Designing Passive Crossovers




In a perfect world, you could enjoy great sound by installing just four full-range speakers – one in each corner of your car. In the real world, things aren't quite that easy. Full-ranges simply aren't up to the task of accurately reproducing the entire music spectrum. That's why top-notch systems employ two or more component speakers – like a woofer and tweeter – per channel. Each component is designed to reproduce a specific range of frequencies,and together they can cover the entire music spectrum accurately.
A complication arises, however, since source components such as CD players deliver all of these frequencies – low, high, and in between – as a single music signal. This is where crossovers come in. A crossover divides the music signal into frequency bands that are compatible with the different types of component speakers.

Crossover Basics

The crossover is a fairly complex creature, and it is imperative that you understand what it is and how it works before you make any decisions about how you'll divide the signal in a high-end system.

Filters

Crossover networks use two types of filters to divide music signals. A high-pass filter ignores, or passes, frequencies above a predetermined frequency but attenuates, or rolls off, those below it. Conversely, a low-pass filter passes frequencies below the predetermined frequency but attenuates those above it. High- and low-pass filters can also be combined (called "cascading") to form a band-pass filter, which passes only those frequencies (called a "pass-band") that aren't attenuated by the two filters. In each case, the predetermined frequency is called the "crossover point" or "cutoff frequency."

Slopes

The rate at which frequencies are attenuated is called the "crossover slope." Slopes are expressed in dB per octave, and typical figures are 6, 12, and 18 dB per octave, with 12 being the most common. The higher the slope, the faster attenuation occurs.
An example: You wire a high-pass filter with a crossover point of 100 Hz and a slope of 6 dB per octave to a midbass. The crossover will gradually filter out signals below 100 Hz so that the level of the signal at 50 Hz (one octave below 100 Hz) is approximately 6 dB less than the level at 100 Hz.

Passive Benefits

There are two basic types of crossovers: passive and active. The most obvious distinction between them is their location in a system's signal path. Passives are placed between amplifiers and speakers, and because they work with amplified signals they are sometimes referred to as "high-level networks." Active, or electronic, crossovers perform their signal-dividing act before the amp, and because they work with non-amplified signals they are often referred to as "low-level networks."Simplicity and economy are the most compelling reasons to choose the passive variety. Since passives go to work after amplification, it's possible to build a multi-speaker system around a single amplifier; systems using one or more active crossovers require a minimum of two amplifiers. And passive crossovers cost a lot less than their active counterparts.
Passives are also more flexible than actives – when you build them yourself or have them customized for your system, that is. (Some component speaker systems come with passive crossovers, and your local car stereo shop sells pre-made passive devices.) Passives are flexible because you can mix and match the various electrical components that make up their filters to achieve any desired response curve – a feat that only the most sophisticated actives can match.
One thing that actives don't suffer from is "insertion loss." This term is used to describe the amplifier output power that's lost when a passive crossover is inserted between an amp and a speaker. The most significant power loss occurs with low-pass filters, since their key components – inductors (see below) – incorporate many turns of wire that have a small but measurable DC resistance. This resistance will reduce the amount of power delivered to the speaker, but in most cases it is not significant.

Inductors and Capacitors

The key components in any passive crossover are its inductors and capacitors. An inductor (also known as a "coil" or "choke") is simply a coil of wire that is usually wrapped around an iron core. Inductors are used in low-pass filters, since their mpedance naturally increases as the frequency of incoming music signals rises. An increase in impedance always causes a decrease in amplifier output, so the result is that high frequencies are attenuated at a rate determined by the filter's slope.
Capacitors consist of interleaved layers of a special foil and an insulating material such as polypropylene or Mylar. They are used in high-pass filters, since their impedance increases as the frequency of an incoming music signal decreases. Again, this increase in impedance lowers the amp's output, and the result is that low frequencies are gradually filtered out.
Every component has a value, which indicates how much resistance the component will present to the amplifier and is largely responsible for determining the crossover point of a specific filter (see "Designing a Network," Impedance, below). An inductor's value is determined by the number of windings of wire around its core and the type of core used (see "Designing a Network," Component Type, below); a capacitor's value is determined by the number of layers of foil and insulating materials it has. The more layers, the higher the capacitance. The values of capacitors are expressed in microfarads (pF), and the values of inductors are expressed in microhenries (uH), and millihenries (mH).

Order

The number of inductors and capacitors used in a passive crossover determines its "order."
A first-order crossover uses one component, a second-order device two, a third-order crossover three. A crossover's order is also tied to its slope: First-order devices always have a slope of 6 dB per octave, second-order devices a slope of 12 dB per octave, third-order devices a slope of 18 dB per octave. (See Figures 1 through 3.) Essentially, this physical use of extra inductors and/or capacitors causes higher-order networks to attenuate the signal more sharply.





 
Building vs. Buying

As mentioned, you can either buy a pre-made passive, use the crossover that came with your speakers (if one was supplied), or design and build your own device.
If you want to take the pre-made route, I suggest sticking with products that have a familiar brand name. They are usually mounted on a circuit board or are encased in a plastic housing. Their primary benefit is that you don't have to build them.
There are a few downsides, though. It's more expensive to buy a pre-made device than to build your own. You also lose some flexibility, since the exact combination of points, slopes, and characteristics you want may not be available. The pre-made device will also be useless if you discover, after installing it, that it doesn't do what you wanted it to do.
I've found that the crossovers packaged with some component speaker systems aren't so hot, since speaker manufacturers often throw in a device that's made of cheap components – and that can lead to headaches. Using "canned" crossovers sticks you with the crossover frequency and slope chosen by the manufacturer, of course – again, less flexibility.
Building your own passive device is by far the best approach. You'll save money, and you'll wind up with a crossover that's precisely tailored to your system. The only drawback is the
time it takes to design and build a passive device – a lengthy process even with the help provided here.

Designing a Network

The easiest way to approach the design phase is to think of the network as a simple collection of filters. The three-way first-order network in Figure 4, for example, is nothing more than three first-order filters – high-, band-, and low-pass – wired together in parallel.
(The pig tail is an inductor, the dual parallel lines a capacitor.) Then you'll need to consider:
filter type; the crossover point (in Hz); the slope; the impedance (in ohms) of the speaker that will be receiving the filtered signals; and component designs and characteristics.


 
Filter Type

To choose a filter type, simply consider what kind of speaker the crossover will be filtering.
Typically, high-pass filters are used with tweeters, band-pass filters are used with midranges and midbasses, and low-pass filters are used with woofers. Schematics of first-through third-order networks for each of these filter types appear in Figures 1 through 3.
The component values that allow you to build these filters to spec – marked with a letter/number designation such as Ll – are given in Tables 1 through 4 (more on this later).

Cutoff Frequency

Of all the variables in the crossover equation, the cutoff frequency is the most difficult to pin down. Factors to consider include the acoustics of your car's interior, the filter slopes you'll be using (see Slope, below), and your own taste regarding sonic character.
Every car interior has its own acoustic character, so you must consider its effect on response when choosing a cutoff. You can use crossover points like an equalizer, for example, to compensate for serious response anomalies like peaks and holes; this is actually preferable to using an equalizer, in fact, because it allows you to use your EQ for
moment-to-moment fine tuning rather than as a crutch to compensate for system deficiencies.
Specifically, crossover points can be overlapped or underlapped to achieve a desired sonic effect. When filters are overlapped, the speakers they feed both produce output at the overlapped portion of the music spectrum. Underlapping cutoff frequencies creates a notch that can compensate for a response bump. Most car interiors create such a bump in the midbass region, and underlapping is a great way to smooth it out. The process is easy either way: Simply set adjacent crossover points so that they overlap or leave a gap in the problem frequency range, then adjust the overlap or gap until your system sounds right.
Use a real-time analyzer (RTA) to pinpoint the location of a frequency-response bump or hole and to gauge its severity.
Even if you don't use your filters to over- or underlap frequencies, the choice of a cutoff will still affect sound quality, and this is a highly subjective matter. Some people like bright-sounding music, for example, while others prefer a full sound. Your best bet here is to consider the other criteria first and settle on a ballpark figure for a cutoff point, then
purchase all of the inductors and capacitors you'll need to experiment with a variety of cutoffs on either side of it.
You can use the following guidelines as a starting point for your cut-off frequency experiments; note that they are based on the use of 12-dB-per-octave slopes.

SUBWOOFERS: Below 100 Hz (low- pass).

WOOFERS/MIDBASSES: Between 100 and 500 Hz (high-pass).

MIDRANGES: Between 300 and 500 Hz (high-pass) and 3,500 and 
8,000 Hz (low-pass).

TWEETERS: Above 5,000 Hz (high- pass).

The cutoff you select for the tweeters is especially critical because they are the easiest component speakers to damage. I've recommended the 5,000-Hz figure since it is high enough to allow virtually any tweeter to live a long and healthy life – besides, your midrange should be able to reproduce signals up to 5,000 Hz. Some tweeters are capable of comfortably handling signals as low as about 2,000 Hz, however, so your best bet here – and with any loudspeaker, for that matter – is to determine the minimum cutoff frequency recommended by the loudspeaker's manufacturer and not exceed it.

Slope

In general, a high-pass filter with a slope of at least 12 dB per octave should be used with midranges and tweeters, since this will protect them from potentially damaging low frequencies.
Setting the slope of a low-pass filter isn't as risky, since high frequencies can't damage woofers, midbasses, or midranges. But your choice will make a big difference in the system's sound. For example, I've found that filtering a woofer or subwoofer with a slope of 6 dB per octave usually results in flabby bass. On the other hand, a slope that's too steep can play havoc with bass response: Slopes of 18 dB per octave or higher (fourth-order networks have a slope of 24 dB per octave) can produce weak bass response, phase disparities between speakers, and excessive insertion loss. Phase problems, like insertion loss, reduce output and can produce a response hole.

Impedance

As mentioned, the value of the inductor or capacitor determines the filter's cutoff frequency.
Speaker impedance comes into play, however, since an inductor or capacitor will produce different cutoffs for any given impedance. Specifically, the cutoff produced by an inductor increases as impedance rises, while that produced by a capacitor decreases under the same conditions. (See Tables 1 through 4.)

Component Type

In addition to picking an inductor or capacitor with a specific value (to produce the cutoff frequency you desire), you also need to choose the type of component you'll use; each type has its own sonic characteristic and will affect the sound quality of your system.
When it comes to high-pass filters, the best-sounding capacitors are the high-voltage Mylar and polypropylene variety. (They're also the most expensive.) With low-pass filters, however, you can use any type of capacitor – it's the type of inductor that counts.
Air-core inductors have lower distortion figures than the iron-core variety, and as a rule they sound best as long as their value doesn't exceed 4 mH. Above this figure, their relatively high resistance becomes troublesome, and low-resistance iron-core inductors are preferred.
Crossovers are also grouped according to their "characteristic." The two most common types are Butterworth, which produces the best frequency response, and Bessel, which produces the best phase response.

A Working Model





When you've made all of the primary decisions regarding the crossover-network's design, you can get down to business.

Sketch the Network

The first step is to sketch the individual filters that will make up your network. We'll use the
network shown in Figure 5 as our working model. It depicts one channel of a common three-way, second-order network; as per its second-order status, each filter consists of two components and has a slope of 12 dB per octave. To flesh out our model, say that the impedance of each speaker is 4 ohms and that you want the following crossover points:
4,000 Hz high-pass for the tweeter, 130 Hz high-pass and 4,000 Hz low-pass for the midrange (creating a band-pass), and 130 Hz low-pass for the woofer.







 
Pick Component Values

The next step is to select the appropriate capacitors and inductors for each of the filters.
Tables 1 through 4 list component values for high- and low-pass filters at common cutoff frequencies and with slopes of 6, 12, and 18 dB per octave. (To find component values for other cutoff frequencies or higher slopes, consult The Loudspeaker Design Cookbook, published by Marshall Jones and marketed by Audio Amateur Publications [603-924-9464].)







 
In our model, we'll start with the inductor and capacitor for the 4,000-Hz high-pass filter.
Since we're dealing with a 4-ohm tweeter, refer to the intersection of the 4-ohm and 4,000-Hz columns in Table 2. In this case, the correct values for the high-pass filter are 6.8 pF for capacitor C2 and 0.22 mH for inductor L2.
The band-pass filter in this network consists of a 130-Hz high-pass filter and a 4,000-Hz low-pass filter. Referring again to Table 2, we find that the appropriate values for the high-pass side of the filter are 200 pF for capacitor C2 and 6.8 mH for inductor L2. For the low-pass side, the values are 6.8 pF for capacitor C2 and 0.22 mH for inductor L2.
For the 130-Hz low-pass filter, check the intersection of the 130-Hz and 4-ohm columns in Table 2. As you can see, you'll need a 200 pF capacitor for C2 and a 6.8 mH inductor for L2. It really is that easy, and building the more complicated networks shown in Figures 6 and 7 is simply a matter of adding a few more components to the picture.
In any case, once you know the type and value of all of the components you'll need to build your custom passive-crossover network, go buy them. The best place to find a variety of high-quality components is your local electronics-parts store.
In our model, we'll start with the inductor and capacitor for the 4,000-Hz high-pass filter.
Since we're dealing with a 4-ohm tweeter, refer to the intersection of the 4-ohm and 4,000-Hz columns in Table 2. In this case, the correct values for the high-pass filter are 6.8 pF for capacitor C2 and 0.22 mH for inductor L2.
The band-pass filter in this network consists of a 130-Hz high-pass filter and a 4,000-Hz low-pass filter. Referring again to Table 2, we find that the appropriate values for the high-pass side of the filter are 200 pF for capacitor C2 and 6.8 mH for inductor L2. For the low-pass side, the values are 6.8 pF for capacitor C2 and 0.22 mH for inductor L2.
For the 130-Hz low-pass filter, check the intersection of the 130-Hz and 4-ohm columns in Table 2. As you can see, you'll need a 200 pF capacitor for C2 and a 6.8 mH inductor for L2. It really is that easy, and building the more complicated networks shown in Figures 6 and 7 is simply a matter of adding a few more components to the picture.
In any case, once you know the type and value of all of the components you'll need to build your custom passive-crossover network, go buy them. The best place to find a variety of high-quality components is your local electronics-parts store.
You should also be meticulous if you're using a case and need to mount it in your car. If it doesn't contribute to the cosmetic appeal of your system, secure it under the dash or behind a panel. If you've fabricated a hot-looking box, however, you should display it – on an amp rack, for example, or inset into a carpeted panel.
Designing and building passive crossover networks is the kind of task tried- and-true tinkerers love. Beyond the many challenges, the degree of control offered by passive networks is irresistible. The process may cost you a month in the shop and a bottle or two of Tylenol, but I guarantee that the rewards of doing the job right will be worth all of your efforts.




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