The Parametric Digital Transducer Array Loudspeaker

For my capstone project that I completed at RMIT University I conducted a bunch of research into experimental loudspeaker designs such as Digital and Parametric Loudspeaker Arrays. As a result of this project I conceptalised a design for the Parametric Digital Transducer Array Loudspeaker, built a prototype, and validated the design by performing a variety of measurements on it that time and resources would allow.

In the spirit of Open Source, I decided to write up this casual, albeit somewhat tech heavy post explaining the basics of true digital loudspeakers, Parametric Loudspeaker Arrays, and the Parametric Digital Transducer Array Loudspeaker design in contrast to the more conventional loudspeaker designs. If you are really interested in a more comprehensive look at this topic, the final report, materials list, images, data, references, and associated code used in the project can be found here.

What is a "Conventional" Loudspeaker?

A moving-coil type loudspeaker with a cone based diaphragm. Source

A conventional loudspeaker is very much like the type of loudspeakers you find in everyday life. They usually utilise various implementations of a moving-coil type design, however also commonly use piezoelectric bimorphs. These designs all achieve the same goal with varying efficiency, frequency response, and total harmonic distortion (THD) levels through the conversion of electrical audio signals into acoustic waves by pushing a diaphragm backwards and forwards.

What is a "Digital" Loudspeaker?

Direct Acoustic Digital-to-Analog Conversion

A digital loudspeaker is a loudspeaker that is capable of performing Direct Acoustic Digital-to-Analog Conversion, or DADAC in its mildly more manageable acronym. DADAC is the process of creating an acoustically decoded sound pressure signal by driving and emitting digital streams through a loudspeaker array, with conversion taking place via acoustic summation. Quite a mouthful, that's for sure! So what does one of these loudspeakers look like, and how exactly is DADAC performed in practice?

Digital Transducer Array Loudspeaker

A few examples of DADAC capable loudspeakers. Source: Direct Acoustic Digital-to-analog Conversion with Digital Transducer Array Loudspeakers

DADAC capable digital loudspeakers come in a variety of topologies, shapes, and sizes, but for relative simplicity's sake I will only detail the One-bit Per Transducer Digital Transducer Array Loudspeaker design, or DTAL.

A visual representation of an eight bit One-bit Per Transducer DTAL performing DADAC.

The One-bit Per Transducer DTAL design works on the principle that each weighted bit in a digital signal is represented by one transducer element. Each transducer element is driven by a signal proportional to its bit weight. This loudspeaker requires an array of transducers that is defined by the bit depth of the digital signal being used. Once these digital pulses are output from the individual transducer elements within the array they recombine in air, reproducing the original digital signal and performing DADAC. This process is made possible by the usage of a bit-spilling operation that converts a digital signal in to multiple one-bit weighted digital signals.

Bit spilled signal example. Top: Double-sided 2 bit signal. Middle: LSB spilled signal. Bottom: MSB spilled signal

Advantages of a "Digital" Loudspeaker?

Compact and thin examples of DADAC capable loudspeakers. Source: Digital sound reconstruction using arrays of CMOS-MEMS microspeakers, Development and Characterization of a Piezoelectrically Actuated MEMS Digital Loudspeaker

It might not look like it from the earlier pictures, but devices that can perform DADAC have the possibility to be smaller, thinner, and more efficient than their conventional counterparts. Due to the arrayed nature of the design, digital loudspeakers have the intrinsic ability to perform beamforming and can potentially steer the direction in which audio is output from the loudspeaker. This beamforming is possible for the entire frequency range of the loudspeaker, not just small segments of the frequency spectrum which is commonly the case when using similar methods in other applications such as cardioid subwoofers.

Disadvantages of a "Digital" Loudspeaker?

Due to the listening path differences that exist between transducer elements, it is impossible to get a perfect summation of all the emitted signals in most listening positions. This results in significant distortion at many listening positions. There are various methods that can be used to reduce this distortion, although without reducing the size of each transducer to sub-centimetre levels, the level of distortion produced struggles to reach the relatively low levels of distortion produced by high quality conventional loudspeakers. One company, Audio Pixels, is currently working on a low cost MEMS digital loudspeaker that is attempting to do just this.

What is a Parametric Loudspeaker Array?

A Parametric Loudspeaker Array, or PLA, is a highly directive loudspeaker that consists of an array of ultrasonic transducers that exploit the nonlinear properties of air to self-demodulate modulated ultrasonic signals with the aim of creating audible sound waves.

Parametric Loudspeaker Array utilising digital processing.

In practice this can be achieved by performing amplitude modulation on an audio signal, and driving transducers directly with the resulting signal. Once the emitted ultrasonic sound waves are a little bit away from the array, they will demodulate and produce a secondary sound beam. This secondary beam will predominantly contain the original audio signal.

This technology has been successfully adopted by companies such as Holosonics, HyperSound, Ultrasonic Audio, and a funded Kickstarter campaign called Sound Lazer.

Advantages of a Parametric Loudspeaker?

Ultrasonic devices such as ultrasonic piezo transducers tend to have narrow directivity patterns, effectively emitting sound waves in well-defined beams. By designing PLAs with such transducers, audio can be output in very precise manner. By using these properties even further, it is possible to produce devices that use beamforming to directly control the direction and dispersion of audio, much in the same way that a DADAC capable loudspeaker can do this.

Disadvantages of a "Parametric" Loudspeaker?

Generally speaker, PLAs produce higher amounts of THD than conventional speakers due to the same non-linear properties of air that allow demodulation in the first place. The amount of THD a PLA produces is highly dependent on the type of modulation scheme that is used. They also suffer from low sound pressure level output, poor efficiency, and poor low frequency response making music playback difficult.

What is a Parametric Digital Transducer Array Loudspeaker?

A Parametric Digital Transducer Array Loudspeaker, or PDTAL, is simply an amalgamation of DTAL and PLA type designs.

Parametric Digital Transducer Array Loudspeaker with beamforming capability diagram.

An digital audio signal is amplitude modulated before being bit-spilled in to different weighted bit streams. These bit streams are then amplified by amplifiers that are weighted according to each bit stream weight. The resulting signals then drive individual or groups of transducers. The digital pulses emitted from these transducers sum in air, reproducing the original amplitude modulated digital signal and performing DADAC. This acoustic wave then demodulates and produce a secondary sound beam which predominantly contains the original audio signal as per the previous PLA design.

Advantages of a Parametric Digital Transducer Array Loudspeaker?

For the same reasons you might want to was a PLA.  Narrow directivity patterns and beamforming capabilities. However there are several advantages of using a PDTAL type design over a PLA design. This includes the usage of digital amplifiers in the amplification stage allowing the elimination of digital-to-analog converters (DACs) in the circuit design, as well as simplified driver amplifier designs. This is significant as a beamforming capable PLA usually requires many DACs and more complicated driving amplifiers. Overall, this reduces system complexity and cost.

Another great benefit of the PDTAL design is the improved low frequency response of the loudspeaker, which I will explain a little further on.

With this being said, the PDTAL suffers some of the same issues as PLA and DTAL type designs. This includes higher THD when compared to conventional loudspeakers which may be considered an acceptable compromise for having a narrow beam pattern with digital steering capability and all digital loudspeaker design.

The Parametric Digital Transducer Array Loudspeaker Prototype

Prototype hardware block diagram.

The design for the constructed prototype had an 8 bit resolution, and a sampling frequency of 97.65625KHz, It utilised an Opal Kelly XEM6010-LX45 FPGA board for signal processing, 4 Texas Instruments LM293D H-bridge amplifiers for amplification, and a 28 element Murata MA40S4S ultrasonic transducer array. 7 groups of 4 transducers were wired in parallel in an attempt to increase the sound pressure level output of the prototype. The weighting of each amplifier was implemented using pulse width modulation and varying duty cycles

Signal flow diagram of prototype system.

Prototype Measurement Techniques

Measurement setup for the PDTAL prototype.

A series of acoustics measurements were conducted in a quiet, but non-anechoic room 30cm away from the loudspeaker using sinusoidal signals with frequencies of 50Hz, 100Hz, 200Hz, 400Hz, 800Hz, 1600Hz, 3200Hz, and 6400Hz. Frequency response, THD, and signal-to-noise ratio (SNR) data was calculated from these measurements when possible. Due to the excessive ambient noise conditions in the room where the measurements took place, as well as the low sound pressure level emitted from the PDTAL prototype, accurate polar pattern measurements were not possible.

Measurement Results

Measured frequency response of the measured prototype.

The above figure shows the frequency response of the prototype as taken over a number of measurements. The 6dB per octave low pass filter with a 900Hz roll off frequency can be observed.

The next figure shows THD against output frequency of the prototype. THD generally decreases as output frequency increases except for frequencies above 6KHz.

Measured THD against frequency of the PDTAL prototype.

Measurement Discussion

The prototype has a flat frequency response up until until 900Hz where a 6dB per octave slope can be observed. This slope is due to the narrow frequency response of the MA40S4S piezo transducer. To extend the high frequency performance of the PDTAL design, a transducer with an extended frequency response could be used. The design appears to be able to produce low frequency signals with frequencies as low as 50Hz with a narrow directivity pattern. This can be considered an excellent attribute seeing as the reproduction of signals bellow 500Hz in PLA type designs is usually very difficult without drastic equalisation. The ability of the PDTAL design to reproduce these low frequencies can be considered a positive design attribute over conventional PLA designs.

The PDTAL Prototype produced similar amounts of THD to that of PLA design that utilise double-sideband modulation with a high modulation indexes. With that being said, It is highly likely that switching to single-sideband modulation would reduce the THD of the PDTAL design to acceptable levels.

But What Does it Sound Like?

Conclusion

Digital and Parametric Loudspeaker Arrays have quite a way to go before they are more widely adopted in the audio world due to their high levels of THD, and poor frequency response. The PDTAL design potentially solves the issue of poor low frequency performance of parametric speakers, and also potentially reduces the excessive THD distortion produced in off-axis positions with digital loudspeakers. All the while the design reduces system complexity when used in beamforming applications.

As mentioned earlier, this post only scratches the surface on the methods of Digital and Parametric Loudspeaker Arrays. More complete information can be found online via the shared project materials.

 

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