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

Investing
Motorcycles
Neural Networks
Physics


Contents

Introduction

Chapter 1
What are Crossovers?
1st order Crossover
2nd order Crossover

Chapter 2
How Crossovers Work
Resistors
Capacitors
Inductors
Combining Components
Frequency Plots

Chapter 3
Speaker Motors
Zobel Networks
Impedance Resonance
Thiele-Small Parameters
Resonance Compensation
L-pads
Final Watt-V Crossover
What We've Learned
Crossover Cookbook

I recommend FireFox

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

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 = 14F.

You can buy a couple .44mH inductors and 14F 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 inexpensive speakers, the inductor is often omitted to save money.

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 14F capacitor, but you can buy a 12F and a 2.2F, and place them side-by-side, resulting in 14.2F.

Alternatively, you can design your cross over as we did above. Now, however, we find out that maybe we can only buy a .41mH inductor. This inductor will move the cross over frequency up by about 8%. We can adjust the other cross over to match: simply change the capacitor value by the same factor. So, instead of using a 14F capacitor, use a 14 * .41 / .44 F = 13F capacitor. You can buy a 10F and a 3.3F capacitor and use them together.

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 Alice Cooper at 110dB, or if you live with teenagers, you might consider putting 1 or 2 amp fuses on your tweeters.


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Copyright © 2002-2005 Mark Lawrence. All rights reserved. Reproduction is strictly prohibited.
Email me, mark@calsci.com, with suggestions, additions, broken links.
Revised Friday, 09-Sep-2016 14:03:10 CDT

Investing
Motorcycles
Neural Networks
Physics