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 mechanical and electric properties of the speaker can, for example, be described through a Thiele-Small parameter representation and associated lumped parameters.
In the time domain, nonlinear effects can be included in the lumped model through parameters that depend on the axial position x or velocity v of the speaker. These are, for example, the typically measured BL(x), CMS(x), or RMS(v). Predefined variables exist for the axial velocity actd.lsb1.v_ax and an ODE is solved for the associated axial position actd.lsb1.x_ax (use the appropriate physics and feature tag). These variables can be directly used in expressions in the electric components in the Electrical Circuit model as they are globally defined.
The properties of a back volume can also be modeled using a lumped representation through either a simple equivalent acoustic compliance or a more general RCL circuit representation. 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:
1
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.
For microtransducer applications it may be necessary to use the Lumped Speaker Boundary or Interior Lumped Speaker Boundary of The Thermoviscous Acoustics, Transient Interface.
Lumped Loudspeaker Driver Transient Analysis with Nonlinear Large-Signal Parameters: Application Library path Acoustics_Module/Electroacoustic_Transducers/lumped_loudspeaker_driver_transient
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 a simple RCL model, 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, or No correction.
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For the Volume compliance enter a Volume Vback (SI unit: m3). The volume represents an acoustic compliance Vback/(ρc2).
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For RCL enter the values of the equivalent acoustic resistance Rac (SI unit: kg/(m4·s)), compliance Cac (SI unit: m4·s2/kg), and inertance Lac (SI unit: kg/m4).
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For No correction, the correction impedance is 0.
When the RCL and the Volume compliance options are selected an ODE is solved relating force acting on the cone Fc and axial velocity vax. For the general RCL option
where SD is the (projected) speaker area.
Initial Value
Enter the initial value of the force Fc and axial speaker position xax, used when solving the associated ODEs. The default value is 0 for both and is typically correct, except if the simulation is started, for example, with an initial excursion of the driver.
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.