# How does the size of a reservoir capacitor affect battery life?

I have a circuit, powered by a 9V alkaline, where a solenoid is actuated via a MOSFET. I have a large reservoir capacitor (4700uF electrolytic) on the high side of the solenoid. I was wondering how changing the value of this capacitor will affect the battery life. Is it the bigger the value cap the better the battery life? For example, increasing the capacitor size from 4700uF to 6800uF should I expect a big increase in battery life?

Thanks everybody!

The cap has little to do with battery life. Ultimately the current thru the solenoid comes from the battery.

A cap can momentarily supply a higher current, which is then backfilled a little later and more spread out in time from the battery. That can be useful for loads that draw currents in large spikes but with a low average. In that case, the cap can let the battery see more the average rather than the spikes. This can be good for a battery.

However, that is not the case here. A solenoid is a inductor with significant series resistance from the circuit's point of view. When switched on, the current thru the solenoid will be a exponential decay towards the steady state value. It won't ever exceed the steady state draw that the battery has to be able to handle anyway. In this case, there is little point in a reservoir cap to power a solenoid.

The only reason I can think of one being useful for solenoid power is if the connection back to the power supply (the battery in this case) had such high resistance that there is significant drop on the solenoid voltage in steady state. This might be the case, for example, if the solenoid and switch is at the end of a long cable. In that case, the cap provides a higher voltage for a short time when the solenoid is switched on. This is likely when it needs more force. Depending on the external mechanics, it may be good to have a initial higher pull, which can then be relaxed a bit once the solenoid has finished traveling. This is common in relays, for example, where the two are often referred to as the turn-on current and the holding current.

I essentially agree with Olin.
There is a special exception which is worth noting.

Special case - summary:

• A special case that is common enough to be worth noting is when the solenoid is provided with pull in current to operate, and coil current is then reduced to a holding value.

• As holding current may be as little as 10% of pullin, a supply capacitor could make a significant lifetime difference in this case.

Solenoids have a pull in current and a holding current. The pull in current is NOT achieved instantly on application of power, as Olin notes, but rises exponentially with a tie constant of about L/R. Usually this time constant is smallish compared to the mechanical pull in time as the high current is needed early in the stroke when the air gap is largest and inductance is the smallest.

While holding current is often much lower than pullin current, no means is usually provided in the solenoid proper to reduce the current once the solenoid has operated. The excess current is thus "wasted" which is usually only important for battery powered equipment.

But some battery powered systems make use of this by providing a large voltage (usually) to cause pullin current to be drawn, then once the solenoid has operated voltage is reduced and/or resistance is raised to decrease current to holdin level.

In SOME cases a significant improvement in battery life may be able to be achieved if a capacitor is used to provide Ipullin and the battery is used to provide i holdin.

• I think my application falls into this special case. The solenoid is used to trip a larger mechanical system. Without a reservoir cap the solenoid doesn't supply enough force to trip the system, which I take to mean the cap is supplying a high pullin current to start the solenoid. So a bigger cap would help better average out the current draw from the battery extending battery life. I guess another technique I could use to improve battery life is to us PWM during hold time to lower wasted current Nov 7 '11 at 17:11

As others have stated, the capacitor does not affect the amount of charge delivered by the battery.

But there's one case where bulk capacitance helps increase battery capacity (which is not the same as battery "life" for a rechargeable battery): namely that the measurement of battery capacity depends on an endpoint which is usually a function of battery voltage, e.g. the battery is considered discharged when voltage is less than some application-dependent threshold.

If you have spiky surge currents, this will temporarily lower battery voltage to a point that could make it be considered discharged. With bulk capacitance, the capacitor will handle the surge currents and the battery voltage will be higher than otherwise, so the point at which the battery is considered discharged is later, giving the battery a larger effective capacity.

As for "life", in a nonrechargeable battery this is effectively the same as capacity; in a rechargeable battery, cycle life (# of cycles until capacity or power delivery drops below a useful threshold) is improved with smoother or lighter loads, so bulk capacitance will help somewhat.