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Why speaker impedance have a peak around cross over frequency?

Peter Chuang

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When I look at speaker impedance graph, interestingly, I found a lot of speakers having impedance peak around crossover frequency.
Take focal 906 measurements by @amirm for example.
There is a peak around 2.5khz.
I understand that tweeter have a high pass filter, while the woofer have a low pass filter.
Impedance of each filter having impedance function as R+jX.
In a certain frequency, where HPF and LPF connect parallel can achieve imaginary part of the impedance to be canceled leaving R only.
(one of the jX of HPF/LPF is positive while the other is negative which makes R+jX(LPF) // R+jX(HPF) = R_eq +j0)
The question is, why R is so high even higher than impedance of the driver unit?
If the woofer driver itself is 4~8 ohm, and tweeter also 4-8 ohm, how come it result in 30+ ohm at 2.5khz.
Can this be explained in the topology?
Thanks in advance.

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Rick Sykora

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Was just getting prepped to do a post about speaker impedance and regret did not see sooner. So, hopefully, better late than never...

The main contributor to the high speaker impedance at 2.5 kHz is the crossover. The higher the order of filters, the higher the impedance. At higher frequencies would expect most of the impedance to come from the woofer filter. If you look at a speaker like the Vandersteen VLR (using 1st order filters), you will see a much lower impedance around the crossover frequency.
 

DonH56

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What he said ^^^

From a hand-waving physical hairy-knuckled engineering point of view, at the crossover frequency you have two drivers contributing more-or-less equally, so to keep from having an increase in SPL you need to "block" some of the signal to each driver, leading to higher impedance seen by the amp. As you go above the crossover frequency looking into the tweeter, high frequencies see lower impedance and low frequencies see higher and higher impedance as low frequencies are blocked from the tweeter, whilst looking into the woofer's side of the crossover the impedance will be lower for low frequencies and rise for high frequencies (blocking high frequency energy from the woofer). This not always completely true, of course, as it depends on the drivers and crossover design, but I did say "hand-waving".

The crossover corner frequencies also tend to be areas of rapid phase changes.
 

HansHolland

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asume:
the woofer and tweeter are perfect = behave like a resistor and have a perfect frequency response for amplitude and phase

Even then such a rise would happen at the crossover frequency (if the crossover keeps the frequency amplitude response flat).

Because at the crossover frequency both drivers are active and this results in a 6 dB higher efficiency. That's why Linkwitz–Riley crossovers reduce the sound pressure of the drivers at the crossover frequency with 6 dB. And then the impedance at the crossover frequency is higher (if using regular coil-capacitor crossovers).

It is possible to create a crossover with a flat impedance without extra impedance corrections. Those are the Butterworth filters. These have a -3 dB reduction of the amplitude of the drivers at the crossover frequency. When creating even order filters with a Butterworth design, then you get a +3 dB bump in the amplitude response. That's why Butterworth filters are mostly odd order filters, then the phase diference cancels the +3 dB. The phase difference can also be created by the difference in distance from the 2 drivers to the ear (only needs to be "correct" around the crossover frequency).

And this also explains why Linkwitz–Riley filters are mostly even order filters.


And then add the impedance rise due to inductance. And all the other corrections for e.g. resonances.
 
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