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

## Designing and building a second order cross over

Now, we'll design a 2nd order cross over for the Watt V. We'll cross over at 2,000Hz, just as we did in the first order cross over. Second order cross overs are typical, and perfectly respectable. In fact, many people think second order cross overs are optimum. Since it's a second order crossover there will be two components, a capacitor and an inductor, for each driver.  R L = 2π f Q
 Q C = 2π f R

The second order formulas above have an additional parameter "Q"; we'll set Q at .7. A Q of .7, as we will learn later, selects a Butterworth cross over which has optimal frequency response. If we select a Q of .58, we'll get a Bessel cross over, which has optimal transient response. Remember, the ScanSpeak woofer has a resistence of 5.5 ohms and the focal tweeter has a resistence of 6 ohms.

For the woofer,
L = R / 2π f Q = 5.5 / (2π 2,000 .7) = .00063 = .63 mH.
C = Q / 2π f R = .7 / (2π 2000 5.5) = 10E-6 = 10µF.

For the tweeter,
L = R / 2π f Q = 6 / (2π 2000 .7) = .00068 = .68mH.
C = Q / 2π f R = .7 / (2π 2000 6) = 9.3µF.

That's all there is to it. These cross overs will work.

### A simple (and simplistic) 2nd order cross over for the Watt V  In the second order formulas, if you're not sure what to use for Q, use .7. If you're not sure what to use for R, use 8. The resulting cross overs will work reasonably well. Later, we'll see what Q and R should really be, and how to make the cross overs work really well. "f" is the cross over frequency, 2,000Hz. "π" is 3.14159, "low pass" is the cross over for the woofer, and "high pass" is the cross over for the tweeter.

Later we'll have a discussion of this parameter Q. Q is not a part of first order systems, a system only has a Q if it's second order or higher. The discussion on Q is long and complicated, but the result is simple. Is you use Q = .5, we say that the speakers are critically damped. That means the system stores the least possible amount of energy. If you use Q = .577, that's a bessel filter. That means the system has the flatest possible time response. If you use Q = .707 that's a butterworth filter and has the flatest possible frequency response. If you use Q > .707 that's a chebyshev filter and it's a really poor choice for an audio system. You'll have ripples in the frequency response, you'll have peaks and valleys in the phase response, and generally speaking you're going to have weird boomy sound. Don't be tempted by the dark side.

Again, you might have trouble finding exact inductor values. I look through my catalogs and I find a .63mH inductor and a .7mH inductor, but no .68. I would just use the .7 and not worry about it. If you're really berserk, you can get a DVM which measures inductance and unwind the .7mH inductor a little bit.

For capacitors, I find a 10µF capacitor easily, and also a 6.8µF and a 2.7µF, which add up to 9.5µF, or a 6.8µF and two 1.5µF, which add up to 9.8µF. Inductors usually measure quite close to the rated value. Capacitors are usually off by anywhere from 5% to 15%, so unless you're going to measure each component, don't bother trying to get too precise.

Of course, there's more to cross overs than this. If this were the whole story, it would have been written down long ago. For now, however, we're going to ignore the other complications and see how these cross overs work. Later, we'll develop better cross overs for the ScanSpeak - Focal two way system.

By the way, if you want to build yourself a set of Watt V alike speakers, the box should have a net internal volume of .26 cubic feet, and a 2 inch vent which is 9.5 inches long. I believe that one of the keys to the superlative sound of the Watt V is the extraordinarily stiff box (about 3 inch thick walls of phenolic), so if you try to build one, make a good box. Wilson Audio sprays damping material on their woofer - if you want to try this, try automotive undercoating spray. Personally, I would be real slow to spray goop on a \$135 driver. Maybe you're a braver man than I.

Mount all power resistors with at least 1/4" of free air space on all sides. This means use the leads of the resistor to stand the resistor off the board, and allow air to flow under the resistor too. Make sure the resistors are non-inductively wound.

Orient inductors as shown below. Inductors have strong magnetic fields and will couple together if you let them. This is how transformers work: they are just two strongly coupled inductors. Remember the speaker motor coils when considering orientation. Use air core, or 300 to 500 watt bobbin (iron core) inductors. The inductors should have a DC resistance of no more than about 1/2Ω. Use capacitors rated for at least 100V AC, or 200V DC. Mylar or Polypropylene capacitors are the best for cross overs. If you must use electrolytics, use film capacitors for at least 40% of the total capacitance value.

This is a series crossover, there's a seperate circuit for each driver and the music must flow through the crossover to get to the drivers.

Well, we've come a long way. If all you want is to build some simple 2nd order cross overs, you know all you need to know right now. You can stop reading here. For better crossovers that have much more accurate frequency response, you'll need to read the next couple of chapters.