Frequency response of a speaker cabinet on the rear axis



April 25, 2018

Approximation of the frequency response of a speaker cabinet on the rear axis with a first-order low-pass filter.

In Room Boundary Simulator the frequency response behind the speaker cabinet is simulated with a first-order low-pass filter. The cutoff frequency of the low-pass filter is shifted according to the baffle width.

This article compares the low-pass filter simulation with measurements. Rear response curves are normalized to the on-axis response (in other words we can see the difference between the frontal on-axis response and the rear radiation in dB).

Before showing the results some additional remarks:

The first measured curve is exported from the polar charts of a pro PA speaker (JBL AC2212-95). The speaker has a 12" woofer and the width of the cabinet is 355 mm. Unfortunately, there is no measured data below 200 Hz.


Normalized rear axis frequency resoponse of a 355mm wide PA speaker, simulation and measurement


The second one is an impulse response measurement of a small, 9 cm wide and 16 cm tall "multimedia" speaker. I've set the gate time to 8 msec, and the microphone distance from the baffle is 45 cm. (In the impulse response the first 8 msec is reflection free, this gives a 125 Hz low frequency limit.)


Normalized rear axis frequency resoponse of a 90mm wide speaker, simulation and measurement


As can be seen on the graphs the first-order low-pass filter approximation gives acceptable results. The maximum error is +- 2 dB between 0 dB and -15 dB, and only becomes larger where the response falls below -15 dB. The cutoff frequency of the low-pass filter can be shifted down or up according to the baffle width. If we need a more accurate calculation, then the geometric theory of diffraction, or modeling wave propagation is a better choice.

Csaba Horváth




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