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Passive Crossover Networks



This is called network that part of a circuit to which is referable a specific function, with explicit allusion to the tangle represented by its electric diagram. So we'll have filtration networks — read crossovers — supply networks, conversion networks, feedback networks, etc. A network is composed in its turn of cells, that's groups of elementary units, the single electric components. So if for example we made reference to the diagram of an improbable eighth-order lowpass filter, we could realize as it is nothing but a combination of four LC cells, each formed by an inductor and a capacitor:

8th-order LP

This preamble needed to say that an impedance equalization network is composed of a non-resonant cell and a non-inductive cell. Their name is self-explanatory to their function. The complete diagram is the following:

Impedance Equalization Network

This correction network must be placed in parallel with the speaker, between this one and the real filter. Keep in mind also that if the filter is second-order or steeper and the crossover frequency is at least three octaves far from the resonance of the speaker, it is unnecessary to compensate the impedance peak at fs and the RCL cell can be eliminated. The correction network will be limited therefore to the only RC cell, always in parallel with the speaker and next to the filter obviously:

Non-inductive Cell

But here are the respective formulas...

non inductive cell

R = Re


C = (Le/Re2)*106


non resonant cell

R = Re*(Qes/Qms)


C = (1/2πfs)*(1/(Re*Qes))*106


L = (1/2πfs)*(Re*Qes)*103


...with a due explanation of the symbols:


direct current resistance of the speaker's voice-coil in ohms (Ω), also quoted as Rdc or Rvc by most american manufacturers


voice-coil inductance in millihenrys (mH) (warning, the figure in the formula must be inserted against conversion in henrys)


free-air resonance of the speaker in hertz (Hz),
also quoted as f0


electrical merit factor of the speaker at fs


mechanical merit factor of the speaker at fs

Nevertheless, getting to this point is not completely a smooth ride. In fact, as everything else was not enough, ninetynine times out of a hundred you'll have a close encounter with another obstacle: some speakers will play stronger than others with which they have to cross. Typically this drawback occurs with tweeters and in general with all dome speakers. Their dedicated filtration row therefore will have to damp this exuberance through the attenuation cells