Acoustic Directional Couplers permit separation of forward and reverse sound pressure waves. This separation opens the way to traceable precision acoustic reflection measurements. In order to span the audio frequency range, multiple couplers will be required, as each operates over a frequency range of slightly more than one octave. To reach 20kHz or above requires vary small, mechanically precise construction. We achieve this by 3D printing techniques. We manufactured two otherwise-identical couplers, one made with a powder-type 3D printer with photopolymer support structure, the other made with an ABS-filament thermoplastic-type 3D printer. We compare the measured acoustic performance of these two couplers. The wavelength of sound at 20 kHz is comparable to that encountered at a microwave frequency of 18 GHz. We expect to be able to fabricate couplers that reach 55 kHz where the wavelength is 6 mm, corresponding to a frequency of 50 GHz in the electromagnetic spectrum

MacDonell, Marcus Scott Glengarry

Scott, Jonathan B.

English

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3D-printed Acoustic Directional Couplers

Research Commons@Waikato

13D-printed Acoustic Directional CouplersMarcus MacDonell and Jonathan ScottAbstract—Acoustic Directional Couplers permit separation offorward and reverse sound pressure waves. This separation opensthe way to traceable precision acoustic reflection measurements.In order to span the audio frequency range, multiple couplers willbe required, as each operates over a frequency range of slightlymore than one octave. To reach 20kHz or above requires varysmall, mechanically precise construction. We achieve this by 3Dprinting techniques. We manufactured two otherwise-identicalcouplers, one made with a powder-type 3D printer with photo-polymer support structure, the other made with an ABS-filamentthermoplastic-type 3D printer. We compare the measured acous-tic performance of these two couplers. The wavelength of soundat 20 kHz is comparable to that encountered at a microwavefrequency of 18 GHz. We expect to be able to fabricate couplersthat reach 55 kHz where the wavelength is 6 mm, correspondingto a frequency of 50 GHz in the electromagnetic spectrum.Index Terms—Acoustical engineering, acoustic measurements,acoustic devices, directional couplers, waveguidesI. INTRODUCTIONA Directional Coupler is a 4-port network in which portionsof the forward and reverse traveling waves on a transmissionline are separately coupled to two of the ports [1]. It is oftenassumed that a directional coupler is inherently an electromag-netic device, since the majority of commercial examples haveeither coaxial or electromagnetic waveguide ports. Neverthe-less, acoustic directional couplers also exist. These are fourport devices and behave much like a conventional directionalcoupler, except that the ports are acoustic waveguides thatconduct pressure waves in a medium, typically air. A designfor an acoustic directional coupler is described in [2]. Foran acoustic coupler the required coupler material thicknessis a non-negligible fraction of the wavelength and needs tobe sufficiently stiff. Because of this a branch coupler is themost suitable design. A Branch coupler uses short sections ofwaveguide to couple the two mainlines. [2] Using a branchcoupler also has an advantage, the thickness of the separatingwall not only contributes to the isolation of the two mainlinesbut also improves the performance of the network. [2]The Coupler can be used as a reflectometer to makeextremely accurate measurements of a materials acoustic prop-erties. These measurements can be used by the audio industryto better isolate recording studios, damp speaker cabinets,design concert halls and theaters. Vector correction techniqueswill allow a user to correct for all shortcomings of a couplerprovided the directivity of the coupler is sufficient (usuallybetter than 6–10 dB). [3]The directionality of a coupler is thus the most importantspecification, and is the specification we are most concernedwith for determining the performance of the acoustic direc-tional coupler. The directionality or directivity is defined asThe authors are with the School of Engineering, the University of Waikato,Hamilton, New Zealand. e-mail: jonathanscott@ieee.org10log(Pc/Pd) where Pc is the power at the coupled port andPd is the power at the decoupled port [1].Recently a version of the Lagasse design has been usedto fabricate an acoustic impedance meter [3]. The couplerused 60 mm-square waveguide and had a design frequencyrange of 1–2 kHz and a usable range of 800–2,200 Hz.1 Itwas constructed by welding sheets and machined blocks ofacrylic material. In [3] it was shown that vector correctionallowed precise measurements of acoustic S-parameters. Inorder to create a measurement system that spans the audiorange from 20-20,000 Hz a set of some 10 different-sizedcouplers would be required. Some applications would benefitfrom an instrument that reached or exceeded 50 kHz.We created a SolidWorks model of the Lagasse couplerdesign. Once established, this design can be scaled, as di-mensions scale inversely with operating frequency. We builttwo versions, 3D-printed on different printers. The first wasa MakerBot Replicator 2X that employs an ABS filamentmaterial. It claims a layer resolution of 200 microns [0.0078inches], and am X-Y resolution of 11 microns. The second wasan Objet30 Pro powder-type 3D printer with photo-polymersupport. This machine claims a layer thickness of 28 micronsand a resolution of 100 microns [0.0039 inches].We wish to determine if there is a minimum 3D printerresolution to maintain directionality or if the resolution has aconsiderable effect on directionality for the chosen operationalfrequency.There is very little literature concerning the use, design andapplication of acoustic directional couplers. The original paperby Lagasse, [2], seems to have been largely ignored. In [3]the authors describe a number of systems in the literature thatdiscrimate travelling waves, but all others use alternatives apartfrom directional couplers. The literature surrounding the useof electromagnetic couplers is very rich, in contrast. [1], [4]II. SOLIDWORKS MODEL AND CONSTRUCTIONThe acoustic directional coupler model was designed tooperate in a frequency range an order of magnitude higherthan that of the hand-built coupler from [3]. The designedfrequency range therefore is 10–20 kHz.Figure 1 shows a block diagram of the coupler in use. Aloudspeaker followed by a small pad introduces signal intoport one. A matched load absorbs energy on port two. Ports 3and 4 also have matching loads but each also has a microphoneto sample the signal going into the side load.1It should be noted that while rectangular electromagnetic waveguides havea theoretical lower cutoff frequency, acoustic waveguides do not. For thisreason an acoustic waveguide will theoretically work all the way from DC tothe frequency at which multimoding is possible. In practice, the air-tightnesswill introduce a rolloff below some frequency. The upshot is that the operatingbandwidth has the potential to be larger than 1 octive.2ZLMic1 Mic2≈Z0≈Z0Fig. 1. “Block diagram of the acoustic hardware. Microphones sense thesound pressure level in the two side arms of the coupler. The source is a smallloudspeaker mounted behind an attenuating pad constructed of the same foamrubber used to make the loads” [3].Fig. 2. SolidWorks model for the acoustic directional coupler.In the SolidWorks model there are side-ports for the place-ment of MEMS (Micro-Electro-Mechanical Systems) micro-phones. The cross section view in Figure 2 also allows us tosee the internal geometry which is responsible for the direc-tionality of the coupler. The Block diagram shows loudspeakerand load placement.The ABS filament type MakeBot created a Coupler with anoticeable grain from its crosshatched layering process. Moreimportantly it also had collapsed portions in the waveguide.The collapsed portions left the surface finish damaged and thecollapsed plastic had to be cleared before experiments could bestarted. The Coupler is also slightly warped from the coolingof the layers of plastic which affects its overall dimensionalaccuracy. These defects can be seen in Figures 3, 4 and 5.Fig. 3. MakeBot coupler surface finish (Top) and collapsed plastic (BottomLeft).The Objet30 is printed with a support structure. The wantedstructure and removable support layers are printed alternatelyFig. 4. Another MakeBot coupler, cross section: Cut with a band saw, poorsurface finish can be seen on the roof of the coupler (upper half in the photo).Fig. 5. MakeBot coupler cross section: At this angle inacurracy in the internalgeometry can be seen, the most extreme left and right wave guide portionsare deformed and almost touching at points. The seperation should be 0.276mm or 276 microns.layer by layer. The support structure makes a significantdifference to the finish of the coupler as well as its dimensionalaccuracy. The support structure is removed with a dilutesodium hydroxide solution.III. MEASUREMENTSWe seek to measure the directionality of the coupler sam-ples. Referring to figure 1, we hope that signal originatingfrom the loudspeaker on port 1 will be mostly passed to port 2(top right-hand port in the figure) and there absorbed by theload ZL, if it is a good match to the characteristic impedanceZ0. A small proportion of the loudspeaker signal should becoupled to port 3 where it is sampled by Mic 2 and absorbedby the load in that arm of the coupler. If no signal is reflectedfrom the load on port 2, no signal should be detected on theisolated port, port 4, sampled by Mic 1. The directionality ofthe coupler, in this case, will be the ratio of signals at Mic 1to those at Mic 2. This directionality is ideally infinite. Inpractice we expect values in the range 10–40dB for realisabledesigns.The measurement of directionality depends upon the qualityof the loads used at ports 2–4. For example, if the load port,port 2, is terminated in a perfect reflection instead of a perfect3load, the directinality will disappear completely as the signalsin the two microponoes will ideally be the same. How thencan we know that our measurement is reasonably reliable,that is that the measurement of directionality has not beencompromised by non-ideality of the terminating loads? Wegauge the quality of the terminating load by sliding it alongthe guide. This has the effect of changing the phase of anyreflected component. As the phase changes, the magnitudesat the microphones are observed. If there is a significantcomponent changing phase, there will be a significant changein measured signal amplitude. We observe very little. Webelieve that our terminations, visible in figure 6, reflect below-20dB of incident signal, and often -40dB.In fact, we chose the material used as the loads by meansof this sliding load method from [3]. It was found that genericyellow earplugs worked relatively well.Fig. 6. Coupler experimental set up. Earplugs can be seen as the yellowfoam inserted at the ends. Microphones are sealed into the top of the couplerwith BlutackTMFor our experiments to measure directionality yellowearplugs were used as acoustic loads on three of the coupler’sfour ports. Measurements were made using an Agilent 33220Afunction generator into a Digitech stereo amplifier which pow-ered a small diaphragm transducer on the input of the coupler.Two MEMS microphones attached to the coupler were usedto detect the tone amplitude through a Tektronix TDS2014Coscilloscope. The MEMS microphones are powered at 3 Vfrom a bench power supply. The experimental set up can beseen in Figure 6. All measurements were done by hand. It ishoped that there will be automated measurements shortly.A. MakeBot Acoustic CouplerIn order to test the coupler we put a swept audio signal intoport one with a matched load on port two. Ideally we wouldsee a strong signal on the coupled port and a much smallersignal on the decoupled port. Figure 7 shows the result of themeasurement. The amplitudes in the MakeBot acoustic couplerwere measured as voltage signals from the microphones. Weare most interested in the ratio of the coupled to decoupledport signals, the directivity of the coupler. Directivity is plottedin figure 8. Directivity is expected to be better than 20 dBfrom 10 kHz to 20 kHz, falling away around 7.5 kHz and22.5 kHz. Directivity is excellent from below 10 kHz to at least15 kHz, but it appears as if the expected characteristic hasbeen shifted towards lower frequencies. The MakeBot couplerdemonstrated apparently excellent performance but not overthe expected frequency range. The directionality was betterthan 15 dB from 6 kHz to 15 kHz, but disappeared completelyat around 18 kHz. (The transducer prevented measurement atlower frequencies.) We attribute this unexpected performanceto the mechanical imperfections of the printing process, andwe believe the extended low-frequency performance is acoincidence upon which it will not be possible to rely.0.11101005 10 15 20 25Amplitude (mV)Frequency (kHz)Microphone Amplitudes (MakeBot)mic1 (mV) mic2 (mV)Fig. 7. The lower resolution print port amplitudes.0510152025305 10 15 20 25Directionaliy (dB) Frequency (kHz)Directionality (dB)  MakeBotFig. 8. The lower resolution print directionality.B. Objet30 Acoustic CouplerUsing the same method the amplitudes on the coupledand decoupled ports of the Objet30 coupler were measured.Directivity is again expected to be better than 20dB from 10to 20 kHz. Figures 9 shows the directionality for the Objet30Coupler. The Directivity for the Objet30 coupler is excellent4and extends outside the designed range. The Directivity ex-tends over a range of 7–22 kHz.We believe the low frequency extension below 7 kHz isunreliable as the signal is heavily attenuated, approaching thenoise floor. The Objet30 coupler behaves as expected and weattribute this to the increased resolution and accuracy of theprinter due to its support structure stopping any collapsingduring printing.05101520255 10 15 20 25Directionality (dB)Frequency (kHz)Directionality (dB) Objet30Fig. 9. Acoustic coupler directionality averages 15 dB over the expectedusable frequency range.IV. CONCLUSIONDirectivity for both printed couplers was expected to bebetter than 20dB from 10 to 20 kHz, falling away around7.5 kHz and 22.5 kHz. Both of the measured acoustic couplersdisplayed excellent directionality. However only the Objet30version behaved as expected with a range of 7–22 kHz. TheMakeBot coupler displayed its directivity over a lower fre-quency band, approximately 7–15 kHz.The altered characteristics of the MakeBot coupler webelieve can be attributed to the decreased resolution of theprinter and the absence of a support structure. The internalgeometry of the MakeBot coupler was inaccurate due to thelower resolution and absence of support structure. The absenceof a support structure caused the walls of the coupler tocollapse. These features and the damaged surface and excessplastic left in the waveguide of the coupler caused a changeto its behavior.The Objet30 coupler did not suffer any of these issues fromits construction and we attribute its performance to its superiorbuild quality.REFERENCES[1] P.A Rizzi, “Directional Couplers” in Microwave Engineering - PassiveCircuits. Englewood Cliffs NJ: Prentice-Hall Inc, 1988, 8, 3, pp 367 -369.[2] Lagasse, P., “Realisation of an acoustical directional coupler”, Journalof sound and vibration, 15(3), April 1971, pp367–372.[3] Scott, J. and K. E. Pennington, “Acoustic Vector-Corrected ImpedanceMeter”, IEEE Transactions on Instrumentation and Measurement, 2014.DOI: 10.1109/TIM.2014.2327474[4] Rytting, Doug, “ARFTG 50 year network analyzer history”, IEEE MTT-S International Microwave Symposium Digest, 2008, pp11–18.[5] ISO 10534-1:1996, “Acoustics—determination of sound absorption co-efficient and impedance in impedance tubes—Part 1: Method usingstanding wave ratio”.[6] ASTM Standard C384, 2004, “Standard test method for impedance andabsorption of acoustical materials by impedance tube method”.

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ARFTG 50 year network analyzer history”,

C384, 2004, “Standard test method for impedance and absorption of acoustical materials by impedance tube method”.

Directional Couplers” in Microwave Engineering - Passive Circuits. Englewood Cliffs NJ:

Realisation of an acoustical directional coupler”,

3D-printed Acoustic Directional Couplers

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