Simplest 1st order high pass and low pass filter

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Hi guys,
Relative audio beginner here, although I have a background in circuit design.
Looking to split stereo AUX into stereo 250Hz+ and mono 250Hz and lower. Basically 2.1 system with AUX leading to a discrete stereo unit for midrange, and another aux leading to a larger speaker to be used as a subwoofer.

I understand the concept and mathematics of simple 1st order high pass and low pass filters, but do not know the optimal way to balance the RC component values.

Thank-you in advance for any advice provided.
 
A single pole passive filter just uses an RC combination. or an LR combination.
The losses of an LR filter mean it is usually not used.

The RC can be used as a High Pass Filter, or as a Low Pass Filter.
The F-3dB (roll-off) frequency is predicted by the formaula: F-3dB = 1/{2 Pi R C}
Assuming that the source impedance is zero ohms and the load impedance is infinite ohms.
The resulting roll-off is a Butterworth type. If either of those conditions are not met then the shape of the roll-off will not be Butterworth.

For a very thorough discussion of speaker filtering go and read the Linkwitz pages.
ESP gives a simpler discussion.
 
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A first-order filter is always unavoidably Butterworth, whatever the source or load resistance. If they are significant in value then you just have to include them in the calculation, but they don't alter the shape.

Assuming RC, the product RC is determined by the corner frequency as AndrewT says.

The value of R depends on the source and load resistances. A good place to start is to choose the geometric mean of these. The bigger the ratio of source to load impedance the easier it is to choose the right R - because choosing the 'wrong' R causes less trouble.
 
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