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One of the most common errors in choosing a crossover for a speaker system is to think of it in its basic outward appearance: nothing more than a heap of components, often in a plastic case, to put between the amplifier and the speakers and that's all.
Actually a crossover is not an independent device but rather a circuit of which the speaker constitutes a pure component. To arbitrarily replace the speaker with a different one expecting that this doesn't alter the functioning of the crossover/speaker circuit, would be like randomly replacing a component inside a radio and hoping that it still works. If this by chance happens it shouldn't be attributed to your technical cleverness but rather to a piece of good luck.
For this and other reasons, before we examine crossover networks it is important to have a close look at the speaker