The filter design of the loudspeakers



 1. Bass - Low Mid

f1= 160 Hz

2. Low Mid - High Mid

f1= 800 Hz

3. High Mid - High

f1= 4000 Hz

All filters consist of 2 second order Butterworth elements in cascade (Linkwitz-Riley). For compensation of the parasitic phase of the other filters the crossover frequencies of the low-mid to high-mid filters are modified to 850 Hz and 750 Hz. The gain of the two middle sections is increased by 7 % to get the overall amplitude response flat.

The difference between the "normal" filter and the "cascade" filter is that in the latter case the low-pass filter of the bass section is taken from the output of the low-pass filter of the low-mid section and the high-pass filter of the tweeter is taken from the output of the high-pass filter of the high-mid section. In that case the slopes of the bass and tweeter
filters is doubled out of band but with extra phase errors as a result. Therefore this option was not selected.

The calculated overall passband and the individual filters look like this :

Enlarged to show the overall characteristic in more detail :

The phase of the sum of the filters in both options :

You can get the worksheet in Excel 97 format here : 4-way 4th order Linkwitz-Riley filters

It is completely reworked now to enable anybody to calculate any 4-way 4th order electronic crossover filters they like. All the following characteristics are graphically presented :

- Frequency response of individual outputs
- Combined frequency response
- Phase response of individual outputs
- Combined phase response
- Group delay

You can calculate resistors and capacitors based on corner frequencies and Q's or you can calculate the circuit responses if you know the component values.

The filters measured with SpeakerWorkshop :

The differences in peak levels take into account the different sensitivities of the drivers and the different gains of the power amplifiers per channel. The light blue curve is the summed output, which is flat as you can see. The slightly darker blue curve is the same frequency response, but now with the baffle step compensation switched in.

A picture of the printed circuit board :

A picture of the finished board :

A picture of the finished filter (one channel) :

A screen print of the filter PCB design (PCB design program Andreas Waldherr) :

If you have any questions regarding this project write me at