Convergence is defined as the ability to obtain a solution to a set of circuit equations within a given tolerance criteria. In numerical circuit simulation, the designer specifies a relative and absolute accuracy for the circuit solution and the simulator iteration algorithm attempts to converge onto a solution that is within these set tolerances.
Star-Hspice uses accuracy tolerance specifications to help assure convergence by determining whether or not to exit the convergence loop. For each iteration of the convergence loop, Star-Hspice takes the value of the previously calculated solution and subtracts it from the present solution, then compares this result with the accuracy tolerances.
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As shown in Absolute and Relative Accuracy Tolerances, Star-Hspice defaults to specific absolute and relative values. You can change these tolerance levels so that simulation time is not excessive and accuracy is not compromised. The options in the table are described in the following section.
Nodal voltages and element currents are compared to the values from the previous iteration. If the absolute value of the difference is less than ABSVDC or ABSI, the node or element is considered to be convergent. ABSV and ABSI set the floor value below which values are ignored. Values above the floor use the relative tolerances of RELVDC and RELI. If the iteration-to-iteration absolute difference is less than these tolerances, then it is considered to be convergent. ABSMOS and RELMOS are the tolerances for MOSFET drain currents.
The number of iterations required is directly affected by the value of the accuracy settings. If the accuracy tolerances are tight, a longer time is required to converge. If the accuracy setting is too loose, the resulting solution can be inaccurate and unstable.
RELV vs. Accuracy and Simulation Time for 2 Bit Adder shows an example of the relationship between the RELVDC value and the number of iterations.
Star-Hspice is shipped with control option settings designed to maximize accuracy without significantly degrading performance. The options and their settings are discussed in Controlling Simulation Speed and Accuracy.
The options listed below are described in this section.
ABSH DCON RELH
ABSI DCTRAN RELI
ABSMOS DI RELMOS
ABSVDC GMAX RELV
CONVERGE GMINDC RELVDC
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Sets the absolute current change through voltage defined branches (voltage sources and inductors). In conjunction with DI and RELH, ABSH is used to check for current convergence. Default = 0.0. |
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Sets the absolute branch current error tolerance in diodes, BJTs, and JFETs during DC and transient analysis. Decrease ABSI if accuracy is more important than convergence time. If you want an analysis with currents less than 1 nanoamp, change ABSI to a value at least two orders of magnitude smaller than the minimum expected current. |
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Current error tolerance used for MOSFET devices in both DC and transient analysis. Star-Hspice uses the ABSMOS setting to determine if the drain-to-source current solution has converged. If the difference between the last and the present iteration's drain-to-source current is less than ABSMOS, or if it is greater than ABSMOS, but the percent change is less than RELMOS, the drain-to-source current is considered converged. Star-Hspice then checks the other accuracy tolerances and, if all indicate convergence, the circuit solution at that timepoint is considered solved, and the next timepoint solution is calculated. For low power circuits, optimization, and single transistor simulations, set ABSMOS = 1e-12. Default = 1e-6 (amperes). |
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Sets the absolute minimum voltage for DC and transient analysis. Decrease ABSVDC if accuracy is of more concern than convergence. If voltages less than 50 microvolts are required, ABSVDC can be reduced to two orders of magnitude less than the smallest desired voltage. This ensures at least two digits of significance. Typically ABSVDC need not be changed unless the circuit is a high voltage circuit. For 1000-volt circuits, a reasonable value can be 5 to 50 millivolts. Default = VNTOL (VNTOL default = 50 µV). |
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Invokes different methods for solving nonconvergence problems
Even if it is not set in an .OPTIONS statement, the CONVERGE option is activated in the event of a matrix floating point overflow, or a timestep too small error. Default = 0. In the event of a matrix floating point overflow, Star-Hspice sets CONVERGE = 1. |
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In the case of convergence problems, Star-Hspice automatically sets DCON = 1 and the following calculations are made:
where V If convergence problems still exist, Star-Hspice sets DCON = 2, which is the same as the above except DV = 1e6. The above calculations are used for DCON = 1 or 2. DCON = 1 is automatically invoked if the circuit fails to converge. DCON = 2 is invoked if DCON = 1 fails. If the circuit contains uninitialized flip-flops or discontinuous models, the simulation might be unable to converge. Setting DCON = -1 and CONVERGE = -1 disables the autoconvergence algorithm and provides a list of nonconvergent nodes and devices. |
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Sets the maximum iteration to iteration current change through voltage defined branches (voltage sources and inductors). This option is only applicable when the value of the ABSH control option is greater than 0. Default = 0.0. |
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The conductance in parallel with the current source used for .IC and .NODESET initialization conditions circuitry. Some large bipolar circuits can require GMAX set to 1 for convergence. Default = 100 (mho). |
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A conductance that is placed in parallel with all pn junctions and all MOSFET nodes except gate (see Figure 6-4 for details) for DC analysis. GMINDC helps overcome DC convergence problems caused by low values of off conductance for pn junctions and MOSFET devices. GRAMP can be used to reduce GMINDC by one order of magnitude for each step. GMINDC can be set between 1e-4 and PIVTOL. Default = 1e-12. Large values of GMINDC can cause unreasonable circuit response. If large values are required for convergence, a bad model or circuit is suspect. In the event of a matrix floating point overflow, if GMINDC is 1.0e-12 or less, Star-Hspice sets it to 1.0e-11. GMINDC is manipulated by Star-Hspice in autoconverge mode, as described in the Autoconverge Process. |
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Sets relative current tolerance through voltage defined branches (voltage sources and inductors). It is used to check current convergence. This option is applicable only if the value of the ABSH control option is greater than zero. Default = 0.05. |
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Sets the relative error tolerance for current from iteration-to-iteration to determine convergence for all currents in diode, BJT, and JFET devices. (RELMOS sets the tolerance for MOSFETs). This is the change in current from the value calculated at the previous timepoint. Default = 0.01 for KCLTEST = 0, 1e-6 for KCLTEST = 1. |
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Sets the relative drain-to-source current error tolerance from iteration-to-iteration to determine convergence for currents in MOSFET devices. (RELI sets the tolerance for other active devices.) This is the change in current from the value calculated at the previous timepoint. RELMOS is only considered when the current is greater than the floor value, ABSMOS. Default = 0.05. |
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Sets the relative error tolerance for voltages. When voltages or currents exceed their absolute tolerances, the RELV test is used to determine convergence. Increasing RELV increases the relative error. In general, RELV should be left at its default value. RELV controls simulator charge conservation. For voltages, RELV is the same as RELTOL. Default = 1e-3. |
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Sets the relative error tolerance for voltages. When voltages or currents exceed their absolute tolerances, the RELVDC test is used to determine convergence. Increasing RELVDC increases the relative error. In general, RELVDC should be left at its default value. RELVDC controls simulator charge conservation. Default = RELTOL (RELTOL default = 1e-3). |
If convergence is not achieved in the number of iterations set by ITL1, Star-Hspice initiates an autoconvergence process, in which it manipulates DCON, GRAMP, and GMINDC, as well as CONVERGE in some cases. The autoconverge process is illustrated in Autoconvergence Process Flow Diagram.
1. Setting .OPTIONS DCON = -1 disables steps 2 and 3.
2. Setting .OPTIONS CONVERGE = -1 disables step 4.
3. Setting .OPTIONS DCON = -1 CONVERGE = -1 disables steps 2, 3, and 4.
4. If you set the DV option to a value different from the default value, the value
you set for DV is used in step 2, but DV is changed to 1e6 in step 3.
5. Setting GRAMP in an .OPTIONS statement has no effect on the
autoconverge process. The autoconverge process sets GRAMP
independently.
6. If you specify a value for GMINDC in an .OPTIONS statement, GMINDC is ramped to the value you set instead of to 1e-12 in steps 2 and 3.
GMINDC is important in stabilizing the circuit during DC operating point analysis. For MOSFETs, GMINDC helps stabilize the device in the vicinity of the threshold region. GMINDC is inserted between drain and bulk, source and bulk, and drain and source. The drain to source GMINDC helps linearize the transition from cutoff to weakly on, helps smooth out model discontinuities, and compensates for the effects of negative conductances.
The pn junction insertion of GMINDC in junction diodes linearizes the low conductance region so that the device behaves like a resistor in the low conductance region. This prevents the occurrence of zero conductance and improves the convergence of the circuit.
DCON is an option that Star-Hspice sets automatically in case of nonconvergence. It invokes the GMINDC ramping process in steps 2 and 3 in Autoconvergence Process Flow Diagram. GMINDC is shown for various elements in GMINDC Insertion.
, if DV = 1000
