HARBETH: M30.1 partnered with subwoofer – theoretical calculations

A member of the Harbeth user group writes: For anyone interested in partnering their Harbeth M30.1 with a subwoofer, I've done some theoretical design simulations to see what sort of combined response might be achieved.

The M30.1 has a quoted –3 dB low-frequency cut-off point of 50 Hz. For the purposes of the simulations, I have assumed that its low-frequency response follows a QB3 vented-box low-frequency alignment. A 2nd-order Butterworth high-pass filter response has been added to the "raw" response of the M30.1. This high-pass filter type is what is commonly found in AV receivers.

The subwoofer is modelled as a system with a 2nd-order Butterworth high-pass filter with a –3 dB point of 20 Hz. A 2nd-order Butterworth low-pass filter with a –3 dB point of 200 Hz has been included in order to model the nominal high-frequency roll-off of the subwoofer's response. The 20 Hz low-frequency response seems to be attainable by a few subwoofers on the market today.

A 4th-order Linkwitz-Riley low-pass filter has been applied to the "raw" subwoofer response. The Linkwitz-Riley filter type is typical of that to be found in subwoofers and AV receivers.

After a few trial-and-error calculations, the –3 dB cut-off frequency for the 2nd-order Butterworth high-pass filter was chosen to be 58 Hz, while the –6 dB cut-off frequency of the 4th-order Linkwitz-Riley low-pass filter was set to 54 Hz. The subwoofer and M30.1 were connected with the same polarity. Owing to the effects of the low-pass filter, the output of the subwoofer needed to be raised by +1.2 dB to produce a smooth blending between the M30.1 and subwoofer. The resulting filtered acoustic responses of the subwoofer and M30.1 cross over at about 55 Hz at –6 dB. The combined low-frequency response is very flat, and the –3 dB point is at about 18 Hz. This is a very worthwhile extension of the M30.1's natural low-frequency cut-off point of 50 Hz or so.

The computed frequency response plots are shown below:

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