Defining the Condenser Microphone System - …



Hed: COMSOL Simulation Holds an Open Mic on Microphone DesignDek: Tips and tricks for dealing with the thermal viscous boundary layer in mic design.01907540A Brüel and Kj?r 4134 condenser microphone undergoing a coupled simulation. The coupled simulations include a thermal viscous model, membrane mechanics and electrostatics. (Image courtesy of COMSOL).A Brüel and Kj?r 4134 condenser microphone undergoing a coupled simulation. The coupled simulations include a thermal viscous model, membrane mechanics and electrostatics. (Image courtesy of COMSOL).02540Microphones are a wonderfully interesting technology from a computer-aided engineering (CAE) and simulation standpoint. These acoustic systems are the definition of multiphysics. One condenser (capacitor) microphones (mics) culminates the use of computational fluid dynamics (CFD), mechanics and electronics all within one itty-bitty system.In fact, when a microphone’s system becomes small enough, as is the case with condenser mics, the physics involves becomes even more complicated. This is because at a small enough scale, the boundary layer of the geometry interferes with the audio signal. This becomes especially prevalent during resonance. To model condenser microphones properly, these energy losses need to be considered.“When most engineers study acoustics they don’t include the thin layer at the wall,” explained Mads J. Herring Jensen, technical product manager at COMSOL. “Normally in room acoustics and loud speakers all these affects can be completely disregarded. But, for microphones you need the correct simulations.”Defining the Condenser Microphone SystemLearning the mechanics behind condenser microphones makes one wonder if MacGyver invented it. The system contains a membrane and backplate that make up a capacitor. The membrane, or diaphragm, vibrates in response to the pressure differentials caused by the sound waves. This vibration is then picked up as change in capacitance which creates an electrical signal.Setting up the thermal viscous acoustic model within a condenser microphone geometry. (Image courtesy of COMSOL.)“The acoustics signal comes form the outside world and then that vibrate the diaphragm. The movements of the diaphragm is measured and that tells you the electrical signal of the sound. The movement of the diaphragm is influenced by the acoustic behaviour inside of the microphone,” explained Jensen.He adder, “In the old days, when you designed these microphones you were working with lumped equivalent circuit models. You would model each part of the microphone separately. This has a lot of restrictions with respect to the precision. This is especially true for complex geometries where these representations are no longer valid. Then need to go to the FEA.”Defining the system takes knowledge of CFD, mechanics and electronics. To control and define the system correctly you need to also take into consideration the geometry of the microphone and how it will affect the thermos viscous layer that weaken and interferes with the signal. “The mathematics behind the thermos viscous layer is nasty,” noted Valerio Marra, marketing director at COMSOL. “We coded it so people don’t worry about it. Before it was crazy for customers to do this and make the model converge.”Tips for Simulating the Thermal Viscous Boundary Layer for Condenser MicrophonesJust like any multiphysics problem the best course of action is to model each physics separately. Going through the model one physics at a time will help to error check the simulation.For COMSOL users, Jensen suggests they use the membrane interface to model the diaphragm and the thermal viscous interface within the microphone’s chamber. As for the microphone’s electronics, that should be left to the electrostatics interface.Once all the boundary conditions are set up and each physics is working you can then use the built in multiphysics coupling within COMSOL to complete the model.“This is easy to set up, just define the boundary conditions as being coupled and the software does it. This becomes a fully two-way multiphysics system,” said Jensen. “Coupling of partial differential equations is a key feature of COMSOL.”Engineers should note that all of the multiphysics simulations involved in the thermal viscous model will make the simulation very computational expensive. To limit the amount of time your high-performance computing (HPC) system is crunching numbers, limit the thermal viscous model type to thin regions where it is valid. Simplified models, like a pressure acoustic simulation, can be used in the bulk to speed things up.01905Viscous and thermal boundary lager thickness based on a sound signal’s frequency. The boundary layer is inversely proportional to the square root of the analysis frequency. (image courtesy of COMSOL). Viscous and thermal boundary lager thickness based on a sound signal’s frequency. The boundary layer is inversely proportional to the square root of the analysis frequency. (image courtesy of COMSOL). Engineers should also ensure they have enough elements to properly define the boundary layer region but not so many that it bogs down the solution time once again. This will take some tight control of meshing parameters. Jensen suggests using an frequency sweep to determine the parameter that define the boundary layer thickness. As seen in figure 1, “The thermal viscous boundary layer is about 0.2 mm at 100 Hz and is inversely proportional to the square root of the frequency,” said Jensen This relationship can be used to limit the thickness of the boundary layer in the mesh.For instance, if the user defines a set number of mesh element for the boundary layer then they will not see a large influx of elements within the mesh.“You will lose time with each parameter sweep as you will need to remesh the model with every parameter change,” said Jensen. “However, the more optimized mesh should save time in the long run.”Though the thickness of the boundary layer changes the number of elements remains the same. This will ensure the model remains accurate but doesn’t create a runaway mesh density. Engineers don’t live forever and computations need to end. Color in the image represents the root mean square velocity of a wavelength in an infinite circular duct of a diameter of 2mm [0.08 inch] (Image courtesy of COMSOL.)A final tip to speed up these simulations is to use a Narrow Region Acoustics model. Due to accuracy issues, this is only advised for engineers working during the early development stages of a microphone’s design. However, Jensen explains that the Narrow Region Acoustics model’s ability to homogenize the fluid model and “smear” the boundary layer meshes over the whole fluid domain is useful and for early development estimations.Build Your Own Simulation App for Microphone Designleft6985This simulation couples a thermal viscous acoustic model with an exterior pressure acoustics model. The thermal acoustic model simulates the acoustics in the small domain between the diaphragm and back plate. The pressure acoustics models the pressure field in the exterior domain. (Image courtesy of COMSOL.)0This simulation couples a thermal viscous acoustic model with an exterior pressure acoustics model. The thermal acoustic model simulates the acoustics in the small domain between the diaphragm and back plate. The pressure acoustics models the pressure field in the exterior domain. (Image courtesy of COMSOL.)Once you have your condenser microphone’s interior simulated, the next logical step is to link the simulation into the bulk. This will scale up the model and offer more information about the design.Jensen notes that the pressure acoustics model can be used to model the bulk environment around the mic. Coupling this acoustic model to your thermal viscous acoustic model can then help engineers determine the mic’s sensitivity.The information created by this larger scaled simulation can be helpful to ore than just design engineers. For instance, sound technicians can use it when setting up the audio in a sound studio.“You can make an app for design and include all the complexity of the mic so that app users can determine the sensitivity curve and internal workings of the device,” said Jensen. “You can also have the app set up ways to mount the mic say, flush on a table or hanging from a boom. These can affect the special sensitivity.”This tool can also be helpful to your microphone resellers so they can guarantee their customers that they will receive the correct equipment to do the job. These apps can go a long way in pushing your customer’s and reseller’s user experience. Once you have the model created anyway, you might want to look into this extra work.To learn more about thermal viscous boundary layers, try reading COMSOL NEWS’ special edition on Acoustics. ................
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