The resolution .DELTA.C of a binary capacitance ladder having a plurality of N branches is precisely determined by appropriately selecting the value of a fixed capacitor in each branch relative to the parasitic capacitance of a corresponding series-connected switch. The capacitance of each respective branch varies by 2.sup.n-1 .DELTA.C, where n is the number of the branch, adjacent branches being numbered sequentially. The total capacitance is variable between C.sub.Total and C.sub.Total -(2.sup.N -1).DELTA.C in steps of .DELTA.C, where C.sub.Total is the sum of the capacitances in the ladder with all switches closed, and C.sub.Total -(2.sup.N -1).DELTA.C is the capacitance of the ladder with all switches open. For any particular branch of the ladder, the switch capacitance may be further controlled by adding a fixed capacitance in parallel with the respective switch. Such a variable capacitance is useful as a tuning capacitor in an electrodeless HID lamp ballast.