LR or butterworth filter, which one and why??

[aaron_garmon]

Provided Link: AJ crossover equations


I'm building a 5.1 HT system with the front mount dayton neo and the tang band W4-654S. I found a crossover calculator on line (see link below) and it give the option of Linkwitz-Riley, butterworth, bessel or chebychev crossovers. I know most people just use the first two mentioned so I'll stick with that, but which one? what's the difference?

still new at this, sorry.
thanks, Aaron Garmon

[hongrn]

Re: LR or butterworth filter, which one and why??


Aaron,

Here's a good summary:

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° 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° phase shift results in a –15° 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 (two-way 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° 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° 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° phase shift results in a +15° tilt in the vertical coverage pattern if the tweeter is wired with normal polarity and a –15° 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° 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 –5 dB crossover point to achieve a nearly flat (+1 dB) amplitude response. The summed group delay is flat. 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.

Copyright 1992-2005 by Harris Technologies, Inc.

[jeffman]

In layman's terms . . .


First, everything said above and here assumes that the response of both drivers is basically flat for an octave or so beyond the cutoff frequency. If that's not true, the summation of your electronic filter (what you build) and the natural rolloff of your driver(s) will be an *acoustic* rolloff very different from the ideal rolloff predicted by the equations.

Okay. For you, the basic difference between between the filters you mentioned is the way the intersecting curves will add together. The LR adds flat. Very easy to visualize this. Under the same conditions, the BW adds a 3 dB hump with its peak at the XO frequency. Very bad if your curves are flat, but perhaps useful if the unfiltered curves have dips at f(xo) or have already started to rolloff (hopefully to about -3dB at f(xo) ). You can also adjust the humps and dips by choosing slightly different cutoff frequencies for your two drivers, but this is a little harder to visualize. Not impossible, but you'll need to stare a lot.

There are also phase issues involved in your choice, but without serious software or a penchant for parabolic and logarithmic equations, you'd do best to ignore them.

Fact is, once you get hold of that serious software, you'll say goodbye to all these dudes and calculate component values based on what yields the best combination of a flat summation and phase integration. The resulting curves might look like a BW or LR or whatever, but the values you got there will have nothing to do with textbook equations.

Best advice for a quick, fun DIY project. Select drivers that will cross with room to spare somewhere in the low 2000s. Pad the tweeter as needed so the average SPL for both drivers is the same or so. Zobel your woofer. Calculate a LR XO using the textbook calculator. Your f(xo) is a function of L * C, so when you select your actual components and have to adjust to the closest available values, if one must go up, the other must go down.

J