COMSOL 6.4 - Lumped Receiver Connected to Test Setup with a 0.4-cc Coupler

Lumped Receiver Connected to Test Setup with a 0.4-cc Coupler

When simulations are involved in the development of mobile devices, consumer electronics, hearing aids, or headsets, it is necessary to consider how the transducers interact with the rest of the system. For some tasks, such as analyzing the vibration isolation of an elastic mounting of the transducer, it may be necessary to include a fully detailed multiphysics model of the transducer itself. In applications where only the electroacoustic response of the device is of interest, a lumped parameter model of the transducer (an electroacoustic analogy as would be implemented in Spice) can be coupled with a multiphysics model of the rest of the system.

In this example a Knowles ED-23146 balanced armature receiver (miniature loudspeaker) is connected to a test setup consisting of a 50 mm (1 mm ID) tube into a generic 0.4-cc measurement coupler.¹ This test setup represents the receiver in a behind-the-ear hearing aid driving an ear canal with a deeply inserted ear mold via a long narrow tube. Data collected when using the 0.4-cc coupler will give a more realistic assessment of acoustic data for deeply inserted devices compared to using the 711 coupler (see Ref. 1). The model shows how to connect a receiver modeled as a lumped Spice network to the acoustic system of the tube and a measurement coupler modeled in the finite element domain. The response at the measurement microphone in the coupler as well as the electric input impedance to the receiver are compared with measurements. The losses in the long narrow tube are in this model included using one of the equivalent fluid models of the Narrow Region Acoustics feature in the Pressure Acoustics, Frequency Domain interface.

Model Definition

A sketch of the measurement set-up analyzed in this model is depicted in Figure 1. It consists of the Knowles ED-23146 receiver which is modeled as an electric Spice circuit using the Electrical Circuit interface. The tube has a length of 50 mm and a diameter of 1 mm and the 0.4-cc coupler is here simply represented by a cylinder with a volume close to 0.4 cm3 (and a small intrusion at one end representing the microphone location). Real measurement couplers have more complex geometries. The acoustics inside the tube and the coupler are modeled using the Pressure Acoustics, Frequency Domain interface.

Figure 1: Schematic representation of the modeled system consisting of receiver, tube, coupler, and measurement microphone. The blue domains are modeled using finite elements.

The actual receiver is depicted in Figure 2. It is of the balanced armature type. Knowles provides lumped models for all their transducers enabling engineers to model the devices where they are used.

Figure 2: Rendering of the Knowles ED-23146 balanced armature receiver. The device is roughly 4 mm wide, 6 mm deep, and 3 mm high. Image credit: Knowles, IL, USA.

In the Spice network used for the Knowles ED-23146 receiver, the current at the output corresponds to a volume flow (m3/s) and voltage over the output terminals corresponds to the pressure (Pa), as measured at the outlet of the transducer. See Ref. 2 and Ref. 3 for further details. The coupling between the lumped electric network and the finite element domain is made using the built-in connection option in the feature. In this way, there is a bidirectional coupling between the finite element domain and the Spice network.

At the boundary where the measurement microphone is normally located in the coupler, a normal impedance condition has been added to account for the compliance of the microphone diaphragm. In this model, the compliance Cmic is equivalent to a volume of 6 mm3. The acoustic mass Lmic and resistance Rmic of the diaphragm are set to typical values. The impedance is given by a simple RCL model

(1)

This is implemented by applying the built-in RCL option found in the impedance boundary condition.

Results and Discussion

The response, as measured at the location of the microphone, is depicted in Figure 3. The model results are compared with measurements performed on an actual system and with results obtained without the viscous and thermal acoustics losses. The measurements are seen to agree well with the full model results. At high frequencies (above 14 kHz), the results start not to match well. Here, the wavelength becomes comparable to length scales of structures in the coupler (a quarter wavelength is 0.6 cm) that are not included in this simple cylinder representation, for example, the protective mesh of the microphone. In addition, of course, the lumped parameter model of the receiver is inexact at these high frequencies. Note that the model curves where no acoustic losses are added still show signs of damping. This is due to the losses included in the Spice model of the transducer.

Figure 3: The microphone response comparing the model including the thermal and viscous losses via the narrow region acoustics feature (blue curve), the model without acoustics losses (red dotted curve), and measurements (green curve). Measurement data provided by Knowles, IL, USA.

The frequency dependency of the electric input impedance (real and imaginary part) of the transducer are depicted in Figure 4. The results are compared with measurements and show good agreement.

Figure 4: The electric input impedance (real and imaginary part) as a function of the frequency comparing model results (blue and green curves) and measurements (red and cyan curves). Measurements data provided by Knowles, IL, USA.

In Figure 5 and Figure 6, the pressure and sound pressure level distribution inside the tube and coupler system are depicted at three different frequencies (around 1200, 3200, and 4600 Hz). The evaluated frequencies correspond to the three first peaks in the response. They correspond to the quarter, half, and three quarter wave resonances of the tube-coupler system, respectively.

Figure 5: Pressure distribution (real part of the pressure) at frequencies close to f = 1200, 3200, and 4600 Hz.

Figure 6: Sound pressure level at frequencies close to f = 1200, 3200, and 4600 Hz.

Notes About the COMSOL Implementation

•

In this model, the viscous and thermal losses associated with the acoustic boundary layer in the narrow tube are modeled using the Narrow Region Acoustics feature in Pressure acoustics. For long structures of constant cross section, the losses are exact when compared to a full thermoviscous acoustic model. The computational cost is low compared to the full thermoviscous model. However, for complex geometrical structures the Thermoviscous Acoustics physics interfaces should be used. Note also that the losses associated with the impedance jump from the narrow tube to the coupler are not modeled correctly with Narrow Region Acoustics. This effect is small when compared to the losses in the long tube.

•

The Electrical Circuit interface uses electrical units. Conversion from electrical to acoustic lumped units are performed automatically in the Lumped port feature with the necessary units. For example, a voltage representing the acoustic pressure at the transducer inlet is transformed to volts, resulting in correct equivalent electric units volts.

•

In the lumped Spice model of the receiver, the effects of variation in the skin depth of eddy currents in the steel armature is approximated by a semi-capacitor, a special component with a complex admittance proportional to the square root of iω. In the imported Spice net-list, the value of this component, here a resistor, is temporarily set to 1, using:

RKarm N0025 N0015 1

Then the correct value for this component is entered manually, as a formula, to fit the COMSOL notation:

1/(4.85e-11[1/ohm]*sqrt(i*2*pi*freq[1/Hz]))

The component is, in the unmodified Knowles Spice net-lists, included as an advanced voltage-controlled current source as:

GKarm N0025 N0015 laplace {V(N0025,N0015)}={4.85e-11*sqrt(s)}

This notation is not supported by the Spice import functionality of COMSOL.

References

1. Generic 711 Coupler: An Occluded Ear-Canal Simulator model in the Application Library of the Acoustics Module: Acoustics_Module/Electroacoustic_Transducers/generic_711_coupler.

2. J. Jensen, F.T. Agerkvist and J.M. Hart, “Nonlinear Time-Domain Modeling of Balanced Armature Receivers,” J. Audio Eng. Soc., vol. 59, pp. 91–101, 2011.

3. Lumped Loudspeaker Driver model in the Application Library of the Acoustics Module: Acoustics_Module/Electroacoustic_Transducers/lumped_loudspeaker_driver.

Acoustics_Module/Electroacoustic_Transducers/lumped_receiver_04cc

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > .

Click .

In the tree, select > > .

Click .

Click

In the tree, select > .

Click

Root

First, import the model parameters, import variables used in the model, and import the geometry. The instructions to the geometry can be found in the appendix at the end of this document.

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file lumped_receiver_04cc_parameters.txt.

Geometry 1

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file lumped_receiver_04cc_geom_sequence.mph.

Definitions

Integration 1 (intop1)

In the toolbar, click

and choose .

In the window for , type intop_mic in the text field.

Locate the section. From the list, choose .

Select Boundary 7 only.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Right-click and choose .

In the toolbar, click

to close the window.

Now, set up the circuit model. It includes the driving voltage source, the subcircuit for the receiver (imported), and the coupling node to the acoustic domain.

Electrical Circuit (cir)

Subcircuit Definition ED23146 (ED23146)

In the window, under right-click and choose .

Browse to the model’s Application Libraries folder and double-click the file lumped_receiver_04cc_ED23146.cir.

In the window for , locate the section.

In the table, enter the following settings:


Node names
P1
N1
P2
N2

The component RKARM needs special attention by manual editing as it is a nontrivial function of frequency. The imported Spice net-list is courtesy of Knowles, IL, USA.

Resistor RKARM (RKARM)

In the window, expand the node, then click .

In the window for , locate the section.

In the R text field, type 1/(4.85e-11[1/ohm]*sqrt(i*2*pi*freq[1/Hz])).

Voltage Source 1 (V1)

In the toolbar, click

In the window for , locate the section.

In the table, enter the following settings:


Label	Node names
p	p1
n	0

Locate the section. In the vsrc text field, type V0.

Subcircuit Instance 1 (X1)

In the toolbar, click

In the window for , locate the section.

From the list, choose .

In the table, enter the following settings:


Local node names	Node names
P1	p1
N1	0
P2	p2
N2	0

External I vs. U 1 (IvsU1)

In the toolbar, click

Set up the external source that couples to the feature. You will need to get back to this feature after setting up the port.

In the window for , locate the section.

In the table, enter the following settings:


Label	Node names
p	p2
n	0

The electrical circuit has now been set up. Proceed and set up the pressure acoustics physics.

Global Definitions

Interpolation 1 (int1)

In the toolbar, click

and choose > .

In the window for , locate the section.

From the list, choose .

Click

Browse to the model’s Application Libraries folder and double-click the file lumped_receiver_04cc_measured_data.txt.

Locate the section. In the table, enter the following settings:


Columns	Type	Settings
Re(VoltageSensitivity)	Function values	Function name=int1a
Im(VoltageSensitivity)	Function values	Function name=int1b
Re(InputImpedance)	Function values	Function name=int1
Im(InputImpedance)	Function values	Function name=int1c

In the table, click to select the cell at row number 1 and column number 1.

In the text field, type Hz.

In the table, click to select the cell at row number 2 and column number 1.

In the text field, type preal.

In the text field, type [Omega].

In the table, click to select the cell at row number 3 and column number 1.

In the text field, type pimag.

In the text field, type [Omega].

In the table, click to select the cell at row number 4 and column number 1.

In the text field, type Zreal.

In the text field, type [Omega].

In the table, click to select the cell at row number 5 and column number 1.

In the text field, type Zimag.

In the text field, type [Omega].

Locate the section. From the list, choose .

Locate the section. Click

Pressure Acoustics, Frequency Domain (acpr)

Pressure Acoustics 1

In the window, under > click .

In the window for , locate the section.

In the T text field, type T0.

In the pA text field, type p0.

Narrow Region Acoustics 1

In the toolbar, click

and choose .

Select Domain 2 only.

In the window for , locate the section.

In the T text field, type T0.

In the pA text field, type p0.

Locate the section. From the list, choose .

In the a text field, type a.

Narrow Region Acoustics 2

In the toolbar, click

and choose .

Select Domain 1 only.

In the window for , locate the section.

In the T text field, type T0.

In the pA text field, type p0.

Locate the section. From the list, choose .

In the a text field, type a_cpl.

Impedance 1

In the toolbar, click

and choose .

Select Boundary 7 only.

In the window for , locate the section.

From the list, choose .

In the Rac text field, type Rmic.

In the Cac text field, type Cmic.

In the Lac text field, type Lmic.

Lumped Port 1

In the toolbar, click

and choose .

The has built-in functionality that couples the port boundary to the Electrical Circuit physics.

Select Boundary 10 only.

In the window for , locate the section.

From the list, choose .

Now, finalize the coupling between the port and the circuit.

Electrical Circuit (cir)

External I vs. U 1 (IvsU1)

In the window, under > click .

In the window for , locate the section.

From the V list, choose .

Now, mesh the geometry and then solve the model.

Mesh 1

Free Triangular 1

In the toolbar, click

and choose .

Select Boundaries 3 and 11 only.

Size

In the window, click .

In the window for , locate the section.

Click the button.

Locate the section. In the text field, type 3*a.

In the text field, type 0.1[mm].

Size 1

In the window, right-click and choose .

In the window for , locate the section.

Click

Select Boundary 11 only.

Locate the section. Click the button.

Locate the section.

Select the checkbox. In the associated text field, type a.

Click

Swept 1

In the toolbar, click

In the window for , locate the section.

From the list, choose .

Select Domain 2 only.

Distribution 1

Right-click and choose .

In the window for , locate the section.

In the text field, type 15.

Click

Free Tetrahedral 1

In the toolbar, click

In the window for , click

Solve the model. First, solve the full model including the equivalent acoustic loss model. Secondly, solve the model without the losses. Do this by deactivating the Narrow Region Acoustics domain features in the second study.

Study 1 - Narrow Region

In the window, click .

In the window for , type Study 1 - Narrow Region in the text field.

Locate the section. Clear the checkbox.

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type 10^{range(2,2.2/199,4.2)}.

In the toolbar, click

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Study 2 - Lossless Acoustics

In the window for , type Study 2 - Lossless Acoustics in the text field.

Locate the section. Clear the checkbox.

In the window, under click .

In the window for , locate the section.

In the text field, type 10^{range(2,2.2/199,4.2)}.

Locate the section. Select the checkbox.

In the tree, select > > .

Click

In the tree, select > > .

Click

In the toolbar, click

Results

Microphone Response

In the window, expand the node.

Right-click and choose .

In the window for , type Microphone Response in the text field.

Click to expand the section. From the list, choose .

In the text area, type Coupler Response (50mm/1mmØ tube on 0.4cc coupler).

Locate the section.

Select the checkbox. In the associated text field, type Level (dB rel. 1V).

Locate the section. From the list, choose .

Global 1

Right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Expression	Unit	Description
20*log10(abs(intop_mic(p)/intop_mic(1))/V0)		Full model
20log10(abs(preal(freq)+ipimag(freq)))		Knowles measurements

Global 2

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the table, enter the following settings:


Expression	Unit	Description
20*log10(abs(intop_mic(p)/intop_mic(1))/V0)		Model without acoustic losses

In the toolbar, click

Click to expand the section. Find the subsection. From the list, choose .

Click the

button in the toolbar.

The modeled and measured microphone response are depicted in Figure 3.

Electric Input Impedance

In the toolbar, click

In the window for , type Electric Input Impedance in the text field.

Locate the section. From the list, choose .

Locate the section.

Select the checkbox. In the associated text field, type Z_in (Ohm).

Click to collapse the section. Click to expand the section. From the list, choose .

Global 1

Right-click and choose .

In the window for , locate the section.

In the table, enter the following settings:


Expression	Unit	Description
real(-cir.V1.v/cir.V1.i)	Ω	real(Zin): Model results
imag(-cir.V1.v/cir.V1.i)	Ω	imag(Zin): Model results
Zreal(freq)		real(Zin): Knowles measurements
Zimag(freq)		imag(Zin): Knowles measurements