This formulation has the advantage that the error in the sum of branch
currents is available as the residuum of the equations system at each
iteration. Furthermore, the implementation of non-linear constitutive relations is simpler
than deriving a linearized companion model. The original MNA formulation
can be related to the above formulation by

Equation (2.21) is of fundamental importance as it allows for conversion between models implemented for

In *MINIMOS-NT* the constitutive relations for the node voltages are defined to be the sum of all
currents flowing *into* this node which must be zero. There is no
separation between passive elements and source terms. It is to note that the
opposite direction of current flow originates in (2.18) where the
negative derivatives are used to assemble the system matrix. This
definition is, of course, arbitrary, but defining the current direction this
way positive main-diagonal elements are obtained as in the conventional
formulation.

The constitutive relation for each node voltage is the sum of the device currents flowing into the node.

f_{} = f^{d}_{} = I^{d}_{n} = 0 |
(2.22) |

Branch currents are normally introduced for voltage sources and ammeters. The latter is a voltage source with zero branch voltage which introduces the branch current into the system matrix so that it can be used to control another element. The branch current constitutive relations state relationships between node voltages, e.g., - =

For an *N*-terminal device with *B* branch currents, one gets *N* + *B* device relations.

f^{d} =
=
with I^{d}_{n} = 0 |
(2.23) |

The partial contribution of the device *d* to the Jacobian matrix is given by

^{d} = |
(2.24) |

where

- 2.3.1 Thermal Simulation
- 2.3.2 Time Discretization
- 2.3.3 Devices
- 2.3.3.1 Conductor
- 2.3.3.2 Resistor
- 2.3.3.3 Linear Capacitor
- 2.3.3.4 Non-linear Capacitor
- 2.3.3.5 Linear Inductor
- 2.3.3.6 Current Source
- 2.3.3.7 Voltage Source
- 2.3.3.8 Voltage Controlled Current Source
- 2.3.3.9 Current Controlled Current Source
- 2.3.3.10 Voltage Controlled Voltage Source
- 2.3.3.11 Current Controlled Voltage Source
- 2.3.3.12 Gyrator
- 2.3.3.13 Power Monitor
- 2.3.3.14 Distributed Device

1999-05-31