Technical Discussions of Audio and Loudspeaker Issues
the Audio Engineering
Topic No. 10
Most examples of crossover circuits are limited to 2-way types with more complex 3-way, 4-way, and higher types left for the user to design for himself. Thats fine if you are an electrical engineer but for many other speaker builders a little help is needed.
What follows is a cookbook description showing how to design 3-way, 4-way, 5-way and higher degree crossovers from the basic building block of a 2-way crossover. While we will be looking only at passive crossovers here, the general method applies to active (line level) crossovers as well.
Most discussions of loudspeaker crossovers are limited to the discussion of 2-way crossover filter pairs as would be used in a 2-way speaker system that employed just two drivers: a woofer and a tweeter. This is because it is a straightforward task for an electronics engineer to expand these circuits into more complex crossovers such as 3-way, 4-way etc. Figure 1 (below) shows a detailed schematic of the simplest type of crossover: a 1st order 2-way type. The high pass filter consists of C1 while L1 makes up low pass filter network. Note that the circuit has one input at the left and two outputs labeled "High Output" and "Low Output" at the right.
Figure 1: Detailed Schematic Diagram of a 1st Order 2-Way Crossover
More complex 2-way crossovers such as 2nd and 3rd order Butterworth types will have 4 and 6 components respectively but will still have one input and the same High and Low outputs. Since the actual details of the particular 2-way crossover are not our concern here, lets simplify things by using a block diagram representation of the 2-way crossover as shown below in Figure 2. The details of the crossover are hidden inside the block. It might be the simple 1st order crossover shown in Figure 1 or it might be a highly complex 4th order Linkwitz-Riley type complete with impedance compensation and tweeter attenuation. We will concern ourselves here with the bigger picture of how we assemble 2-way crossovers to create 3-way, 4-way and higher degree crossovers.
Figure 2: Block Diagram of a 2-Way Crossover
As a speaker system increases in complexity to employ three drivers (woofer, mid, and tweeter) a 3-way crossover is required to divide the full spectrum signal into the three separate frequency bands that will feed the three drivers. The high frequency signals need to be sent to the tweeter, the mids to the mid range driver, and the lows to the woofer. Figure 3 shows a block diagram of a 3-way crossover.
Figure 3: Block Diagram of a 3-Way Crossover
Notice that the 3-way crossover is composed of two 2-way crossovers connected in such a way that the input signal is now divided into three frequency bands feeding the Low, Mid, and High outputs. The first 2-way crossover represents the lower crossover, at 500Hz in this example. The second crossover accepts the high (H) output from the first crossover and splits that intermediate signal further into High and Low frequency bands. Because the Low output from the second crossover has already been high-pass filtered by the first crossover and has been low-pass filtered by the second crossover it becomes the Mid output for the 3-way crossover. Similarly, the High output from the second crossover becomes the High output for the overall 3-way crossover.
Notice that we are not concerned with the internal details of either pair of crossover filters, just with the interconnection of the input and outputs of the crossovers.
Now, lets take it a step further and look at how a 4-way crossover is configured. Figure 4 shows a block diagram of a 4-way crossover with a single input and four outputs: Low, Low-Mid, High-Mid, and High. Such a crossover might represent a 3-way speaker along with a subwoofer.
Figure 4: Block Diagram of a 4-Way Crossover
Hopefully you see a pattern emerging here. The next step would be to create a 5-way crossover. We would take the high output from the 4-way crossover above and split it yet again with another 2-way filter pair.
This is all fine you say, but how do I create a detailed schematic from these block diagrams? First, draw yourself a block diagram of your system. Then replace each crossover block with the details of the crossover type you have selected for use at that block. Since even the most complex 2-way crossover type has just one input and two outputs this is a straightforward task. Lets create a detailed 3-way crossover from the block diagram in figure 3. Well start by detailing just the lower crossover. Figure 5 below shows the 3-way crossover with details for the 1st order Butterworth (lower) crossover and the upper crossover still shown as a block.
Figure 5: Partial Detail on the 3-Way Crossover
Next lets detail the upper crossover as a 2nd order Linkwitz-Riley type. This crossover is more complex than the 1st order Butterworth type used at the lower crossover. The upper crossover will employ a total of four components: two capacitors and two inductors. The detailed 3-way crossover is shown below in Figure 6 along with the ground connection. If you are not familiar with ground symbol notation (the triangle symbol) just note that the lines connected to ground are actually just all tied together. It saves a lot of drawing!
Figure 6: Detailed Schematic Diagram of a 3-Way Crossover
Now, as the final step we will remove the blocks from the crossovers and include the three drivers. See Figure 7 below for the schematic of the complete 3-way speaker system.
Figure 7: Schematic Diagram for a 3-Way Speaker System
Gaining Perspective on Multi-Way Crossovers
OK. Now that you know how to make a 20-way crossover . . . should you do it? Probably not.
As I see it, crossovers are evil, . . . but a necessary evil. If I could make all my loudspeaker systems full range types with no crossovers at all, I would. Thats because accurate acoustic summation of the separate outputs from a woofer and tweeter remains an elusive goal that is rarely, if ever, achieved in practice. The best you can even hope for is to have reasonably accurate summation over a narrow listening angle for a given 2-way speaker system.
Crossover summation problems remain the most significant flaw in most production speaker systems made today. Real world systems have a roughness in the frequency response through the crossover region that changes with the listening geometry.
One popular listening test is the so called "stand up, sit down" test. Often the sound of a speaker changes depending on whether you are standing up or sitting down. Much of this difference is due to the change in geometry as you stand or sit. If the tweeter is on top then you move relatively closer to the tweeter as you stand and then move relatively closer to the woofer as you sit. This has the effect of changing the relative arrival times from the two drivers and therefore changing the summed frequency response characteristics. If there is an audible difference in the stand up, sit down test it is probably due to geometry dependent crossover summing error.
But alas, most designers do find it necessary to use at least two different drivers, a woofer and a tweeter, in order to realize a full range speaker system with adequate performance at the frequency extremes. This means that the first crossover is almost impossible to avoid. But that second crossover . . . can often be avoided or at least kept far enough away from the first crossover frequency so as to not compound the imperfections of the first crossover.
Getting just two transducers to combine in any reasonably coherent fashion is difficult enough, when you throw in another driver and crossover you can just imagine the chances of achieving a precision summation. With a two-way crossover at least we can start out knowing that the crossover filter pair we are using sums accurately on its own. That is, you can take the outputs of most (but not all!) 2-way crossovers and electronically sum them (as if you were using perfect acoustic transducers in perfect time alignment) and achieve a good result. Most of the 2-way crossovers pass this test quite well. The one exception that comes to mind is the 2nd order Butterworth crossover. Combine these filters in-phase and you get a deep notch in the response centered at the crossover frequency. Yuck. Invert the polarity of one output and you get a 3 dB bump at crossover. Not as bad, but not exactly precision summing either.
The bad news is that when you cascade two crossover filter pairs to create 3-way crossovers (passive or active) they tend to run into summing problems right from the start. Even ideal electronic summation often results in response aberrations that strongly depend on the spacing of the two crossover frequencies and the filter type. As a rule, the more widely spaced the crossover frequencies the more accurate the summation. As you move your crossover from the ideal world of electronic summation to the much more difficult arena of acoustic summation the problem grows. You now have to consider not just the responses of the crossover filters but the responses of each driver in combination with the crossover filters.
There is one wonderful exception to the generally nasty behavior of 3-way and higher crossovers: the 1st order Butterworth crossover. The ideal performance of this simplest of all crossover types holds up even in 3-way and higher crossover types. The electronic summation characteristics are absolutely perfect. This crossover sums to deliver not only a flat frequency response but a flat phase response as well . . . regardless of the complexity of the crossover. This essentially perfect behavior of the first order filter pair once led me to use them for a 13-way crossover I designed for a consulting client in the recording industry. Yes, I said 13-way!
So what can we do? Well, here are my suggestions for getting good performance from multi-way speaker systems.
First, I recommend avoiding anything more complex than a 2-way system whenever possible. Always be reluctant to add another crossover.
Second, if you must add another driver and crossover in order to reach your design goal then try to keep the crossover frequencies spaced as far apart as possible. My circuit simulations show that the combination of a 1st order Butterworth with a 2nd order Linkwitz-Riley (as in the above example) results in a 3 dB dip below the crossover frequency when the two crossover frequencies are spaced two octaves apart. Spacing the crossovers three octaves apart (250 Hz and 2kHz for example) reduces the theoretical best case error to -1.5 dB. Increasing the spacing further to four octaves reduces the error to just -.25 dB. Combining two 2nd order Linkwitz-Riley crossovers results in summing error as great as 1 dB even when the crossover frequencies are spaced at four octaves.
Third, use 1st order Butterworth crossover types for as many of the crossovers in your multi-way system as possible.
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