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Open Josephmbradel-MS-Thesis.Pdf The Pennsylvania State University The Graduate School INVESTIGATION OF TRANSDUCERS IN SMALL ENCLOSURES A Thesis in Acoustics by Joseph Bradel © 2020 Joseph Bradel Submitted in Partial Fulfillment of the Requirements for the Degree of Master of Science December 2020 The thesis of Joseph Bradel was reviewed and approved by the following: Stephen C. Thompson Research Professor of Acoustics Thesis Advisor Micah R. Shepherd Assistant Research Professor Robert W. Smith Assistant Research Professor Victor W. Sparrow Director, Graduate Program in Acoustics United Technologies Corporation Professor of Acoustics ii Abstract Recent applications of active noise control (ANC) have been aimed at canceling noise passing through a building’s window, and while attempts have been made to implement this in a laboratory setting, the choice of driver and its enclosure is imperative to accurate sound reproduction, specifically between 500 Hz and 3000 Hz. While choosing a driver based on characteristics listed on its specification sheet is easy, these specifications often lack vital information. With the requirements of having a flat frequency response, small physical size, and low distortion, four drivers were chosen and subjected to further testing. An impedance test, which when analyzed calculated driver parameters, allowed theoretical models to be made that predicted the drivers’ behavior when sealed in their smallest possible cuboid enclosure. Frequency responses measured using a maximum- length sequence excitation signal showed how each driver-enclosure assembly prototype behaved in practical application. Various nonlinear measurements taken by the Klippel Analyzer 3 apparatus showed the low-level distortion produced by each driver along with nonlinear behaviors of driver parameters such as stiffness and force factor. Ultimately, the Tang Band W2-2243S driver-enclosure assembly proved to be best for this ANC application based on its frequency response, low distortion, and acceptable nonlinear parameter behavior. iii Table of Contents List of Figures vii List of Tables xvii List of Symbols xviii Acknowledgments xxiii Chapter 1 Introduction1 1.1 Background and Motivation......................... 1 1.2 Electromagnetic Transducers and Enclosures................ 3 1.2.1 Components.............................. 3 1.2.2 Electromechanical Coupling..................... 4 1.2.3 The Damped Mass-Spring System.................. 5 1.2.4 Mechanoacoustical Coupling..................... 5 1.2.5 Enclosures............................... 6 1.2.6 Sound Radiation and Acoustic Size................. 6 1.2.6.1 Radiation from a Baffled Piston.............. 6 1.2.6.2 Directivity through Acoustic Size............. 8 1.2.6.3 Source Level ........................ 9 1.2.7 Radiation Impedance......................... 10 1.3 Published Literature ............................. 12 1.4 Objectives................................... 13 Chapter 2 Driver-Enclosure Designs 14 2.1 Finding The Right Drivers.......................... 14 2.1.1 Frequency Response Curves ..................... 14 2.1.2 Impedance Curves and Resonant Frequency ............ 15 2.1.3 Diaphragm Size and Driver Depth.................. 15 2.1.4 Rated Power and Maximum Excursion Distance.......... 15 2.1.5 The Chosen Drivers.......................... 16 2.1.5.1 Tang Band W1-2121S ................... 16 iv 2.1.5.2 Tang Band W2-2243S ................... 17 2.1.5.3 Visaton FRS 5X-8 ..................... 17 2.1.5.4 Tectonic TEBM36S12-8/A................. 18 2.2 Constructing Testable Enclosures...................... 18 2.2.1 Enclosure Shape and Material Choice................ 19 2.2.2 Enclosure Size Variability ...................... 20 2.3 Final Assembly................................ 22 2.4 Estimating Internal Volume ......................... 23 Chapter 3 Modeling Electromagnetic Transducers 26 3.1 Overview.................................... 26 3.2 Domains.................................... 26 3.2.1 Lumped Elements........................... 27 3.2.2 The Impedance Analogy....................... 27 3.2.3 The Electrical Domain........................ 28 3.2.4 The Mechanical Domain....................... 29 3.2.5 The Acoustical Domain........................ 31 3.3 Connecting Domains ............................. 35 3.3.1 Electrical to Mechanical ....................... 37 3.3.2 Mechanical to Acoustical....................... 37 3.4 Using Simulation Software [LTSpice] .................... 38 3.5 The Full Transducer Model ......................... 39 Chapter 4 Simulating Impedance and Frequency Response 40 4.1 Measuring Impedance............................. 40 4.2 Calculating Characteristics.......................... 44 4.3 Simulating Frequency Response....................... 51 Chapter 5 Measuring Frequency Response and Nonlinear Behavior 59 5.1 Measuring Frequency Response ....................... 59 5.1.1 The Maximum-Length Sequence................... 60 5.1.2 The MATLAB Impulse Response Measurement App . 61 5.1.3 Frequency Response Measurement Method............. 62 5.1.4 Frequency Response Results..................... 63 5.2 Measuring Nonlinear Behavior........................ 68 5.2.1 Loudspeaker Distortion........................ 68 5.2.2 The Klippel Analyzer 3 System................... 70 5.2.3 KA3 Measurement Methods..................... 72 5.2.4 Comparing Measured Linear Parameters.............. 73 5.2.5 Measured Multi-Tone Distortion................... 76 5.2.6 Measured Parameter Nonlinearities................. 78 v Chapter 6 Conclusion 88 6.1 Choosing The Best Driver-Enclosure Assembly............... 88 6.2 The Use of Acceptable Displacement Percentages ............. 90 6.3 Future Work.................................. 91 Appendix A Specification Sheets 93 Appendix B Engineering Drawings for Enclosure Components 99 Appendix C MATLAB Code 110 C.1 Volume Finder ................................110 C.2 Linear Parameter Characterization .....................117 C.3 Impulse and Frequency Response ......................123 C.4 KA3 Data Plotter...............................126 Appendix D Impulse Response Measurement Results 144 Bibliography 153 vi List of Figures 1.1 The cross-section of a typical moving coil driver taken from Müller and Möser [1], p. 29................................. 4 1.2 The visual setup for the baffled circular piston pressure radiation as described and drawn by Blackstock [2], p. 446. By summing the pressure observed radiating from differential elements of differential rings, the full shape of the piston will be realized as the radiation source......... 7 1.3 The normalized directivity in decibels of the baffled circular piston at various values of ka [2]. As ka increases, side lobes are formed producing nulls in the pressure radiation......................... 9 1.4 The normalized real and imaginary specific radiation impedance as well as its magnitude [2]. The magnitude nearly matches the imaginary impedance when ka < 0.5 showing that the imaginary impedance is dominant at low frequencies. Similarly, the real impedance is dominant at high frequencies when ka > 3. ................................. 12 2.1 The W1-2121S Driver (left) and its frequency response and impedance curve (right), given in red (left scale) and in blue (right scale) respec- tively, as reported by Tang Band [3]. The specification sheet did not give any information about the methods used to measure the frequency response, such as the power of the input signal, the distance the mea- surement was taken, or if the driver was placed in an acoustically infinite baffle. This driver was small in size and fairly inexpensive. Images were taken directly from http://www.tb-speaker.com/uploads/files/ e99c0126812ca22379a2179932b9e840.pdf. ................ 17 vii 2.2 The Tang Band W2-2243S Driver (left) and its frequency response and impedance curve (right), given in red (left scale) and in blue (right scale) respectively, from Tang Band [4]. Like the W1-2121S, this drivers specification sheet did not specify anything about the measurement method for the frequency response including the physical placement of the driver. This was the most expensive of the drivers chosen. It also had a more robust design, taking up the more volume behind the face plate. Images were taken from http://www.tb-speaker.com/uploads/files/ e4964df0494335751327c45c1160fc73.pdf. ................ 18 2.3 Visaton’s FRS 5X-8 Driver (top) and the frequency response and impedance curve (bottom), given in red (left scale) and in green (right scale) respec- tively, reported by Visaton [5]. As labeled on the frequency response and impedance curve, the frequency response measurement used a 1 Watt input signal being measured 1 meter away from the driver. The specifica- tion sheet does not specify if these measurements were taken while holding the driver in a baffle. This driver had a fairly large dust cap in its design. The magnet was nearly the diameter of the cone, but the overall depth was the same as the W2-2243S [5][4]. Images were taken from https: //www.visaton.de/sites/default/files/dd_product/frs5x_8.pdf. 19 2.4 The Tectonic TEBM36S12-8/A Driver (top) and its frequency response and impedance curve (bottom), given in red (left scale) and in blue (right scale) respectively, as reported by Tectonic [6]. The specification sheet reported that the frequency response measurement used a 1 Watt input signal and was measured 1 meter away from the driver but did not spec- ify the mounting technique used. The TEBM36S12-8/A was incredibly shallow, allowing for a small enclosure design. The frame
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