# Bill Jones

The capacitor to be analyzed is shown in Figure one. It is desired to find the capacitance C (A+B) and how it varies with respect to d.

Figure one shows two capacitors. For our analysis they will be connected in parallel.  The stators are separated by a distance x and the distance d is from stator A to the rotor. We are interested in the total capacitance C (A+B). The rotor thickness is negligible for our purpose. We normalize for simplicity.

A=area in cm. squared. K=1 (dielectric constant).  d=distance in cm.  C in pf.

We set x=1 and P=1 for simplicity since we are not interested in the absolute value. This will give equation2. A plot of the equation is shown in Figure 2.  If we imagine the rotor plate to be perfectly centered at d=0.5, the capacitance is a minimum value.  If d varies in either direction from d=0.5 the capacitance increases.  If d changes from 0.5 to 0.15 (or d=0.85), the capacitance will almost double.  If d changes from 0.5 to 0.4 (or 0.6) the capacitance varies from 4 to 4.17 and this is only 4 percent but for a typical 300 pf. capacitor this would give a 12-pf variation.   This can detune the circuit. This is an important result.It is  advisable to be extremely careful when aligning these variable capacitors.

Thanks, Bill.

1
Equation 2   C(A+B) = C(total) ,            C(total) =   
d( 1 – d)