The Last Loudspeaker System

By Stig Erik Tangen
15 Dec 1997

Crossover

The crossover is the brain of any speaker, the most important and most difficult part. The best drivers are useless without a crossover to feed them the right signals. To obtain near-perfect results there are so many things that must be considered; frequency response, phase response, impedance, phase correlation between the drivers, overall level, crossover slope symmetry, driver directivity, lobing patterns, off-axis response... I could go on forever. Let me just say that all these things have been considered thoroughly when designing this speaker, but I shall only discuss a few of them here.

Before I started to design the crossover, I measured the impedance of both drivers, and imported the data along with frequency reponse measurements into CALSOD. Below 3-400 Hz I discarded the measurement data for frequency response, and relied purely on theory, as my measurements are not reliable below 400 Hz because of room interference. The rest of the curves shown here are from CALSOD simulations, but I've checked with the TEF to make sure they are representative.

Now then, what is the right theory to use below 3-400 Hz? All computer programs use the Thiele/Small model for low frequency simulations, a model which prescribes a resistive acoustic loading. These programs also relies strictly on half-space acoustic loading. In the real world, with real life speakers and listening rooms, pure resistive half-space acoustic loading does not exist. Of this reason, no box-calculators tells us how the speaker eventually will perform in our listening room.

Now some words about acoustic loading. A single point source radiates its sound energy omnidirectional, 360 degrees. This is called free-field acoustic loading; no abstacles to change the radiation pattern. When we put this source on a baffle, the sound energy is not radiated omnidirectional, but in a 180 degrees sphere. The baffle prevents the sound from radiating behind the baffle. This leads to a 6 dB increase in sound pressure. However, the baffle's acoustic loading is dependant on it's size. For frequencies which have wavelengths more than 1/4 of the baffle's size, the baffle can no longer reflect the sound wave, and will not provide acoustic loading. The loading will gradually change from half-space to free-field, and the radiation will change from 180 degrees to omnidirectional.

When we consider loudspeakers, the baffle of the box produces half-space acoustic loading down to the frequency where one-quarter wavelength of sound equals the baffle size. A 20 cm wide baffle will start to "unload" from about 400 Hz, and the speaker's response will drop by 6 dB below 400 Hz. This phemonemon is often referred to as "the baffle step". The "step" is not absolute, but more like a 1st order function.

When we put the speaker in a room, an other acoustic effect is produced; the boundaries of the room will start to acoustically load the speaker. An "average" room loading curve is recommended by Martin Colloms in his book "High Performance Loudspeakers", and it looks like this Fig. 3. Room gain function.

When we add the baffle loading of our box to the room loading shown above, we get something like this Fig. 4. Room gain with baffle loading.

This is theory. According to my own experiments and measurements, a speaker designed for true halfspace loading will exhibit an approx. 3 dB dip centered around 150-200 Hz in a room. This makes the speaker sound bright, and it may also sound bass-heavy at the same time if the low frequency extension is sufficient. An absolutely flat frequency response from 100 to some 2000 Hz is in my opinion extremely important. Almost all fundamentals in music happen in this area. Big dips in the response are a lot worse here than below 100 Hz or above 2 kHz.

The above discussed 3 dB dip at 150-200 Hz leaves us with a low frequency sensitivity of about 85dB/1W/1m with the Seas woofer. A quick calculation tells us we have to burn 7 dB (or 80% !) of the tweeter's sensitivity in the crossover to obtain a flat frequency response at 85 dB, and at least some 4-5 dB of the midrange. Do we really want that? Instead I have designed a crossover that crosses over at the selected frequency and slope, but creates a total frequency response that rises smoothly by 7 dB from 100 Hz to 2 kHz. This frequency rise is corrected by a simple passive equalizer placed somewhere in the signal chain at line-level (preferrably between the control and power amp). We now have a speaker that has quite nice sensitivity in the important midrange, and is capable of playing more than loud enough with a 50W amplifier.

I decided to cross over at 2750 Hz. I always use a 4th order Linkwitz-Riley type of filter and this case is no exception. The goal of the filter is NOT to create a true 4th order electrical function, but to create an acoustic response from the drivers that complies to the 4th order function.

For the woofer it is absolutely necessary to kill the resonance peak at 5 kHz. I do this with a L-C parallell circuit. This circuit together with a series inductor does it all; both 4th order rolloff and kills the resonance peak. This is the filter type Seas recommends for the Excel magnesium drivers.

The tweeter looked simpler to design a filter for, since it's rolloff is more relaxed that the wild Seas mid/woofer. Even so, I struggled a lot with this. I ended up with a third order filter topology.

I also designed impedance equalizing networks to flatten the total impedance of the speaker. These are shown in red colour on the crossover schematic below. These parts may be skipped, but most amplifiers benefit from a flatter impedance load.

Here's the final crossover Fig. 5. The final crossover.

The 12.5 mH inductor should as well as all the others be an air-core type. I used an inductor with 0.8 mm wire. This coil has a DCR of 3.6 ohm, but that's not a problem here since I put a 8 ohm resistor in series.

To minimize the coloration of the crossover, I used CFAC inductors (except for the big 12.5 mH in the impedance equalizer). There may be some sonic differences between different brands of polypropylene caps, but the difference between CFAC and all other inductors is really great. The quality of the CFAC really shows off through the Seas Excel mid/woofer. If you can't afford CFAC's all the way, at least use it in series with the mid/woofer.

I used Reoderstein ERO MKP1840 caps, but other polypropylene types may be used without spoiling the sound quality.

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