Capacitance — Question 10

Question 10

A supplied capacitance matrix exposes coupling beyond the ideal two-terminal model

Two conductors referenced to a distant ground obey $q_A=3cV_A-cV_B$ and $q_B=3cV_B-cV_A$, with c>0.

1. For antisymmetric drive $V_A=v/2$, $V_B=-v/2$, find qA, qB and the effective differential capacitance qA/v.

2. For common drive $V_A=V_B=u$, find both charges and explain why the ideal two-terminal relation is insufficient.

Question 10 - Solution

A supplied capacitance matrix exposes coupling beyond the ideal two-terminal model

(a) Method and calculation

$$q_A=3cv/2+cv/2=2cv,\quad q_B=-2cv.$$$$C_{\mathrm{diff}}=q_A/v=2c.$$

(b) Interpretation and further calculation

$$q_A=q_B=(3c-c)u=2cu.$$$$q_A+q_B=4cu\ne0\quad(u\ne0).$$The ground supplies the compensating charge in this three-conductor model.

Physical check

A mutual coupling term and coupling to ground respond differently to differential and common-mode voltages.