Active Crossovers and DSPs

Active Crossovers are crossovers that operate on line-level signals before the amplification stage, unlike the passive crossovers used in most loudspeakers that operate on amplified, speaker-level signals.

Digital Signal Processors (DSPs) are components that modify signals in the digital domain rather than using LCR (Inductor, Capacitor, Resistor) networks to modify signals in the analog domain. DSPs are often used to process signals for the purpose of surround sound or other “effects” processing and are also used to implement active crossovers with some important benefits that we will discuss.

Crossover slopes describe the rate at which, beyond the crossover frequency, the signal is attenuated by the crossover. Crossover slopes are generally described in decibels (dB) per octave, and are often referred to by their “order” as a shorthand notation for the rate of attenuation. The following tables shows commonly-used orders and their attenuation rates:

The following diagram shows an example of how much the signal level is reduced by different crossover slopes assuming a 100Hz low-pass crossover. As you can see, a first-order crossover still allows substantial high-frequency content above the crossover frequency whereas the fourth-order crossover has attenuated the signal by 72dB at 800Hz (three octaves above 100Hz) and by more than 80dB at 1kHz.

Phase shift describes the angular delay between the original signal and the resulting output (in the case the crossover output) in degrees. This phase shift is generally introduced by capacitors in LCR crossover networks due to their lagging charging/discharging behavior. There is quite a bit of math involved in describing this phenomenon, and that is made more complicated by the fact that there are different types of crossover filters (or alignments) such as Butterworth and Linkwitz-Riley (LR). It can generally be stated that each “order” of a crossover introduces a +- 45 degree phase shift¹ between input and output. The 4^th-order LR crossover is a special case where relative phase delay between outputs is 360 degrees, causing output signals to be effectively in phase with each other and 4×45 = 180 degrees out of phase with the input signal. Slopes are sufficiently steep to provide good attenuation of out-of-band signals. An undesirable example of phase shift is the full cancellation caused when two signals are out of phase (a 180 degree phase shift) with each other. In these cases, reversing the polarity of one driver will reverse its phase and address the problem.

¹References:
Linkwitz-Riley Crossovers: A Primer – Dennis Bohn, Rane, 2005

Group Delay describes the delay in seconds that a signal “group” experiences when passing through a system such as a crossover network or a loudspeaker driver. Linear group delay is desirable because it allows the “impulse response” of drivers to be realigned such that transients are correctly reproduced. It should be noted that 4^th-order LR crossovers exhibit zero phase shift but are not strictly “linear phase” as different frequencies experience slightly different amounts of group delay. 4^th-order LR crossovers also must be time-aligned (the acoustic centers of all drivers must be placed in a vertical plane) or the resulting output will not be perpendicular to the front of the loudspeaker (referred to as lobe tilting²).

Impulse response refers to the output of a system resulting from a momentary input, or impulse. A perfect impulse response would look exactly like the momentary input, but in practice most systems respond imperfectly due to physical restrictions (i.e., driver mass, insufficient damping, physical driver separation, differing group delay, the lagging compression of air, etc.)

Echoes are an extreme example of time misalignment, where you hear the original, direct sound, followed by a reflected, delayed version sometimes seconds later. In loudspeakers, a more subtle version of this problem occurs in cases like these:

1. A small, shallow high frequency driver is mounted on the same flat baffle as a much larger, deeper low-frequency driver. The low frequency driver’s acoustic center is slightly farther away from the listener and its sound arrives later than that of the high frequency driver.
2. Drivers are mounted far apart on a speaker baffle, with one driver close to ear level and the other driver close to the floor. The lower driver is farther from the listener’s ear, resulting in its sound being slightly delayed.
3. Left and right stereo speakers are placed in a room are different distances from the listener. The sound from the speaker that is a greater distance from the listener will arrive later, causing time alignment, imaging, and channel balance issues.

²Lobe titling – Wikipedia – 2024

Though DSP is often used in surround sound applications to intentionally add time delayed effects signals (echoes and reverb), it can also be used to address time alignment issues by introducing corrective digital delays. DSP can also be used to implement crossovers with very steep slopes that are linear phase using a time-limited sampling process called Finite Impulse Response (or FIR). Combining DSP-generated FIR crossover filters with digital delay can correct issues with time alignment, impulse response, and group delay, resulting in a much more ideal output than can be achieved via passive or analog active crossovers alone.

As discussed above, it is possible to implement active crossovers in either the analog or the digital domain. The following are some pros and cons of each approach:

For pros and cons of passive crossovers, see our primer article on “Passive and Active Loudspeakers”

Examples of analog active crossovers:

• Bryston 10B-Sub Active Stereo Crossover Network
• Wilson Audio ActivXO Dual Subwoofer Crossover and Controller
• Outlaw Audio ICBM-1 Analog Bass Management / Multi-Channel Active Crossover

Example of DSP active crossover:

• Legacy Audio Wavelet