Solution Process

As Q3D Extractor solves for the matrices you have requested, it goes through the following steps:

1. Uses the appropriate field simulators to generate a field solution. Different field simulators (field solvers) are used to compute the various matrices. For example, the electrostatic field simulator is used to simulate the electric fields from which capacitances are computed. Similarly, the magnetostatic field simulator is used to simulate the magnetic fields from which inductances are computed.
   Note:

   Because circuit parameters are computed using the final mesh generated during the field solution, adequate refinement of the mesh during the field solution increases the accuracy of circuit parameter solutions.

2. After the field solutions are complete, the simulator performs an error analysis in each triangle in the mesh. The triangles with the highest energy error are broken down into smaller triangles — producing a more accurate solution in these areas.
3. Individually applies one volt (for CG parameters) or one amp (for RL parameter problems) to each conductor you have defined — objects made of conducting materials may or may not be defined conductors for your problem. The rest of the conductors are temporarily set to zero (volts or amps).

• As each conductor is excited, the field solution is used to compute a capacitance, inductance, or resistance for that conductor relative to the reference ground and to the other conductors.
• The resulting parameter is entered in the matrix (the desired end result). For instance, in the capacitance matrix, the capacitance of the first conductor relative to ground is element C₁₀. The diagonal elements of the matrix would represent self-capacitances, and the off-diagonal elements would represent mutual capacitances (mutual elements).

The resulting matrix is in Maxwell matrix format. These cannot be used to generate SPICE equivalent subcircuits in capacitance and conductance problems, so a SPICE matrix is generated.

4. If both capacitance and inductance matrices are requested, the Q3D Extractor automatically generates a modal solution of voltage and current modes once both matrices have been computed. The software uses per unit length capacitances and inductances to compute:

• The modal transformation matrix that converts voltage signals into voltage modes and current signals into current modes. This matrix is used to generate a distributed SPICE equivalent subcircuit that models voltage and current signals carried on the transmission line as decoupled modal lines. This provides a more accurate representation of the line than modeling it using lumped circuits.
• The velocity of each mode.
• The characteristic resistance matrix (Z0) of the physical transmission line structure.