Redefining the Ground Reference for the Capacitance Matrix

Using an already computed capacitance matrix, it is possible to determine what the capacitance matrix would have been if a different conductor were selected as the ground reference.

Consider the two-terminal capacitance network of the figure below.

Assume that nodes 1, 2, and 3 have known voltages, and suppose that it is desirable to make node 3 the new ground reference. The new situation is shown below.

A few features of this new situation are worth noting:

• The remaining nodes 1 and 2 still have the same capacitors connected to them, and the self-capacitance terms in the Maxwell capacitance matrix remain unchanged.
• The coupling capacitances to the new node 3´ are the former capacitances to ground.

By inspection of this network, determine the new Maxwell capacitance matrix:

Comparing with the original Maxwell capacitance matrix, the redefinition of ground can be accomplished by replacing row 3 and column 3 with new entries. The off-diagonal entries are the former capacitances to ground, and the diagonal entry is the sum of the capacitances to ground from the original system.