the basics of
Linkwitz Riley

Linkwitz-Riley filters are a type of crossover filter commonly used in audio processing, particularly in speaker systems. These filters are named after Siegfried Linkwitz and Russ Riley, who developed this design to overcome some of the limitations found in simpler crossover networks. They are especially favored in high-fidelity audio applications due to their excellent phase and amplitude characteristics.

What are Crossover Filters?

Crossover filters are used in multi-driver speaker systems, where different speakers (drivers) are responsible for reproducing different parts of the audio spectrum. For example, tweeters handle high frequencies, woofers handle lows, and midrange speakers handle the middle part of the spectrum. Crossover filters divide the audio signal into separate frequency bands that are sent to the appropriate driver.

Characteristics of Linkwitz-Riley Filters

Type: Linkwitz-Riley filters are a type of Butterworth filter. Specifically, they are created by cascading two Butterworth filters of the same order, leading to a steeper attenuation slope.

Slope: The standard slopes of Linkwitz-Riley filters are 12 dB per octave, 24 dB per octave, and higher, per each doubling of the order. This steepness allows for more precise control of frequency division between different drivers, reducing overlap and potential interference.

Phase Response: One of the defining features of Linkwitz-Riley filters is their phase coherence. When two filters of this type are used in a crossover (high pass and low pass), they maintain a phase difference of zero degrees at the crossover frequency, resulting in a seamless transition between drivers. This is crucial for maintaining the spatial characteristics and integrity of the sound.

Amplitude Response: At the crossover frequency, where the high-pass and low-pass filters overlap, the outputs of these filters combine in-phase, resulting in a flat amplitude response. This ensures that there is no dip or peak at the crossover point, which is common in less sophisticated crossovers.

Applications

Linkwitz-Riley filters are used extensively in both consumer and professional audio products. Their superior phase and amplitude response characteristics make them particularly useful in:

Studio Monitors and High-Fidelity Speakers: Ensuring accurate sound reproduction without coloration or distortion.

Audio Processing Equipment: Used in electronic crossovers and digital signal processing (DSP) units for dividing frequency bands accurately.

Live Sound Systems: Where precise control over speaker outputs is necessary to cover large areas evenly without frequency overlap or cancellation.

Implementation

The implementation of Linkwitz-Riley filters can be done through analog circuitry or through digital signal processing. In digital implementations, the precision and flexibility of DSP allow for complex configurations and easy adjustments to the crossover frequency and filter characteristics.

Linkwitz-Riley filters represent a sophisticated solution in audio processing, providing high-quality sound by ensuring coherent phase and flat amplitude response across crossover points. This makes them indispensable in applications requiring precise and clear audio reproduction.

Slope Example:

courtesy of Andy Wehmeyer
President, Audiofrog, Inc.

  • 24dB/octave slopes are red and dark green.

  • 48dB/oct slopes are light green and orange