A back-loaded horn speaker is a loudspeaker design that channels the rear sound wave of a driver through a folded horn inside the cabinet to amplify bass efficiently and reduce distortion.
 Unlike standard boxes, a back-loaded horn utilizes a complex, winding internal pathway that expands gradually like a musical instrument. The sound waves radiating from the back of the speaker cone travel through expanding channel (the horn), which acoustically amplifies the lower frequencies.

A back-loaded horn speaker is a loudspeaker design that channels the rear sound wave of a driver through a folded horn inside the cabinet to amplify bass efficiently and reduce distortion.
Unlike standard boxes, a back-loaded horn utilizes a complex, winding internal pathway that expands gradually like a musical instrument. The sound waves radiating from the back of the speaker cone travel through expanding channel (the horn), which acoustically amplifies the lower frequencies.

You can download the original drafts at the official Fostex link. And right from the start, I want to emphasize that this is not a true Hi-Fi quality speaker, but simply a small experiment with which I wanted to test the characteristics and efficiency of this type of speaker box. At the very beginning, I studied the method of designing this type of box, which, by the way, despite the many software for that purpose, is still quite complex and requires a lot of work and testing. When designing, it is necessary to know the basic characteristics of the driver, among which the most basic are the Resonant Frequency and Thele Small parameters given by the manufacturer.
Of course, there is simply no data for this small, cheap driver. At home, without using expensive instruments, we can measure the resonant frequency with great precision, and that is the basic data for making any type of sound box. We need a computer or phone with an audio frequency generator application, an audio amplifier, a resistor with a value of about 10 to 47 Ohms, and a digital multimeter.

  I will use online ton generator. I connect the output of the amplifier through a series resistor to the speaker. Then I connect the multimeter directly to the speaker terminals and let the speaker hang freely in the air so that there is no influence from the environment. Now I gradually change the frequency from 40Hz and up.  As the frequency increases, the voltage changes, and when it reaches its maximum value, we read the resonant frequency of the speaker. For this speaker in particular, it is about 170Hz.

This is the sound box in the construction phase where the sound path from the driver to the exit (mouth) can best be seen.

Immediately behind the driver where the sound is generated, there is the first chamber which represents a semi-open sound box in which a damping material is placed. Then the sound continues through a channel which expands exponentially and whose dimensions depend mostly on the resonant frequency of the driver. It should be known that proportional reduction of dimensions does not work like with classic boxes where you can simply reduce the volume proportionally. However, in this specific case, with rough calculations, I came to the result that the resonant frequency of this box is approximately equal to the one I measured for the driver. This was much simpler for me than designing a completely new box with minimally better results.

  Next comes the most interesting part, which is testing the characteristics of this small speaker. Unfortunately, you will not be able to capture the exact sound through the recorded audio, but I will try to convey it to you, based on my listening tests. For obvious reasons, for testing I will be using songs from the YouTube library. So that you can at least roughly get a feel for what kind of sound it is, along with this speaker, I connected my NAD 801mm to the other channel to make a rough comparison. I put a red LED on both speakers as an indicator of the active speaker at the moment. By changing the balance, I will test the sound of both speakers.

As I said at the beginning, we should not expect some super high-quality hi-fi sound, but still, unlike a regular compression box, we have a noticeable boost somewhere in the higher bass or low midrange (around 150–300 Hz) which results in a slightly "more aggressive" sound in vocals, unlike a closed box which often results in a very thin and quiet sound. Although this box does not produce true sub-bass, it will still produce much more energy and noise in the mid-bass than a miniature closed box. The sound is more vivid, and the box looks like a work of art on the desk.
  Now I am going to try to do an extremly rough test to determine the frequency response of the two speakers. Fotr this purpose I am using a online pink noise generator and free spectral analysis software. With small microphone I am going to pick up the sound from two speakers separately. I am practically interested in the low frequency responce because this microphone is relatively insensitive to higher frequencies.

As I said at the beginning, we should not expect some super high-quality hi-fi sound, but still, unlike a regular compression box, we have a noticeable boost somewhere in the higher bass or low midrange (around 150–300 Hz) which results in a slightly "more aggressive" sound in vocals, unlike a closed box which often results in a very thin and quiet sound. Although this box does not produce true sub-bass, it will still produce much more energy and noise in the mid-bass than a miniature closed box. The sound is more vivid, and the box looks like a work of art on the desk.
  Now I am going to try to do an extremly rough test to determine the frequency response of the two speakers. Fotr this purpose I am using a online pink noise generator and free spectral analysis software. With small microphone I am going to pick up the sound from two speakers separately. I am practically interested in the low frequency responce because this microphone is relatively insensitive to higher frequencies.