Index LoudspeakersPassive Crossover

Passive Crossover

Two-way component values with the acoustic sum drawn for each alignment.

Ct1 · tweeter series5.31µFnearest E12: 5.6 µF

Lt1 · tweeter shunt764µHnearest E12: 820 µH

Lw1 · woofer series1.02mHnearest E12: 1 mH

Cw1 · woofer shunt3.98µFnearest E12: 3.9 µF

Acoustic sum

Woofer low-pass
Tweeter high-pass
Sum

Circuit

Values assume each driver behaves as a resistor at the crossover point. Add a Zobel network to the woofer if its impedance is rising there.

Input

Slope and alignment

Crossover frequency

f_c

Woofer impedance at crossover

Z_w

Tweeter impedance at crossover

Z_t

Tweeter wired in reverse polarity

Try both. The summed curve shows which connection is right for the chosen alignment.

How it works

Splitting the band

A passive crossover is a pair of ladder filters between amplifier and drivers. Inductors in series pass lows, capacitors in series pass highs, and each added element steepens the slope by 6 dB per octave. For a driver of impedance $Z$ at frequency $f_c$ , every part is a scaled copy of a normalised value $g$ :

L = \frac{g\,Z}{2\pi f_c}

C = \frac{g}{2\pi f_c\,Z}

\text{(low-pass)}

C = \frac{1}{g\,2\pi f_c\,Z}

L = \frac{Z}{g\,2\pi f_c}

\text{(high-pass)}

Alignments

6 dB Butterworth ( $g = 1$ ): the two outputs add back to the input exactly, but drivers overlap over a wide range.
12 dB Linkwitz-Riley ( $g = 2,\ \tfrac12$ ): each section is 6 dB down at $f_c$ . With the tweeter reversed the sum is flat.
12 dB Butterworth ( $g = \sqrt2,\ 1/\sqrt2$ ): 3 dB down at $f_c$ , giving a 3 dB bump when summed.
18 dB Butterworth ( $g = \tfrac32,\ \tfrac43,\ \tfrac12$ ): flat sum in either polarity.
24 dB Linkwitz-Riley: flat sum, drivers in phase, minimal overlap. The modern default.

The summed curve

The plot evaluates the ideal transfer functions and adds them as complex numbers, so phase is accounted for:

H_{LP}(s) = \frac{1}{D(s)}

H_{HP}(s) = \frac{s^{n}}{D(s)}

s = j\,\frac{f}{f_c}

Flip the polarity switch on the 12 dB Linkwitz-Riley to see a deep notch appear. Real drivers add their own roll-off and offset, so treat these values as a starting point and confirm with a measurement.

References

S. Butterworth, “On the Theory of Filter Amplifiers,” Experimental Wireless & the Wireless Engineer, vol. 7, pp. 536–541, 1930. Issue scan
S. H. Linkwitz, “Active Crossover Networks for Noncoincident Drivers,” J. Audio Eng. Soc., vol. 24, no. 1, pp. 2–8, 1976. AES