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Filter & Crossover Types for Loudspeakers

by August 29, 2004
Contributors: Shane Rich

The filter type can be described in several different ways. Low-pass and high-pass filters in two-way crossover networks are often identified by their "Q". The Q is the resonance magnification of the filter and it is recognized by the shape of the "knee" of the amplitude response. Filters with a high Q tend to "ring" and exhibit poor transient response. Unlike drivers and boxes which use only numerical values for Q, filters are sometimes named after the engineer(s) who first described them. Some examples are shown in the amplitude response graph below.

Filter Types

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The filters in three-way crossover networks (and some two-way networks) are often identified as either "APC" or "CPC" depending on the way they combine. APC stands for "All-Pass Crossover" and it refers to those crossover networks whose filters sum to create a flat voltage output. APC networks are generally considered the best choice because they make it possible for the speaker to have a flat on-axis amplitude response. Common APC networks include 1st- and 3rd-order Butterworth filters and 2nd- and 4th-order Linkwitz-Riley filters. CPC stands for "Constant-Power Crossover" and it refers to those crossovers whose filters sum to provide a flat power response. The power response of a speaker is the total of both its off-axis and on-axis amplitude response. In other words, it is the total acoustical power that is radiated into a space. CPC networks can be beneficial in reverberant environments where the off-axis response is important.

The difference between APC and CPC networks can be understood electrically by a comparison of their input to output voltages. APC networks satisfy the following expression:

[VI] = [VL + VM + VH]

This means the absolute value of the input voltage will equal the absolute value of the sum of the output voltages of each filter at all frequencies. CPC networks satisfy the following:

VI^2 = VL^2 + VM^2 + VH^2

This means that the square of the input voltage will equal the sum of the squares of the output voltages of each filter at all frequencies.

Filter Summary

These generalizations assume that the drivers are properly aligned at the crossover frequency. This means that they are mounted in such a way that the direct sound from each driver arrives at the listener's ear at the same time at the crossover frequency. Another important assumption is that the impedance response of each driver has been equalized so that it appears to be approximately resistive to the crossover network. Also, the sensitivity of the drivers is assumed to have been equalized with an appropriate L-pad.

Finally, the following descriptions assume that all filters in the crossover network are of the same type. If a two-way crossover network has a 4th-order Linkwitz-Riley low-pass filter, it is assumed that it also has a 4th-order Linkwitz-Riley high-pass filter. If you choose to use mismatched filters, you'll have to rely on the your own measurements and experience to determine the results.

1st-order Filters

Advantages: Can produce minimum phase response (Butterworth only) and a maximally flat amplitude response. Requires the fewest components.

Disadvantages: Its 6 dB/octave slope is often too shallow to prevent modulation distortion, especially at a tweeter's resonance frequency. Achieving minimum phase and a maximally flat amplitude response requires very careful driver alignment and only occurs when the listener is located at exactly the same distance from each driver. It has a 90 degree phase shift which can result in lobing and tilting of the coverage pattern.

Two-Way

1st-order Butterworth: Produces a -3 dB crossover point to achieve a maximally flat amplitude response, minimum phase response and flat power response that qualifies it as both an APC and CPC network. The 90 degree phase shift results in a -15degree tilt in the vertical coverage pattern if the tweeter and woofer are vertically separated by no more than one wavelength at the crossover frequency and if the acoustical depth of the tweeter and woofer are carefully aligned at the crossover frequency. The tilt will increase and lobing can become severe if the drivers are separated by a greater distance or are misaligned. These problems appear as a ripple in the amplitude response. Filter Q = 0.707.

Two-Way & Three-Way

1st-order Solen Split -6 dB: A custom version of the 1st-order Butterworth filter (twoway crossovers) or 1st-order APC filter (three-way crossovers) that uses a -6 dB crossover point to minimize the disadvantages of a crossover network with standard 1st-order Butterworth or APC filters.

Three-Way

Note. 1st-order filters are usually not recommended for three-way crossover networks because their shallow 6 dB/octave slopes do not provide adequate separation. 1st-order APC: Produces -3 dB crossover points to achieve a flat amplitude response.

1st-order CPC: (Seldom used.) Produces -3 dB crossover points to achieve a flat power response.

2nd-order Filters

Advantages: Can produce a maximally flat amplitude response. Requires relatively few components. Has a 180 degree phase shift which can often be accommodated by reversing the polarity of the tweeter and which produces minimal or no lobing or tilt in the coverage pattern. Is less sensitive to driver misalignment than 1st-order filters.

Disadvantages: Although the 12 dB/octave slope is better than a 1st-order filter, it may still be too shallow to minimize the modulation distortion of many drivers.

Two-Way

2nd-order Bessel: Produces a -5 dB crossover point to achieve a nearly flat (+1 dB) amplitude response. The summed group delay is flat. It has a low sensitivity to driver misalignment and resonance peaks. Filter Q = 0.58.

2nd-order Butterworth: Produces a -3 dB crossover point that sums to a +3 dB amplitude response and a flat power response that qualifies it as a CPC network. It has a medium sensitivity to driver misalignment and resonance peaks. Filter Q = 0.707.

2nd-order Chebychev: (Seldom used.) Produces a 0 dB crossover point to achieve a

+6 dB amplitude response with about ±2 dB of ripple. The summed group delay has a significant peak just below the crossover frequency. It has a medium sensitivity to driver misalignment and resonance peaks. Filter Q = 1 .0.

2nd-order Linkwitz-Riley: (Very popular.) Produces a -6 dB crossover point to achieve a maximally flat amplitude response that qualifies it as an APC network. It has a -3 dB dip in the power response. The summed group delay is flat. It has a medium sensitivity to driver misalignment and resonance peaks. Filter Q = 0.49.

Three-Way

2nd-order APC: Produces -6 dB crossover points to achieve a flat amplitude response but the power response will have approximately 3 dB of ripple.

2nd-order CPC: (Seldom used.) Produces -3 dB crossover points to achieve a flat power response but the amplitude response will have approximately 3 dB of ripple.

3rd-order Filters

Advantages: Can produce nearly flat amplitude response. With an 18 dB/octave slope, it is better able to minimize modulation distortion. Less sensitive to driver misalignment.

Disadvantages: Requires more components. Has a 270 degree phase shift which can result in lobing and tilting of the coverage pattern.

Two-Way

3rd-order Butterworth: (Popular for some D'Appolito mid-tweeter-mid designs.) Produces a -3 dB crossover point to achieve a maximally flat amplitude response and flat power response that qualifies it as both an APC and CPC network. A 270 degree phase shift results in a + 15 degree tilt in the vertical coverage pattern if the tweeter is wired with normal polarity and a -15 degree tilt if the tweeter is wired with reverse polarity. (D'Appolito mid-tweeter-mid designs overcome much of this tilt problem and produce a more symmetrical coverage pattern.) It has better group delay than a 1st- and 2nd-order Butterworth network. Filter Q = 0.707.

Three-Way

3rd-order APC: Produces -3 dB crossover points to achieve a flat amplitude response but the power response will have a modest ripple (usually less then 1 dB) that increases slowly as the spread between the two crossover frequencies increases.

3rd-order CPC: (Seldom used.) Produces -3 dB crossover points to achieve a flat power response but the amplitude response will have a varying amount of ripple (typically 1 to 3 dB) depending on the spread between the two crossover frequencies.

4th-order Filters

Advantages: Can produce a maximally flat amplitude response. With a 24 dB/octave slope it provides the best isolation between drivers resulting in the least modulation distortion. Has a 360 degree phase shift which results in "in-phase" response and which promotes minimal or no lobing or tilt in the coverage pattern. Is the least sensitive to driver misalignment.

Disadvantages: Requires the most components. The increased number of inductors can result in substantial insertion loss because of inductor DCR.

Two-Way

4th-order Bessel: Produces a -7 ½ dB crossover point to achieve a nearly flat (-1 ½ dB) amplitude response. The summed group delay produces a moderate bump just below the crossover frequency. Filter Q = 0.58.

4th-order Butterworth: Produces a -3 dB crossover point that sums to a +3 dB amplitude response and flat power response that qualifies it as a CPC network. The summed group delay has a significant peak just below the crossover frequency. Filter Q = 0.707.

4th-order Gaussian: (A seldom used filter that is constructed with an asymmetrical filter topology.) Produces a -6 dB crossover point to achieve a nearly flat amplitude response with moderate ripple. The summed group delay produces a moderate bump just below the crossover frequency.

4th-order Legendre: (A seldom used filter that is constructed with an asymmetrical filter topology.) Produces a -1 dB crossover point that sums to a +5 dB amplitude response with minor ripple. The summed group delay has a significant peak just below the crossover frequency.

4th-order Linear-Phase: (A seldom used filter that is constructed with an asymmetrical filter topology.) Produces a -6 dB crossover point to achieve a nearly flat amplitude response with moderate ripple. The summed group delay produces a moderate bump just below the crossover frequency.

4th-order Linkwitz-Riley: (Very popular. Sometimes called a "squared Butterworth" filter. Also used for some D'Appolito mid-tweeter-mid designs.) Produces a -6 dB crossover point to achieve a maximally flat amplitude response that qualifies it as an APC network. It has a -3 dB dip in the power response. The summed group delay produces a moderate bump just below the crossover frequency. Filter Q = 0.49.

Three-Way

4th-order APC: Produces -6 dB crossover points to achieve a flat amplitude response but the power response will have approximately 3 dB of ripple.

4th-order CPC: (Seldom used.) Produces -3 dB crossover points to achieve a flat power response but the amplitude response will have approximately 3 dB of ripple.

Source : Xover Pro Harris Technologies

Acknowledgements: I would like to thank Shane Rich (Technical Director of RBH Sound, Inc) for helping with the compilation of this information to serve as a tool in forthcoming technical articles and reviews of loudspeakers.

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About the author:

Gene manages this organization, establishes relations with manufacturers and keeps Audioholics a well oiled machine. His goal is to educate about home theater and develop more standards in the industry to eliminate consumer confusion clouded by industry snake oil.

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