Example of Cascading Crossovers
31st December 2003
This report or test is made due to a request and to further facilitate explanation to another person. It is hoped that this exercise will help and benefit all others.
A simulation will be used to illustrate this example. Although it is only on a simulation level, but please trust that it will become reality, assuming the real crossover used behaves true to it's purpose and design.
Only active filters simulation will be used because they are the most effective.
Bostwick's woofer model 1248 will be used for this example. It is a 12" woofer using regular thick magnet and 8 ohms.
The woofer is measured on-axis "near-field" to obtain it's frequency response before simulation. Please notice the purple curve in the graph below. It is too good to be a woofer. Should have been used for "Professional Audio" loudspeakers because it poses a very smooth and near flat response from around 30Hz to 400Hz before starting the cone breakup phenomenon behaviour. Even the cone breakup level of the 1st major frequency is not significant nor radical for a woofer. It's sound is expected to be nice and warm, friendly. Not Hi-Fi, but in the "Pro-Audio" league. It would be Hi-Fi quality. However cone breakups after 1kHz is back to the usual "significance" hence very unfriendly. This is fine as "Pro-Audio" loudspeakers always employs "Horn Tweeters" to take over around 1kHz. Some times as low as 500Hz, which will yield a "re-production" of even higher sound quality. Assuming the "Horn Tweeter" is not harsh itself :)
Still this is not a woofer's review, so the impedance, Q etc will not be discussed. Also since this simulation only concentrate on "active" therefore no worries on impedances and what lot is required :)
All filter family are Linkwitz-Riley for ease of use.
Filter 1 = Low-pass at 100Hz using 24dB/oct
Filter 2 = Low-pass at 200Hz using 12dB/oct
Filter 3 = Low-pass at 320Hz using 12dB/oct
Filter 4 = Low-pass at 100Hz using 12dB/oct
The point of this exercise is to proof that certain method of cascading the filter will not work and render the secondary filter ineffective, hence like "disappeared" of it's presence.
Please see green color curve - nearly disappeared. Mostly because covered under the yellow and red curves. This is the woofer with Filter 1 only. Not cascaded.
Then it will be cascaded by Filter 2. Please see the red color curve. The cascade exist but not significant. Only noticeable after -30dB. It is so little that it is dictated as ineffective.
When it is cascaded using Filter 1 and 3 only. The results is even more apparent that the secondary filter literally "disappear" completely. Please see yellow color curve. Only noticeable after -30dB, near the bottom of the graph. This is because Filter 1 have successfully and effective filtered out the original source and there are nothing left to be filtered again.
Finally a truly effective cascading always needs to be set on the same frequency as demonstrated by cascading Filter 1 and Filter 4 on the same frequency, yielding a -36dB/oct filter. Please see light blue color curve.
Actually a 24dB/oct filter are cascade of two 12dB/oct filters.
Please realise also that levels dropped below 10dB is nearly impossible to be heard because it is masked by higher levels.
It will be further masked because the mid range usually plays as low as 100Hz at -6dB point if using 24dB/oct. This means when the woofer's frequency after low-pass filtered, entering into the 1st octave forward, it would literary be -24dB below the mid. This would render it's sound nearly impossible to be heard "directly" or "primary".
"Reserve" will be noted because sound is in time domain an that human brain's processing of sound is also in time domain. The time in which the filter sound decays plays an unknown psychological role is human feelings parameters.
Not only the time in which the filtered sound decays, but also the way it decays also plays an untold psychological role in human feelings phenomenon.
Therefore all issues small or large must be taken into considerations. However this exercise proofs that the primary or the so-called immediately "felt able" by all mass life forms lie true that levels below 10dB are impossible to be head because masked by higher levels. However the significance of how it goes down and how long it goes down remain a part of sound's understanding mystery.
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