About

A passive crossover network splits an audio signal into frequency bands before it reaches individual speaker drivers. Incorrect component values cause lobing at the crossover point, driver damage from out-of-band energy, or audible frequency response dips exceeding 6 dB. This calculator computes inductor (L) and capacitor (C) values for 1st through 4th-order passive networks using Butterworth (maximally flat magnitude), Linkwitz-Riley (matched driver sum to 0 dB at crossover), and Bessel (maximally flat group delay) alignment polynomials. All values assume resistive driver impedance Z at the crossover frequency f_c. Real drivers present reactive impedance that deviates from nominal, so Zobel networks or impedance compensation may be required for precision applications.

Formulas

For a 1st-order (single-pole) passive crossover, the low-pass section uses a series inductor and the high-pass section uses a series capacitor. The fundamental component equations are:

L = Z2πf_c

C = 12πf_cZ

For higher-order filters, each component is scaled by a normalized coefficient a_k derived from the filter alignment polynomial. The general denormalization is:

L_k = a_k ⋅ Z2πf_c

C_k = a_k2πf_c ⋅ Z

Where Z = nominal driver impedance in Ω, f_c = crossover frequency in Hz, a_k = normalized coefficient for the k-th component from the chosen polynomial (Butterworth, Linkwitz-Riley, or Bessel), L_k = inductance in H, and C_k = capacitance in F. Linkwitz-Riley filters use squared Butterworth polynomials, producing even-order filters (2nd, 4th) with −6 dB at the crossover point so that the summed acoustic output is flat.

Reference Data

Filter Type	Order	Slope	Q Factor	Summed Response at f_c	Phase Shift (per section)	Lobing Risk	Common Use
Butterworth	1st	−6 dB/oct	0.707	+3 dB	90°	Low	Simple 2-way, full-range + tweeter
Butterworth	2nd	−12 dB/oct	0.707	+3 dB	180°	Moderate	General purpose 2-way
Butterworth	3rd	−18 dB/oct	0.707	+3 dB	270°	Moderate	3-way systems
Butterworth	4th	−24 dB/oct	0.707	+3 dB	360°	Low	High-performance 2-way
Linkwitz-Riley	2nd (LR2)	−12 dB/oct	0.500	0 dB	180°	Low	Studio monitors, hi-fi
Linkwitz-Riley	4th (LR4)	−24 dB/oct	0.500	0 dB	360°	Very Low	Professional audio, reference
Bessel	1st	−6 dB/oct	0.707	+3 dB	90°	Low	Time-aligned systems
Bessel	2nd	−12 dB/oct	0.577	+1.6 dB	180°	Low	Phase-critical applications
Bessel	3rd	−18 dB/oct	0.511	+0.8 dB	270°	Low	Transient-sensitive playback
Bessel	4th	−24 dB/oct	0.466	+0.3 dB	360°	Very Low	High-end time-aligned
Standard E12 Preferred Component Values (μF / mH)
1.0		1.2		1.5		1.8
2.2		2.7		3.3		3.9
4.7		5.6		6.8		8.2

Frequently Asked Questions

Butterworth filters are each −3 dB at the crossover frequency. When low-pass and high-pass outputs sum acoustically with matched phase, the result is +3 dB. Linkwitz-Riley filters are −6 dB at crossover. Their in-phase summation yields exactly 0 dB, producing a flat combined response through the transition band.

Passive crossover calculations assume a purely resistive load equal to nominal impedance Z. Real drivers exhibit impedance peaks at resonance (often 2× to 4× nominal) and rising impedance due to voice coil inductance. At the crossover frequency, if actual impedance deviates more than 15% from nominal, the effective crossover point shifts. A Zobel network (series R-C across the driver) can flatten the impedance curve before the crossover network.

Bessel filters prioritize maximally flat group delay, meaning they preserve the shape of transient waveforms (impulses, percussion) through the crossover region. The tradeoff is a gentler magnitude rolloff compared to Butterworth at the same order. Choose Bessel when time-domain accuracy matters more than sharp frequency separation - typically in high-fidelity listening environments where driver spacing is optimized for time alignment.

No. Linkwitz-Riley alignments are defined only for even orders (2nd, 4th, 8th). They are constructed by cascading two Butterworth filters of half the target order. An odd-order Butterworth cannot be squared to produce the required all-pass summed response. If you need an odd-order slope, use Butterworth or Bessel alignment instead.

Three approaches: (1) Reverse the polarity of one driver, which creates a −3 dB dip instead of a peak - sometimes preferable for off-axis behavior. (2) Stagger the crossover frequencies of LP and HP sections by approximately 0.5 octave to reduce overlap energy. (3) Switch to Linkwitz-Riley alignment, which eliminates the peak by design.

Rounding to the nearest E12 preferred value introduces error in the crossover frequency. A 10% component tolerance shifts f_c by approximately 10% for first-order filters. For higher orders, the interaction between multiple components can amplify or partially cancel individual errors. The calculator displays both exact and nearest E12 values so you can evaluate the tradeoff.