reliable enough when used together with IEM, and they
will be refused by Eldo.
• Accuracy Control
1260
Eldo® User's Manual, 15.3