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The Crossover Design Cookbook
Chapter 3: Speaker Motors and Crossovers
by Mark Lawrence

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Motorcycles
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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

Impedance resonance compensators

To compensate the tweeter's impedance at resonance, we need a "resistor" in parallel with the speaker, but the "resistor" should only work at frequencies near the resonance. The R-L-C Band pass circuit (the last in our list) is exactly what we need. We design it like this: the L and C should resonate at the same frequency as the speaker, so 1 / (2π √LC) = speaker resonant frequency. The Q of the R-L-C circuit should match the Q of the driver. Finally, the R of the R-L-C circuit is chosen using the parallel resistor law so that the circuit R paralleled with the speaker at resonance equals the DC resistance. As we see in the impedance graph, this circuit pretty much gets rid of the hump in the impedance curve, but doesn't do anything for the high frequency rise due to the voice coil inductance.

To put this another way, we waste power in a resistor chosen to pull the impedance hump down. We block off this resistor at low frequencies with a capacitor, much like we did with the Zobel circuit above. We also block off the resistor at high frequencies with an inductor. Finally, an R-L-C circuit has a resonance and a Q, so we choose these values to match the Q of the driver.

Now, we need to measure the tweeter's Thiele-Small parameters.

An R-L-C resonance compensated driver

Driver impedance without and with resonance compensator

Designing impedance resonance compensation circuits

Now, we have the data we need to design the R-L-C resonance compensator. Here's the equations:

R = Rr * Re / (Rr - Re)

C = 1 / (R 2π Fr Qtc)

L = (R Qtc) / (2π Fr)

The Focal 120ti tweeter has a resonance at about 1,000Hz, Qtc of .5, and Rr of 25Ω. So, the resonance compensator has the following values:

R = 25 * 6 / (25 - 6) = 150 / 19 = 7.8Ω

C = 1 / (7.8 2π 1000 .5) = 1 / 24,800 = 40μF

L = (7.8 .5) / (2π 1000) = 1.2mH

So, our cross over now looks like this:

Crossover for Focal Tweeter with resonance compensator

The major remaining problem is a miss-match in driver efficiency. The Focal tweeter produces 92dB per watt, and the Scan Speak woofer produces 87dB per watt. So we have to do something to equalize these two drivers, or the speakers will sound incredibly bright. Somehow we have to turn down the tweeter response by 5dB.


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Copyright © 2002-2019 Mark Lawrence. All rights reserved. Reproduction is strictly prohibited.
Email me, mark@calsci.com, with suggestions, additions, broken links.
Revised Thursday, 15-Aug-2019 09:30:53 CDT

Investing
Motorcycles
Neural Networks
Physics