Linkwitz-Riley filter (low pass & high pass)

1. Introduction to filters
　　"Linkwitz-Riley" is the Chinese translation of Linkwitz-Riley. The Linkwitz-Riley filter was designed by Siegfried Linkwitz and Russ Riley in 1976. It is mainly used in active filter circuits, such as in many sophisticated multi-channel electronic crossover systems. Of course, the passive speaker Crossover networks can also be used. The characteristic of this filter is that it has an attenuation slope of up to fourth order. In other words, every other octave frequency, the sound will attenuate 24dB of energy, that is, the attenuation slope is -24dB/Oct (Oct is Octave, an octave meaning). At the same time, the Linkwitz-Riley filter has a flat phase response in the entire audio range (20Hz-20kHz), and the signal will not produce serious phase distortion after passing through the filter.
 
2. Simulation test.
　　Through simulation, it can be seen that the gain at the crossover point (2kHz) is around -3dB, and it shows excellent phase synchronization. Therefore, it can reduce the phase distortion caused by electrical signals and is suitable for active applications. Audio two-way system.
 
　　The theoretical amplitude-frequency characteristics are as shown in the figure:
 
3. Physical test
　　Amplitude-frequency test: The input is a 2Vpp 2kHz sine wave, and the output is a 1.40Vpp 2kHz sine wave, without distortion and the gain is about -3dB.
 
　　Phase-frequency test: Use the XY mode of the oscilloscope. The graph is approximately a straight line with small phase difference.