Crossover Tips

If you are looking for a nice cookbook of formulas here, you won't find them.  You can find formulas in a myriad of places from the internet to The LoudSpeaker Design CookBook by Vance Dickason, as well as other speakerbuilding books.  Instead, what I want to cover are some points about crossovers that most people don't think about.

The typical speakerbuilding newbie goes through a scenario something like this, "I will buy so and so drivers, build the box according to formulas or programs, pick a crossover point somewhere between the limits of the woofer and tweeter, and depending on the driver's impedance rating, plug 4 ohms or 8 ohms into the textbook formulas and I should have a great sounding speaker."  Wrong, wrong, wrong.  Unless the newbie is extremely lucky, his speaker will sound like crap.  Why?  Because crossovers depend on the exact impedance at the crossover point, as well as the acoustic offset of the drivers.  Also, various crossover types such as second order Butterworth will alter the frequency response by as much as 3 dB if executed properly!  Finally, there is baffle step which causes a loss of bass.  Let's look a little more closely at these problems.

Impedance Issues
Textbook formulas are difficult to execute properly when based on the driver's nominal impedance.  Look at the impedance curve for any 6 1/2" woofer.  You will see the typical impedance peak at the resonant frequency usually somewhere below 100 Hz.  This may be as high as 100 ohms.  Then the impedance droops back to the nominal value after a few hundred Hz, but then rises smoothly after this due to the voice coil inductance.  This rising impedance may become as high as the impedance at the resonance!  By the time the frequency is up to typical crossover frequencies (say 2 kHz to 3.5 kHz), the impedance may be between 10 and 20 ohms!!!  This will cause the crossover values to be significantly different than those for nominal impedances of 4 or 8 ohms.  This is one of the reasons that using nominal impedance with textbook formulas rarely will yield satisfactory results.  Likewise, tweeter crossovers may be affected by the impedance peak at the tweeters resonance.  This is why it is suggested to crossover the tweeter one to two octaves above the resonance.

There are two ways to deal with the problem of rising woofer impedance.  One is to actually measure (or read from a graph) the actual driver impedance at the crossover frequency.  At least design the woofer crossover based on about 12 ohms impedance.  This should get you in the ballpark.  The only problem with this approach is that the impedance on either side of the crossover is not constant, so you will get some wiggle around the crossover.  Of course, as mentioned, cross the tweeter over about 1 1/2 to 2 times its resonance, and it should be okay to use the nominal tweeter impedance for the tweeter crossover.

The second way to deal with rising woofer impedance is to use impedance compensating circuitry - a Zobel.  A Zobel is a capacitor and a resistor in series placed across the woofer leads.  Using a Zobel will flatten the rising impedance and bring it down to the nominal range throughout the upper frequencies of the woofer.  Then use the nominal woofer impedance to design the woofer crossover.  The main drawback is that it will interfere with the woofer's frequency response to an extent, but this is relatively minor compared to the actual crossover network's changes.  Again, look to the LDC or the internet for more information and formulas.

Acoustic Offset
Textbook formulas assume that there is no acoustic offset between the drivers.  Acoustic offset is the difference in the distance of the voice coils of the two drivers from a vertical plane.  Actually, it isn't exactly the voice coil centers, but it's close enough for our purposes.  Basically the woofer's acoustic center is further back than the tweeter's, and this difference introduces phase differences which affects the summation of the driver's frequencies at the crossover point.  There are really only two things you can do without measurement and crossover modeling software. 

One, you can estimate the center of the voice coil for each driver as the distance from the baffle to the center of the driver top plate.  Subtract the distance for one driver from that of the other, and if this difference is half the wavelength of the crossover frequency, then reverse the tweeter's leads if you normally shouldn't, or don't reverse them if you normally should.  When the acoustic offset is one half the wavelength of the crossover frequency, the phase is reversed 180 degrees.  Of course if the offset distance is an even multiple of the crossover wavelength, then the phase difference is technically zero, and the textbook formulas should work as they are.

Two, you can build a step into the baffle to align the tweeter and woofer centers.  You can assume that the acoustic center is at the center of the top plate.  That isn't entirely true, but it's as close as you can get without measurement software.

One final note, also try to keep the distance between the driver's centers (as mounted on the baffle) less than the wavelength of the crossover frequency.  Don't put the woofer at the bottom of a tower, and the tweeter at the top, and try to cross them over at a high frequency ;-)

Crossover Types
First order crossovers are notoriously difficult to implement properly.  Don't get me wrong, many speakers that only have a capacitor on the tweeter, and nothing (or an inductor) on the woofer can sound quite good.  But usually it's difficult to combine the drivers to have a true 6 dB/octave crossover because the driver's curves will roll off faster than that, and the acoustic centers should be time aligned.  Sometimes it's better to use steeper slopes on the crossovers so that the drivers interfere with each other less. 

Second Order Butterworth networks actually don't sum flat.  They will sum to a +3 dB peak around the crossover.  One way to overcome this effect is to spread out the crossover frequencies.  Let the woofer's crossover frequency be, say X/1.3, and the tweeter's be 1.3 * X, where "X" is the crossover frequency.  This will cause the crossover to sum flatter by causing a dip where there would normally be a peak.  The peak and dip cancel each other out, and the response will be flat.

Personally, I would recommend the following crossover types:
Second Order Linkwitz/Riley
Third order Butterworth

These crossovers are more forgiving of acoustic offsets, and don't cause peaks at the crossover frequency when implemented properly.  Note that the fourth order Linkwitz/Riley network is really difficult to implement properly, since a true fourth order acoustic response can actually be attained with lower order networks.  This is because the driver's actual roll off combines with the electrical network to give the true acoustical slope of the crossover.  Often a second order network on the tweeter can be combined with a third order on the woofer to give a fourth order acoustical response.

Baffle Step

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