Conductance computation is one of the primary goals of an electrostatic analysis. For the definition of ground (partial) and lumped conductance matrices see Vago and Gyimesi([240]). The knowledge of conductance is essential in the design of electrostatic devices, Micro Electro Mechanical Systems (MEMS), transmission lines, printed circuit boards (PCB), electromagnetic interference and compatibility (EMI/EMC) etc. The computed capacitance can be the input of a subsequent MEMS analysis using the electrostructural transducer element TRANS126; for theory see TRANS126 - Electromechanical Transducer.
The conductance matrix of an electrostatic system can be computed (by the GMATRIX command macro). The conductance calculation is based on the energy principle. For details see Gyimesi and Ostergaard([250]), and for its successful application, see Hieke([251]). The energy principle constitutes the basis for inductance matrix computation, as shown in Inductance, Flux and Energy Computation.
The electrostatic energy of a linear three conductor (the third is ground) system is:
 | (5–184) |
where:
| W = electrostatic energy |
| V1 = potential of first conductor with respect to ground |
| V2 = potential of second conductor with respect to ground |
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By applying appropriate voltages on conductors, the coefficients of the ground conductance matrix can be calculated from the stored static energy.
The currents in the conductors are:
 | (5–185) |
 | (5–186) |
where:
| I1 = current in first conductor |
| I2 = current in second conductor |
The currents can be expressed by potential differences, too:
 | (5–187) |
 | (5–188) |
where:
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The lumped conductances can be obtained by lumped conductors as shown in Figure 5.5: Lumped Conductor Model of Two Conductors and Ground. Lumped conductances are suitable for use in circuit simulators.
