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four π loudspeaker performance data

Frequency Response


Horizontal Off-Axis Response (tweeter side)

Horizontal Off-Axis Response (port side)

Vertical Off-Axis Response (down)

Vertical Off-Axis Response (up)


  • All measurements were done halfspace, with the speaker resting in a cradle and the microphone suspended above it on a boom.
  • No post-processing or smoothing was applied.
  • Measurements were taken at a distance of 10 feet from the baffle and drive voltage was 8.62vrms. This is equivalent to 2.83v/M and 1W/1M values since average impedance is 8Ω.
  • The loudspeaker was driven with a 60Hz sine at 40vrms to pre-heat for 15 minutes immediately before measurement. This was done to bring it to a realistic operating temperature.
  • Off-axis measurements were done at 10 increments. The forward axis was taken as the cabinet centerline, midpoint from top to bottom and side to side. Small vertical angles upward therefore position the microphone closer to the tweeter's forward axis.
  • The tweeter is offset horizontally relative to the cabinet centerline, so horizontal off-axis measurements are slightly different in one direction than the other. One direction has the tweeter slightly closer, the other has the woofer slightly closer.

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Helpful Documents and Software

π Speaker Whitepaper explains the concepts and evolution of modern waveguide and constant directivity loudspeakers
π Speaker Crossover Document analysis of circuits used in waveguide and constant directivity loudspeakers
"Crossover Electronics 101" Seminar Handout
JBL Professional Sound System Design Manual
Passive Crossover Spice models, complete with the AIM Spice modeling program
Pialign Analysis Software to help you design your enclosures. This is the old Altair original from 1977.
Plot the response curve of your design with Carlson's BoxPlot program
Plot the response curve of horns with the HornResp program
Convert Metric and Imperial measurements with the Madison Measurement Converter

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