12dB Crossover
Calculation of a 2nd order loudspeaker crossover with 12dB attenuation per octave
Crossover Calculator
12dB Crossover (2nd Order)
Crossover with two components per way: One inductor and one capacitor for woofer and tweeter. Attenuation: 12dB per octave (Butterworth characteristic).
Circuit Diagram
Circuit diagram of a 12dB crossover (2nd order)
The calculated values are automatically inserted into the circuit diagram. Both ways use identical component values.
Calculation Formulas
Inductor (Butterworth 2nd Order)
Capacitor (Butterworth 2nd Order)
Variable Legend
| \(L\) | Inductor (Henry) |
| \(C\) | Capacitor (Farad) |
| \(Z\) | Impedance (Ohm) |
| \(f_C\) | Crossover frequency (Hz) |
| \(\sqrt{2}\) | Butterworth factor ≈ 1.414 |
Phase Behavior
With 12dB crossovers, both speakers move in phase. No polarity reversal required!
Characteristics of 12dB Crossover (2nd Order)
Operation
A 2nd order crossover requires 2 components in each branch and provides a slope steepness of 12dB per octave. The values of the capacitors and inductors in the high-pass and low-pass are identical. This crossover is based on the Butterworth characteristic with a Q-factor of 0.707.
Advantages
- Better separation (12dB/octave)
- Standard for HiFi applications
- No polarity reversal required
- Flat frequency response
Disadvantages
- More components required
- Higher costs
- More complex circuit
- Higher losses
Technical Details
Phase Behavior
Since in the low-pass at the crossover frequency, the current lags the voltage by 180° and in the high-pass the voltage also lags the current by 180°, the speaker membranes move in phase.
Butterworth Characteristic
The 12dB crossover uses the Butterworth characteristic with a Q-factor of 0.707. This provides a maximally flat response in the passband.
Typical Application
12dB crossovers are the standard for high-quality HiFi speakers. They provide a good balance between selectivity and phase behavior.
Calculation Example
Given: 8Ω speaker, crossover frequency 2400Hz
\[L = \frac{\sqrt{2} \cdot 8Ω}{2π \times 2400Hz} ≈ 0.75\text{ mH}\]
\[C = \frac{\sqrt{2}}{4π \times 2400Hz \times 8Ω} ≈ 5.9\text{ µF}\]
Comparison of Crossover Orders
| Order | Attenuation | Components per way | Phase behavior | Application |
|---|---|---|---|---|
| 1st order | 6dB/octave | 1 (L or C) | Polarity reversal needed | Simple systems |
| 2nd order | 12dB/octave | 2 (L and C) | No polarity reversal | HiFi standard |
| 3rd order | 18dB/octave | 3 (L-C-L or C-L-C) | Polarity reversal needed | Professional |