Microspeaker enclosure design for headphones

Question

I want to embark on an acoustic project of designing an enclosure for some 40mm microspeakers, identical to ones found in a typical on-ear headphone solution. Are microspeaker enclosures treated in the same way as a typical loudspeaker enclosure, Just with smaller dimensions? I ask this because every acoustic/loudspeaker design book including ones with chapters on headphones in, I have read does not mention anything on enclosure design for headphones and earbuds and google is nearly a complete deadend for the level of information I am looking for...

If headphone/earbud enclosures are not treated as loudspeaker enclosures with reduced dimensions, what is the design procedure/equations for the desired acoustic & frequency response from the enclosure?

Thank you in advance

Answer 1

the equations scale linearly for the linear dimensions of enclosures. However, here is why micro-enclosures don't get designed according to the same laws and equations used for full-sized speaker boxes:

the primary objective of full-sized speaker enclosure design is to manage the resonances of the box/driver system so as to prevent large response peaks in the bass range while extending bass response to the lowest frequencies possible. This is a solved problem in the field and results in the so-called Theile-Small parameters for ported enclosures, which nearly everyone uses when designing hi-fi speakers.

But a tiny little 40mm speaker is going to have a response peak between 5 and 10kHz and except in the so-called near field (speaker is closer to your ear than one speaker diameter), that speaker is going to put out very, very small amounts of audible bass energy. So there is no need to vent or horn-load the driver to smooth out the bass response.

Furthermore, the bump in the response curve at, say, 7.5kHz can be managed simply by turning down the treble knob on the amp that is driving the little speaker.

This is why speakers that small are usually mounted in equally small enclosures (like the ear cups of old-school Koss headphones, for example) that are just stuffed with a little loose cotton.

Answer 2

Earbuds do not work the same way as loudspeakers, because an earbud is working into a small sealed volume of air (the space between the earbud and the wearer's eardrum) while a speaker is designed to radiate sound into an (infinite) volume of free air.

The bass response for the two systems is completely different. For the earbuds, the motion of the driver is changing the volume of the sealed space, and hence changing the air pressure in the space. At low frequencies, the transmission of the pressure waves at the speed of sound is irrelevant - the pressure changes can be assumed to be instantaneous. On the other hand, a loudspeaker radiates sound by creating a travelling wave in the air, and for low frequencies the amplitude of the speaker cone must be (approximately) inversely proportional to the frequency to generate the same sound pressure variation.