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The Crossover Design Cookbook
Chapter 1: Simple Crossovers
by Mark Lawrence

## Designing and building a first order cross over

We'll cut to the chase: if you want to build a simple cross over for a two way system, here's the simplest formula:
 R L = 2π f
 1 C = 2π f R

The calculations for a 1st order simple crossover are available on-line at www.calsci.com/audio/FirstOrder.html.

A first order cross over is pretty much idiot proof, but is not typically considered very respectable in high end audio gear. In the above formulas, if you're not sure what to use for R, use 8. The resulting cross overs will work. They won't work especially well, but they'll work. Later, we'll see what R should really be, and how to make cross overs work well. Most commercially available speakers use cross overs just like these, designed just like this, that is to say simplistically and poorly.

"f" is the cross over frequency - in a two way system, this is probably about 2,000Hz. "π" is 3.14159, a numerical artifact which pops up because we don't usually work in the same units as God does. "Low pass" is the cross over for the woofer, and "high pass" is the cross over for the tweeter.

Now, we'll work a real design example: we'll design a cross over for the Watt V. The ScanSpeak 18W/85 7.5" woofer has 5.5 ohms of DC resistance, and the Focal T120ti tweeter has a DC resistance of 6 ohms. We learn this by looking up the manufacturer's specifications for these drivers. First, we'll do a 1st order cross over at 2,000Hz. From the formulas above, we see that

L = R / 2πf = 5.5 / 2π 2000 = .00044 = .44mH.

C = 1 / 2π f R = 1 / 2π 2000 5.5 = 14E-6 = 14µF.

You can buy a couple .44mH inductors and 14µF capacitors, wire them up as shown above, and this will work. In fact, many commercially available speakers have less than this for a crossover: in very inexpensive speakers, the inductor is often omitted to save money. You have to put in the capacitor or the tweeter will melt the first time you turn up the volume.

That's it. Here's our first order cross over:

### A simple (and simplistic) 1st order cross over for the Watt V

When we calculate values, it's important to remember that real components are typically ±10%. So, for example, if you actually do the math above, you'll find the required inductor is .43767646 mH. Unless you carefully wind your own inductors, and have some rather high- precision measuring gear, you'll have to settle for what you can actually buy. So, we round the numbers off, in this case to .44mH.

In fact, sometimes you cannot even get a component with the rounded value. For example, perhaps the closest inductor you can find is .43mH. Go ahead and use this: it will just move the cross over frequency by 100Hz or so. You'll never hear it. You cannot buy a 14µF capacitor, but you can buy a 12µF and a 2.2µF, and place them side-by-side in parallel, resulting in 14.2µF.

Alternatively, you can re-design your cross over for actual components you can buy. If we find out that we can only buy a .41mH inductor, that will move the cross over frequency up by about 8%. We can adjust the capacitor to match: simply change the capacitor value by the same factor. We switched the inductor from .44mH to .41mH. So, instead of using a 14µF capacitor, use a 14 * .44 / .41 µF = 15µF capacitor. You can buy a 10µF and a 5.1µF capacitor and use them together in parallel.

With a first order cross over, you're putting a fair amount of low frequency power though the tweeter. This won't have much sonic effect. It can, however, blow up your tweeters, so if you like to listen to AC/DC at 110dB, or if you live with teenagers, you might consider putting 2 or 4 amp fuses on your tweeters.

It's called a first order crossover because of the math, but you can tell it's a first order crossover at a glance: there's one capacitor or inductor per driver. A second order crossover would have two inductors or capacitors per driver, a fourth order crossover would have four. Later we'll learn about higher order crossovers.

This is called a series crossover because the components are in series with the driver. The music must go through the crossover to get to the driver. Later we'll learn about parallel crossovers.

Inductors are measured in a unit called a "Henry," after Joseph Henry who worked with inductors in the 1800s. A one henry inductor is a huge thing and only useful for the power company. We'll be working with inductors whose value is roughly a thousandth of a henry, which we call a milli-henry, abbreviated mH.

First order crossovers divide up the music precisely into two halves. If you have done a good job selecting precise components and add up what the crossovers put out, they sum to the exact same music that was put in. No higher order crossovers can do this. All higher order crossovers will distort the sound to some extent such that it cannot be reassembled back to exactly the original input. For this reason some people prefer first order crossovers.

Unfortunately there's a price for this. First order crossovers have very shallow slopes - 6dB per octave. That means if your crossover is at 2,000Hz, then at 1,000Hz, one octave down, the tweeter is still getting 1/4 of the music power; at 500Hz, two octaves down, the tweeter is getting 1/16th of the music power, about 6%. This is a lot of excess power to be putting into your tiny little tweeter. This also means your midrange driver is getting 1/4 of the power at 4,000Hz and 6% of the power at 8,000Hz. There's a good chance your midrange drive does very poorly at 3,000Hz - 8,000Hz.

None the less, because they're the only crossovers that sum back to the original input, many audiophiles think they're the only crossovers you should use. And a lot of good speakers do use these.