|The Crossover Design Cookbook|
Chapter 3: Speaker Motors and Crossovers
by Mark Lawrence
What are Crossovers?
1st order Crossover
2nd order Crossover
How Crossovers Work
Final Watt-V Crossover
What We've Learned
I recommend FireFox
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.
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:
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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Revised Friday, 25-Jun-2021 20:24:15 CDT