Spectre DC Analysis

In DC analysis, equilibrium points are calculated. It is important to understand that:

• Circuits sometimes have more than one DC solution.
• The DC solution computed by the citcuit simulator may be unstable.

Newton-Raphson Method

Newton’s method solves nonlinear algebraic equation by iteration. For equations

\[f(\hat{v}) = 0\]

starting with an initial guess \(v^{(0)}\) and repeatedly solving the Newton-Raphson iteration equation

\[v^{(k+1)} = v^{(k)} - J^{-1}(v^{k}) f(v^{(k)})\]

where \(J(v) = \frac{d}{dv} f(v)\) is called the Jacobian of \(f\) at \(v\). It represents the circuit linearized about \(v\).

It is guaranteed to converge to \(\hat{v}\) if \(f\) is continuously differentiable, if the solution is isolated, and if \(v^{(0)}\) is sufficiently close to \(\hat{v}\). In circuit simulation, none of these three conditions are guaranteed, and so neither is convergence.

Convergence Criteria

In Spectre it uses both of two criteria. The first one is called Newton update convergence criterion.

\[|v_n^{(k)} - v_n^{(k-1)}| < \text{reltol} \cdot v_{n,max} + \text{vntol}\]

where typically

\[v_{n,max} = \text{max}(|v_{n}^{(k)}|, |v_{n}^{(k-1)}|)\]

By default, reltol is 0.001 and vntol (called vabstol in Spectre) is 1uV.

The second one is called Newton residue convergence criterion

\[|f_n(v^{(k)})| < \text{reltol} f_{n,max} + \text{abstol}\]

where typically \(f_{n,max}\) is the absolute value of the largest current entering node \(n\) from any one branch.

Typicaly, abstol (called iabstol in Spectre) is 1pA.

Very Small Resistors

Very small resistors put difficulties to the Newton residue convergence criterion. Since very small voltage error can create large currents.

• Try to avoid small resistors.
• Use 0-volt voltage sources as current probes rather than small-valued resistors.
• Discard overly small parasitic resistors in semiconductors.
• Spectre automatically deletes all parasitic resistors smaller than a particular value, given by the model parameter minr.
• If it is necessary to use small valued parasitic resistors, increase iabstol to avoid convergence problems.

Isolated Solutions

If you attempt to simulate a circuit that does not have isolated solutions, the simulator usually fails with an obscure complaint about the matrix or the Jacobian being singular.

Examples:

• Voltages of the subcitcuit can be raised or lowered by any amounts.
• loop of ideal inductors.