Back-loading generally is not as efficient as a front-loaded horn, all things being equal.

The gain of back-loading is that the horn's frequency response bandwidth is increased over a comparable front-loaded horn.

Rear-loading a horn generally requires a driver with a higher Fs than the horn's Fc, and a "rising response curve" for the driver in question.

A front-loaded horn is best utilized with a LOWER Fs driver than the horn's Fc of relatively linear (flat) response. However, if I remember correctly, Bruce Edgar advocates a driver of a higher Fs (than Fc) and lower Qt for a front-loaded application. So there is plenty of arguments both ways.

One note of precaution, though: a rear-loaded horn often requires that the high(er) frequencies be limited by some method (i.e., a tortuous horn pathway, or an acoustic filter of some sort) to prevent them from going through the horn, which will result in comb-filter distortion when the same frequencies are being produced by the front of the cone at the same time. Having an indirect (i.e., downward or rear-firing, etc.) horn mouth may eleviate this effect somewhat.

DM

This is my definition of how most reasonably sized BLH work. Others might, and probably will, strongly object to this dexcription of how a BLH works. Based on my definition the low frequencies produced by the hybrid TL/horn reinforce the rolling off SPL response of the driver. Typically low Qts full range drivers are used by most BLH builders so they need help down low.

But to answer the oriiginal question, if done correctly the efficiency of the system will not be increased across the entire frequency spectrum. For example, if your full range driver has a SPL level of 95 dB/W/m and a Qts of 0.2 then the goal of the BLH design is to provide bass output that extends down to maybe 40 or 50 Hz at the same 95 dB/W/m. In most cases this is easier said then done.

Response bandwidth increase is what I was going for. I don't expect efficiency gain per se. What I wanted was to prevent cone excursion from bass to free the midrange and keep it from gargling.

The increase in bandwidth is due to less acoustic resistance being applied to the driver because typically the front of the cone is radiating into atmospheric pressure (the horn presents higher pressure to the rear of the driver than the front which is atmospheric). That also tends to reduce the overall efficiency of the horn/driver combination compared to a sealed back chamber typical of front-loaded horn.

So the trade off is higher bandwidth with a lower efficiency, that is, what is gained in one aspect is lost to the other. It also follows that a higher amount of IM distortion may be present, too, due to driver excursion being less limited in the forward direction compared to the rear, but careful back chamber/throat area/reactance adjustments can provide some ability to balance that for lower distortion, within the imposed limitations, of course. The best method of balancing this would be a front-horn AND a back horn feeding from the same driver.

Most of this is a moot point from what I see because like Martin said, most small footprint rear-loaded "horns" are not true LF horns but are more likely to act like a 1/4 wave transmission line at best or at worse, a somewhat wide-band resonating column. Peaky response at best, but covered up somewhat by the directly radiating driver output, hence their seeming popularity.

DM