# Calculate Q of Second-Order Crossover (12dB)

 For optimal filter operation it is important to use the impedance (Z) of the loudspeaker at the cut-off frequency. The DC resistance is NOT optimal to calculate crossover filters! If you don't know the loudspeaker impedance at Crossover frequency use the DC resistance of the loudspeaker, How to measure Loudspeaker Impedance

 Loudspeaker Impedance [ Z ]: ohm C: uF L: mH Q value of network: crossover frequency:or Hz  kHz Looks like a

## Second order Linkwitz-Riley ( LR2 )

(The Linkwitz-Riley filter has a crossover frequency where the output of each filter is 6dB down, and this has the advantage of a zero rise in output at the crossover frequency.)
Second-order Linkwitz-Riley crossovers (LR2) have a 12 dB/octave (40 dB/decade) slope. They can be realized by cascading two one-pole filters, or using a Sallen Key filter topology with a Q value of 0.5. There is a 180° phase difference between the lowpass and highpass output of the filter, which can be corrected by inverting one signal. In loudspeakers this is usually done by reversing the polarity of one driver if the crossover is passive.

## Bessel filter

( Maximally flat phase, Fastest settling time, Q: 0.5 to 0.7 (typ) )
A Bessel filter is a type of linear filter with a maximally flat group delay (maximally linear phase response). Bessel filters are often used in audio crossover systems. Analog Bessel filters are characterized by almost constant group delay across the entire passband, thus preserving the wave shape of filtered signals in the passband.

## Butterworth filter

( Maximally flat amplitude, Q: 0.707 )
The Butterworth filter is a type of signal processing filter designed to have as flat a frequency response as possible in the passband. It is also referred to as a maximally flat magnitude filter.

## Chebyshev filters

( Fastest rolloff, Slight peaks / dips, Q: 0.8 to 1.2 (typ) )
Chebyshev filters are classified by the amount of ripple in the passband, for example a 1 dB Chebyshev low-pass filter is one with a magnitude response ripple of 1 dB. Chebyshev filters are popular because they offer steeper roll-off rates than Butterworth filters for the same order, but for audio applications the Chebyshev is virtually never seen due to the superior magnitude and phase responses of the Butterworth class.

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