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Passive Crossover Networks



In this lesson we'll try to destroy the myth which the impedance of a speaker would correspond to as stated by the builder. In our opinion, to believe in rubbish as this is the same as believing that children are carried by the stork.

Actually the nominal impedance, that specified on catalogs, has the only purpose to divide speakers in families, depending on the type of use which they are intended for. So we'll have 4Ω speakers for car-audio, 8Ω speakers for home hi-fi and 16Ω or more for professional applications. The nominal datum would approximate to the closest of these values the real impedance, measured on the moving coil at certain frequencies — typically 100hz, 400hz, 1Khz, but not only, according to the builder and the type of speaker. Being the nominal datum referred to an only frequency, what's more in approximate way, and being instead the impedance variable with the frequency in real life, it stands to reason that you can't refer to this value for the calculation of the filter. If we then add it's not rare to come up against builders that pass off for 4Ω components speakers of even double impedance, the picture is complete.

It is possible to describe the impedance assumed by the moving coil at different frequencies in graphical form on a cartesian plan, with the scale of frequencies in abscissa (Hz) and the impedance values in ordinate (Ω). The drawing that results is called an impedance curve and visually represents the modification of the ohmic value assumed by impedance at different frequencies. See for example that of a cone midrange rated for 6Ω nominal:

Impedance Curve

The first thing you notice is a peak of impedance with an ascending front and a descending front specular between them (well, this specularity is verifiable only if the frequency scale in abscissa is logarithmic). To it corresponds the resonance frequency of the component, recognizable exactly because at the resonance all transducers show a sudden increase of impedance. Moving toward the right, that's going up with the frequency, we meet a saddle where it should be possible to read a value near to that declared as nominal — see what has already been said about some builders — after which the effect of the moving coil inductance begins to make itself felt, in the form of a gradual increase of measurable impedance.

Through the graph below you can realize as a generic second-order bandpass calculated with the provided formulas produces definitely different responses if closed on a resistor (green) or on a real midrange (yellow):

Resistor vs/ Speaker

Both to resonance of the midrange and to the highest frequencies, the filter sees a greater load impedance and filters less. Result: the curves are equal only in the octave 1Khz–2Khz while the portions of frequency that the filter had to reject are instead in overbearing evidence. Really awful!

To make the response of the set filter/speaker coincide to the model theorized by formulas it must modify the speaker in order to achieve in its terminals an impedance as much resistive as possible, that's constant with the frequency. Provide to this really them, the equalization networks