Optimum Capacitor Charging Efficiency for Space Systems

In space systems the efficient utilization of energy can be critical. Many pulsed-operation devices, e.g., a plasma engine, involve charging a capacitor bank C periodically. The efficiency of energy transfer ¿ to an initially uncharged bank when a dc-source voltage is applied through a resistance R, with inductance L assumed zero, is limited to 50 per cent even if R varies arbitrarily during the charging process. If L>0, ¿ can be made to approach 100 per cent by charging in a periodic mode and terminating at the end of the first ¿-cycle. The requisite L, which is a function of R, C and charging time T, can be formidable and its weight large, often being excessive for space applications. To provide guide lines in the selection of practical voltage shapes, the techniques of the Calculus of Variations are used to derive a series of general theorems for the "perfect" time-shaped source voltages that optimize ¿ when the delivered energy, L, C and T are fixed. Four modes of prescribing R, as a function of time t and/or current i, are treated: 1) Constant R; the key condition is constant i for the full charging time allowed; the voltage is a modified "elevated ramp"; ¿opt= 1/(1+2RC/T), can approach 100 per cent and is independent of L. 2) R(t). 3) R(i). 4) R(t, i). The ¿opt for each case, showing the highest theoretically possible, are useful as a basis for an efficiency figure of merit.