A crossover network consists of passive filters realized by components forming a specific circuit. This circuit's formation or topology has been studied quite a lot by professional engineers and DIYers. Their conclusions will prove quite useful to us.
What is our next move ?
We must deal with the cost category. The speaker's cost category has serious implications to the crossover cost and therefore to its complexity and effectiveness. Would anyone invest 20-30 working hours and a serious amount of money for a crossover that is expected to drive very cheap loudspeakers for a PC desktop ?
We all know that such a discussion does not lead to unique conclusions and straightforward answers. There are several cases where cheap loudspeakers will definitely give an astonishingly good sound if driven by a well-designed crossover network. We may not be able to listen to such a speaker at high SPL levels but we will surely impress its listeners (and potential buyers) at moderate sound levels.
In our case we will define two different circuit topologies (Low-cost, High cost) which will be used throughout the design process. We will use them as limiting cases. This means that we will not make a crossover with fewer components than the 'Low cost' topology or one more complicated than our 'High cost' topology.
For the time being we present the 2-way version of these circuit topologies, beginning with the 'Low-cost' one:
This circuit comprises second order filters at both sides. A series resistor will be responsible for high frequency attenuation often needed in speaker systems. The resistor below the capacitor of the low pass filter will be valuable as will be shown later on. If before finalization its value becomes too low we can remove it. In the same filter the inductor is chosen to have a core. This will not raise problems because we do not expect our 'end-product' to operate at high levels and electric currents. Usually these inductors are very cheap and easily available. Next figure illustrates our 'High cost' topology:
In this configuration we have fourth order filters. We can also observe an RC subcircuit placed in parallel to each driver. This subcircuit will be explained in detail in the next paragraphs.
It is important to understand that in many cases the low-frequency acoustic branch may better fit in our target curves with a second or a third order filter. We will let our software start with the topology above and our first results will eventually drive us to the removal of one or two of the low pass filter's components. The same holds for the highpass section.
It is also very important to realize that lowpass and highpass sections are rarely of the same order. Most crossover networks are asymmetrical.
-What is the third step ?
We must decide what our design targets are. What SPL curve is our target ? Our major design goal is to have the overall speaker SPL Response approach a target curve. It is not the only design goal we have for a quality speaker system. But its is the major one.
One could easily say that our target SPL curve is simply that of a flat shape. Well, a lot of speaker designers disagree with that. Even if this problem were eliminated we would still have to face mother nature: The range 10-1000Hz suffers from the diffraction effect which introduces an SPL anomaly to all hifi speakers. We have already mentioned in a previous tutorial that 'diffraction step' introduces a negative step (-6dB approximately) at very low frequencies. This negative dB step fades out at higher frequencies. It is also important to consider the fact that (passive) crossover networks can not boost the SPL curve. In that sense they can not cancel the diffraction step out.
As a result out target SPL response can generally take the form of one of the following cases:
SPL DESIGN TARGET 1 FOR A 2-WAY SPEAKER SYSTEM
We let the diffraction step be there in all its grace! Above 500 Hz we go after a flat overall speaker response. The two acoustic branches cross each other at 3000Hz and exhibit a high slope. This value is not mandatory. However its is a good compromise. Woofer is not expected to operate above 2kHz. Its cone breakup resonances will not add colouration and harshness at high power levels. Tweeter will not heat up with too much energy below 2000Hz.
The acoustic branches sum up in a rather qood way as can be seen in the above figure in the range 2-8 kHz. Most quality speakers (of a small size or with up to one 6.5'' woofer) adopt this design target. Such speakers can sound well balanced in a room environment. Certainly the 'body' of a large orchestra or a jazz piece will not be there. But who would expect more from such a speaker size and category.
Another advantage of this approach is the high sensitivity value (SPL measured @ 1kHz) which is always paid a lot of attention by buyers and end-customers.
SPL DESIGN TARGET 2 FOR A 2-WAY SPEAKER SYSTEM
In this case many designers look for a different SPL shape. They prefer having the old 'loudness' boost. The only thing our crossover network has to do is to let the high frequency branch shift to the right and its series resistor to keep a low value. This gives more protection to the tweeter operation from low and mid-low frequency energy heat up. In addition treble is a bit dominant in the overall sound impression. Such a design has a lot of fans in the eastern hemisphere due to music spectral content in that part of the world.
Several rock music masterpieces would give their inherent roughness out with such a speaker system. However we still talk about small sized speakers. This approach also provides the end-product with a high sensitivity spec.
The third option is the one that follows:
In this case we go after an almost flat overall SPL shape. We assign the low frequency branch the task to suppress the mid frequencies and compensate for the diffraction step. Even if a small (1-2dB) SPL level difference is left over, the sound image of this speaker system changes significantly. Listener is overwhelmed by what we call 'music body'. Large orchestras and music pieces incorporating acoustic or electric bass instruments will unfold their strength in the listening room. The overall picture of such a speaker is that of a large-sized one even if it comprises a 4'' or 6.5'' woofer !
Certainly this picture will not be available at high SPL levels if large-diameter woofers are not there to handle the increased electric power effectively. Additionally this design scenario has a serious drawback. The final speaker sensitivity will be far below the psychological limit of 90dB. You will need a strong amplifier to drive such a speaker realization at moderate SPL levels. If this speaker is not intended for high sound levels then there won't be any problem at all.
Another disadvantage of this SPL target curve is that in small rooms it sometimes creates the impression of boominess at higher power levels. This is due to bass enhancement that is inherent to small rooms.
-Eventually what is the best scenario for our target SPL curve ?
We have already answered this question: The target curve is a matter of personal taste and experience. It is not an issue in our design procedure. Nor there are no other options. One can derive as many SPL targets as one likes. We presented the most common types. Our simulation and design program will treat them all successfully.