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  Crossover Networks for Loudspeakers



Critical, Bessel, Butterworth & Cheybyscheff Calculate Second-Order Q Value Second-Order Linkwitz-Riley Filter


Show Network Circuits (6, 12, 18 & 24dB)




Important Information

Unless you are willing to completely rely on trial and error procedures, start your network design project by measuring the impedance of the drivers and correcting the impedance if necessary with a RC filter.

How to measure the driver impedance curve ?

Calculate here the Impedance Equalization Circuit


It is very helpfull if you are able to measure the frequency response of the drivers to choose the best crossover frequency.

How to measure the driver frequency response ?

If you choose a crossover point in a range where the driver's frequency response is changing rapidly off-axis, the off-axis response will have large response anomalies.
Large variations in the off-axis response degrade the power response the listener perceives. Reflected and reverberant response will be significantly different from the on-axis response, and generally devalue the overall quality.

Have a look here for recommended measuring software


Selecting the best slope is important, both to protect the tweeter (in particular), and to ensure that the drivers are all operated within their optimum frequency and power handling ranges.

A 6dB/octave (first-order) filter has the most predictable response, and is affected less by impedance variations than higher orders. On the negative side, the loudspeaker drivers will be producing sound at frequencies that are very likely outside their upper or lower limits.

12dB/octave (second-order) filters are better at keeping unwanted frequencies out of the individual speakers, but are more complex, and are affected by impedance variations to a much greater degree. The tolerance of the components used will also have a greater effect. The capacitance used must remain predictable and constant over time and power, which specifically excludes the use of bipolar electrolytics.

A 18dB/octave (third-order) filter requires closer tolerances than a second order, and is again even more susceptible to any impedance variations than the 12dB filter.

24dB/octave (fourth-order) filters increases the complexity and tolerance requirements even further - a point must be reached where the requirements versus the complexity and sensitivity will balance out.

How does it work?

For this example i use a second order (12dB) Highpass crossover network for 1 kHz.

The capacitor and also the inductor both have a specific resistant at any frequency.
  • Crossover frequency: 1 kHz ( Linkwitz-Riley Crossover )
  • Driver resistent: 10 ohm
  • Inductor: 3.0 mH
  • Capacitor: 8 uF
At the crossover frequency (1 kHz) both components have the same resistanc (20 ohms).

Now, the capacitor is in series with the driver and the inductor is parallel with the driver.

The resistance of the driver (10 ohm) together with the inductor (20 ohm) is:
  • Zi = impedance of inductor
  • Re = Driver impedance
(Zi * Re) / (Zi + Re) = (20 * 10) / (20 + 10) = 6.66 ohm

The capacitor and the inductor together with driver are a voltage divider.

Calculation of this divider:

6.66 ohm / (6.66 ohm + 20 ohm) = 0.25

That means a input-voltage of 1 volt will be a output-voltage of 1 * 0.25 = 0.25 volt

And how much dB is that?

20 * log(0.25) = -12dB

Isn't it easy?
More information about Passive Crossover Network Design: Elliot Sound Products


Crossover Calculator:
Critical, Bessel, Butterworth & Cheybyscheff


If you want a small phase difference as possible, the slope has to be 6dB at the crossover frequency [Fx]

Fx [Hz] = Crossover-Frequency to calculate (3dB or 6dB Slope)
Slope = Slope at Rolloff-Frequency (fx)
R [Ohms] = Loudspeaker resistant at Rolloff-Frequency

Fx [Hz]: Slope [dB]:
R [Ohms]: Order [dB]:
Crossover type:

 
Characteristic      Part 1    Part 2    Part 3    Part 4
Linkwitz/Riley [Critical]  
Bessel  
Butterworth  
Cheybyscheff +1 dB  
Cheybyscheff +2 dB  

Linkwitz/Riley [Critical]  -  Bessel  -  Butterworth  -  Cheybyscheff +1dB  -  Cheybyscheff +2dB




Brief explanation


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.






Calculate Q of Second-Order Network (12dB)


Re  ohms
C  uF
L  mH

Q value of network:

crossover frequency:
or 
 Hz
 kHz
Looks like a










Second-Order Linkwitz-Riley Crossover


This 12 dB per octave crossover is designed to solve the problem of centering the main lobe of the forward radiation pattern of a two-way speaker system.

This crossover is unusual in that each filter is down 6 dB at crossover and that the two drivers are actually "in phase" at all frequencies when the drivers are wired in opposite polarity. That is, even though the filters have their own characteristic phase responses the phase difference between the two output signals is the same at all frequencies. As a result, each filter section has the same group delay.

This crossover is recommended over the 2nd order Butterworth type due to its accurate summed frequency response and forward pointing main lobe.

Inverted polarity is required for one of the drivers.


Second-Order Low Pass Filter Bandpass Filter Second-Order High Pass Filter
C1 = .0796 / ( Rh x f )        C2 = .0796 / ( RL x f )
L1 = (.3183 x Rh ) / f        L2 = (.3183 x RL ) / f
 
Tweeter Impedance ( Re )  Ohms     Highpass     Lowpass  
Woofer Impedance ( Re )  Ohms     C1 uF   C2uF
Desired Crossover Frequency ( f )  Hertz     L1 mH   L2mH