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I am trying to design a very small solenoid with a very fast charge time. Working backwards from a charge time of approximately 500 μs, I want to see if it is possible to create solenoid to meet this requirement.

I have read that a reasonable approximation for charge time is 5L/R. Are there rough formulas for the inductance and resistance for multilayer multirow solenoids?

When I measure an existing commercial solenoid on my scope, I am seeing a charge time of over 10 ms so I know creating a solenoid with a charge time of 500 μs is going to be a challenge. So at this point, I am looking for rough calculations to see if I can get within the ballpark before I do more serious calculations.

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  • \$\begingroup\$ As a practical matter, you don't have to wait \$5\tau\$ for a solenoid to engage. Stuff happens sooner. You can test this out with commercial devices. (By the way, that is something you should do before designing your own.) You will learn from the details written down in your engineering notebook. But there's no possible way for others to help with those details unless and until you also provide many details far beyond the \$500\:\mu\text{s}\$. Details about the purpose, the actuation force, the length of the stroke, the expected duty cycle, and its physical size and core material, etc. \$\endgroup\$ Commented 2 hours ago

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Solenoids take time because they are inductive and if you could reduce the series resistance to zero an inductor's current would rise at this rate: -

$$\dfrac{di}{dt} = \dfrac{V}{L}$$

So, you need a certain amount of inductance to get the physical magnetic pull but, you are quite at liberty to drive your solenoid at twenty times the steady state rated voltage (for a short time circa 500 μs) then reduce the voltage to keep the current at the regular steady state value.

It's not something I'm inventing; many solenoids are driven this way. The only thing you need to ensure is that the insulation on the windings doesn't fail due to the short period of over-voltage.

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