Antithesis Subwoofer

Purpose

The Antithesis Subwoofer project was meant to section off part of the Rapture Audio System into a managable chunk. The design centered around building a folded transmission line subwoofer with a accelerometer based servo tracking loop.

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Introduction to Anithesis

The Electrodynamic Loudspeaker

The electrodynamic loudspeaker is foundation of the audio industry. The input electrical signal on the voice coil creates a magnetic field that interacts with the magnetic field due to the magnet in the speaker. The diaphragm or cone is moved by the force created by the voice coil. The pistonic motion of the diaphragm is coupled to the air which produces sound waves.

Problems with the Electrodynamic Loudspeaker

Newton's first law of motion teaches us about inertia. Therefore we know that once we get the cone moving in one direction, we need to apply a force to stop its motion before it can move in the other direction to properly react to the incoming electrical signal. This form of inertial distortion is one of the most prominent causes of distortion intrinsic in electrodynamic subwoofers. The other major form of distortion is diaphragm breakup, where the motion of the cone is not perfectly pistonic, but proper construction and materials can alleviate this.

The other major problem with electrodynamic loudspeakers is electrical to acoustic power transfer. The mass of the diaphragm is much much greater than the mass of the air it is acting on. By an analogy the impedance of the speaker is not equal to the impedance of the air. The impedance mismatch decreases the total power transfer, which causes these speakers to be very inefficient. The work of Neville Theile and Richard Small, which modeled the mechanics of speakers after electrical circuit components, brought about a revolution in loudspeaker design and construction. Using a driver's Theile/Small parameters, a desired implementation could be calculated and the output predicted. To correct the impedance mismatch as best as possible, the driver is placed in an enclosure of certain properties. The two most widely known enclosures are Acoustic Suspension (sealed) and Bass Reflex (vented/ported). However, both of these designs have problems with resonance and roll off.

Antithesis as a solution

The two results of the Antithesis project will be to correct the problems of inertial distortion and enclosure impedance and frequency mismatch. Antithesis will utilize two separate methods to do this. Inertial Distortion will be corrected by a closed loop feedback system. An accelerometer will measure the position of the diaphragm of the loudspeaker. The position signal will be used to create an error signal with the input to the system by taking the difference. The error signal will then be amplified and sent to the voice coil of the speaker. In this manner inertial distortion will be corrected. Also, this system has the ability to alleviate thermal compression at high power levels. The enclosure will not be a standard Acoustic Suspension or Bass Reflex Enclosure, but an Acoustic Transmission line. The idea was developed and has been used since the 1950s. However, recently Bose of the 901 fame has capitalized on the technique for their flagship product the Bose Waveguide Radio. The idea uses a tuned tube on the back of the loudspeaker to invert the sound wave so it reinforces the output of the driver while nullifying the effects of resonance on the driver.

Alternate Considerations

There are other methods of measuring the acceleration/position of the speaker cone instead of using a MEMS based accelerometer. One such method is to use a piezoelectric transducer as an accelerometer. Another method is to bounce light off the cone and measure the intensity reflected to determine position in a manner similar to how a CD player focuses on the tracks in a CD. Using the MEMS accelerometer will most likely be more expensive than these other options, but it will be easier initially to get started. This is because the MEMS accelerometer is a drop-in calibrated solution that will absolutely work.

Although this system may be adequate and reach its goals, introducing a closed feedback loop introduces an element of delay and is a form of post-correction. No matter how fast the system responds (at the expense of power consumption, cost and ease of construction) the servo loop is always trying to correct for errors already made. It would be advantageous to mathematically model the motion of the loudspeaker and "pre-warp" the signal feeding it to correct for errors before they are reproduced. Then a closed-loop system could be used to update the mathematical model. This is where this project should go in the end.