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I want to use a STA540 amplifier IC in Stereo plus bridge configuration (page 11, figure 6).

The idea is to have the chip drive two 4 Ohm tweeters and one 8 ohm Mid/Woofer.

Since passive crossover are quite expensive, I thought of using an active one before amplification. Could this work? Are there any fall backs?

The input signal comes from a Baxandall active volume control (not shown) and is biased at VCC/2.

VCC is 16V to aim to: 1x16W into 8 Ohm and 2x8W into 4 Ohm
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Yes, this will work. It is essentially equivalent if the crossover (filter) is before or after the amplifier.

Basically the crossover is a filter. However the common implementations do have dependency on the source and load impedance driving it, so the same component values used in the load end won't work equivalently when placed in the source (e.g. amplifier input) end of the signal chain.

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