Lumped Speaker Boundary
The Lumped Speaker Boundary condition is used to model a loudspeaker (dust cap, cone, surround assembly, and motor) or another transducer using a lumped representation with a coupling to an Electrical Circuit interface. The condition is applied at the location of the speaker diaphragm (on a surface with the driver equivalent area). The mechanical and electric properties of the speaker can, for example, be described through the classical Thiele-Small parameters and associated lumped circuit. In general, any circuit representation can be set up in the Electrical Circuit interface and used.
The properties of a back volume can also be modeled using a lumped representation through either a simple equivalent acoustic compliance, a more general RCL circuit representation, or a user-defined impedance. On the other hand, if the air domains on both sides of the speaker are modeled explicitly (included in the model) then there are two possible setups:
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If the speaker diaphragm is represented by an interior boundary (a “shell” with air domains on both sides); then use the Interior Lumped Speaker Boundary condition.
2
If the speaker diaphragm is represented by a domain (a “solid” with air domains on both sides); then use two Lumped Speaker Boundary features, one applied to the upper side and one to the lower side. Make sure the speaker axis is the same on both sides and that the back volume correction is disabled (the No correction option). Finally, in the Electrical Circuit add two External I vs. U nodes in series, when setting up the coupling.
Note that the lumped representation of a speaker is an approximation that assumes piston motion. So in effect, it is a low frequency approximation that does, for example, not model breakup of the membrane. The method is efficient to get fast results in early development phases, for testing several driver configurations, or to use as a validation guide of full multiphysics driver models.
The approach is typically also valid in a larger frequency range when modeling tweeters and especially microtransducers. For the latter application, the Lumped Speaker Boundary also exists for The Thermoviscous Acoustics, Frequency Domain Interface. For time domain simulations see the Lumped Speaker Boundary for the The Pressure Acoustics, Transient Interface.
Speaker Geometry
Define how the Speaker area (projected) of the speaker is computed by selecting either Selected boundaries (the default) if all boundaries are present, or Use symmetries if the speaker surface is only partially represented.
When Use symmetries is selected, select the Speaker area multiplication factor Ascale as Automatic (the default, the model is analyzed for the presence of symmetry conditions); or User defined and enter a value (default is 1). The settings are required in order to compute the effective area of the speaker which is used to compute the acoustic load and radiated power.
Define the Speaker axis direction eax by selecting Automatic (the default) or User defined. For the automatic option, the axis is computed as the average of the surface normals; this option is valid if a full speaker surface is selected. The User defined option should be used if the speaker surface is only partially represented and is the only option when Use symmetries is selected.
Back Volume Correction
The Lumped Speaker Boundary does not model the acoustics on the back side of the speaker cone explicitly. The properties can be entered either through a volume giving a simple compliance effect, through an RCL circuit, or through a user defined acoustic impedance of the back volume.
Select the Acoustic impedance of the back volume as Volume compliance (the default), RCL, User defined, or No correction.
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For Volume compliance, enter the Volume Vback (SI unit: m3), this results in an equivalent acoustic compliance Cac = Vback/(ρc2).
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For RCL, the back volume impedance is represented by a serial RCL circuit. Enter the Equivalent acoustic resistance Rac (SI unit: kg/(m4·s)), the Equivalent acoustic compliance Cac (SI unit: (m4·s2)/kg), and the Equivalent acoustic inertance Lac (SI unit: kg/m4).
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For User defined, enter an Acoustic impedance Zac (SI unit: kg/(m4·s))
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For No correction, the correction impedance is 0.
Circuit
This section gives information about the state of coupling/connection to an Electrical Circuit interface. If the Interior Lumped Speaker Boundary is not connected, the text Connect to ‘External I vs. U’ in the Electrical Circuit interface text will be displayed. Once connected, a reference with a tag to the associated External I vs. U node, in the Electrical Circuit interface, is displayed.