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This small calculation is dedicated to a question which looks fairly simple and is subject of student's and even school guides on electronics, being of high practical importance for electromagnetic accelerators building (not necessary of "reluctance" type). Suggest we have a DC voltage source The question is: what would be the effieicy if we try to charge a capacitor battery of some electromagnetic accelerator from such source through a resistor ? In other words, what part of energy spent from the source will be transferred to the capacitor till the end of charging (when In vain. The fact is that the simplifed examination of the problem inplies that initial cap voltage is Let us examine the process more detailed (see fig. 1).
Energy increment in the capacitor makes And joule heating during the charging process will be As there are no other losses in our simple system, a total efficiency will be A graph of this uncomplicated function is shown on fig. 2 in dependence of _{ }relation. It is clear that being 0.5 at U=0, it approaches 1 when _{0}U increases._{0}/U_{i}
It occurs that "school" value of 50 % efficiency suggested as a postulate is often wrong. How does it concern gauss-building? Directly. First, we should "exonerate" the forward converters. The calculations above show that they can be used freely in transistor-commutated coilguns. To obtain a substantial efficiency while charging empty capacitors (from the "storage mode" of a coilgun) a little choke should be connected between the secondary wining and the cap. Indeed, such an inductor is really added in majority of commercial converters for ripple current suppression (see fig. 3):
Secondly, provided a battery has high enough voltage, it can be The most wonderful feature of this approach is that the power of recharging is limited only by current capacity of the corresponding source and mentioned above resisitances, and can reach as high as kilowatts, which is absolutely incredible for compact voltage converters of any scheme. For example, common LiPo accu of 14.8V and 75C (which allows 135A for 1800 mAh capacity) can give 14.8·135 = 2000 W output power. As illustration: recently, there have been many attempts of utilizing relatively high-voltage chemical power sources (as LiPo acccus or supercapacitors) for driving accelerating coils of coilguns. It occurs that the active resistance of those elements is too large to actuate the windings directly, so some untermediate capacitance is necessary. Thus, the construction appears to be what was just discussed.
Our calculation shows that these constructions have a high potential of development.
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