use of a personal computer to model the electroacoustics of hearing aids

Use of a personal computer to model the electroacoustics of hearing aids

Priscilla F. Bade, A. Maynard Engebretson, Arnold F. Heidbreder, and Arthur F. Niemoeller

Central Institute for the Deaf 818 $. Euclid•4venue, St. Louis, Missouri 63110

(Received 16 September 1983; accepted for publication 3 November 1983)

The electro-acoustic behavior of a heating aid receiver in an acoustic system similar to that found in many heating aids was predicted by the method described by Egolf [D. P. Egolf and R. G. Leonard, "Experimental scheme for analyzing the dynamic behavior of electro-acoustic transducers," J. Acoust. Soc. Am. 62, 1013-1023 { 1977}] using an inexpensive desktop computer.

PACS numbers: 43.88.Si, 43.66.Ts, 43.85.Ta

LIST OF SYMBOLS

a

c

D

E

i

I

1

P

SPL

U

radius of tube (cm) four-pole parameter (V cm2/dyn) four-pole parameter (V s/cm 3} sonic velocity (cm/s} four-pole parameter (A cm2/dyn} four-pole parameter {A s/cm 3} complex voltage amplitude (V}

complex current •mplitude (A} Bessel function of the first kind of order 0 {dimensionless} Bessel function of the first kind of order 1 (dimensionless} length of tube {cm} complex sound-pressure amplitude (dyn/cm 2} sound-pressure level (dB re: 0.0002 pbar} complex volume velocity amplitude (cma/s}

Z impedance of a particular element, electrical {/2 } or acoustic {dyn s/cm 5}

a complex term (1/cm} /• complex term (1/cm) y ratio of specific heats of fluid medium, Cp/C•, {di-

mensionless) F propagation operator { 1/cm) p absolute viscosity of fluid medium { g/cm -- s) co radian frequency {rad/s} /2 ohms

p density of fluid medium { g/cm 3} cr Prandtl number of fluid medium (dimensionless)

Subscripts i pertaining to input terminals L pertaining to load n pertaining to tube n o pertaining to output terminals R pertaining to receiver

INTRODUCTION

The mathematical modeling of acoustical systems is, in general, a difficult task. The exact solution to the acoustic wave equation is complicatedand often must be simplified in practical applications. A common simplification is to as- sume a frictionless medium. In this case, the acoustic input impedance of a closed cavity takes the simple form

Z = -- (ipc/•ra•n) cot(co//c). (1)

Beranek • used this approximation and others to produc•l

simplified models of acoustic circuits. Egolf has pointed out that the physical dimensions of the tubing and passageways used in hearing aids are small and therefore a better approximation is obtained by using more exact equations that were developed by Iberall: for applications involving transient fluid flow in pipes. For this case the acoustic input impedance of a closed cavity is

Z= Z n coth(Fnln}, {2}

where

pc

•a n JrO( t•a n )

and

Fn= ico (l + 2(y-1)[J•(Ctan)/CtanJø{Ctan)],) 1/: c 1 -- 2• 1 •an )//•an JoVan ) '

where

Cg = { -- ico po'/p}l/2cm -1 ,

CtanJo(Ctan } !

(3)

and

(4) • = {-- ico p/•}l/2cm-l.

One can see that Eq. {2) reduces to Eq. {1) if the viscosity of the fluid medium is small. An example of the difference between these two approximations is shown in Fig. 1 for a system consisting of a constant pressure source, a plastic tube, a test cavity, and a microphone.

617 J. Acoust. Sec. Am. 75 (2), February 1984 0001-4966/84/020617-04500.80 ¸ 1984 Acoustical Society of America 617

Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 130.209.6.50 On: Sat, 20 Dec 2014 13:43:10

Egolf implemented the more complicated equations to obtain more accurate predictions of the complex sound pressure level in a hearing aid system. The hearing aid system is modeled as a series of coaxial cylindrical sections in which plane-wave propagation of sound is assumed. Transmission through each cylindrical section is defined by Eq. (5).

U, = Cn Dn X Uo ' where

A. = cosh(F. 1. ),

B. = Z. sinh{F. 1. },

C2 D2 . C• D• C.

where the R subscripted parameters refer to the receiver, the numeric subscripted parameters refer tO the acoustic sections, and ZL is the acoustic load at the output of the hearing aid system. By assuming Pi = 1/_0' and calculating Ei, the ratio Pi/Ei represents the sound pressure at the load for 1-V rms at zero phase into the receiver. This ratio times the actual input voltage is the sound pressure for arbitrary input voltages. This procedure is applied for each test frequency.

Egolf's method for determining the receiver transfer function requires the measurement of the current and voltage at the receiver input and the resulting sound pressure level in a test cavity for two conditions of acoustic loading. His measurements were made automatically with a mea-

(a) 20 180.• 0 90• , 102 . 103

-20 0 u) -90 -40 LU

• -180 ß ß

= •d• •o3 ,o• "'

• FREQUENCY, Hz u• FREQUENCY, Hz

u) 20 u) 180 t (b)• < u• 0 90

1:•20 O 10• k• .iO• 4 t . . -90

-->-40

< -180

m 10 2 10 3 104• FREQUENCY, Hz

(c) 2O

-20

-40

10 2 10 3 10 4

FIG. 1. Sound pressure level at microphone in system composed of a constant-pressure sound source, plastic tube (radius = 0.08 cm, length = 6.25 cm), 2-cc test cavity (radius = 0.926 cm, length = 0.7 cm), and B&K 4132 microphone. (a) As predicted using approximations given by Beranek. (b) As predicted using Egolf's formulas. (c) Measured SPL (magnitude only). Note high frequency resonances.

Cn __- Zn --1 sinh(F n/.),

Dn ---- cosh(-/"•n ]n), (6)

and Pi, Ui and Pc, Uo are the pressure and velocity at each end of the cylindrical section of length 1,. Z, and F• are defined by Eqs. (3} and (4). The acoustical transmission matrix of each section is dependent only on the cross-sectional area and length of each section and the physical properties of the fluid, in this case, air. If the electro-acoustic transmission matrix is known for the heating aid receiver, it is then possi- ble to calculate an overall transmission matrix for the hear-

ing aid system under study. The problem is reduced to the evaluation of the matrix expression

Dn X PL /ZL ' (7)

surement system that included a computer and a fast Fourier transform analyzer. In a modification of his technique, we used a small personal computer and a simpler system to obtain similar results. Such a system is often available in a small acoustics laboratory or hearing clinic. The programs were written in an enhanced version of BASIC, which is a common programming language of small computers.

I. METHOD AND RESULTS

To model a hearing aid system, it is sufficient to know the four-pole transfer parameters of the hearing aid receiver and the inside diameters and lengths of the tubes and passageways comprising the acoustic transmission path. The receiver parameters were determined using the apparatus shown in Fig. 2. A computer program was used to control the function generator, filter, and rms voltmeter. It also stored the experimental data for the two loads needed for Egolf's method.

(•)ref V

t•)SPLL

TO KYBD

TO IARD

FIG. 2. Schematic of experimental setup used to measure complex voltage, current, and SPL,• for determining system transfer functions using a Knowles BK- 1604 hearing-aid receiver. Key to numbers: (1) HP-85 personal computer, (2) Fluke 1120A IEEE-488 translator, (3) HP 3325A synthesiz- er/function generator, (4) power supply for receiver, (5) Knowles BK-1604 receiver, (6) load I (2-cc cavity) or load II (10-cm stainless steel tube and 2-cc cavity), (7) B&K 4132 microphone and cathode follower, {8)B&K 2112 audio frequency spectrometer, (9) Rockland 751A brickwall filter, (10) Fluke 8922A true rms voltmeter, ( 11} Krohn-Hite KH 6200 phase meter.

618 J. Acoust. Soc. Am., Vol. 75, No. 2, February 1984 Bade et al.' Use of a computer to model hearing aids 618


The magnitude and phase of(1) the receiver input voltage, (2} the voltage across a 10-a9 resistor placed in the re- turn path (ground} of the receiver, and (3} the sound pressure in a test cavity were measured for selected frequencies from 100-6000 Hz. The function generator and voltmeter were connected to the computer via an IEEE-488 interface so that frequency was controlled by the computer and voltages were read directly by the computer. Oth•r measurements such as phase and sound pressure were read by the operator and entered into the computer via keyboard under prompting by the computer program.

The four-pole parameters of the complete acoustic path (the lead matrices} at each of the test frequencies were calcu- lated for the two different loading conditions by another program and stored on tape. A third program used the experimental data and the stored lead matrices to compute the four-pole parameters of the receiver. Our results, shown in Fig. 3, are very much like Egolf's. 3

2'

• 1 E

E 0

; -1

-2

0.5.

0

-0.5-

•1•: _ 1.0 ' -1.5.

E 1.0

'" 0.5 E < 0

,- -1.0'

'• - 1.5,

E

10 3 10 4

FREQUENCY, Hz

60-

• 40 • 20

,

• -20

ß • -40

• -60

A R

ß (•4 n: E

-5-

FREQUENCY, Hz

BR

10.

-10 FREQUENCY, Hz FREQUENCY, Hz

,• lO

10 3 . 4

04 • _ -10

CR D R

FIG. 3. Four-pole parameters of BK 1604 receiver.

signal

lO

•

FIG. 4. Earhook and earmold lead used to predict sound pressure levelß Key to numbers: (1) B&K 4132 microphone and cathode follower, (2) B&K 2-cc cavity, (3) earmold-to-cavity adapter, (4) sealing compound, (5) earmold, (6) # 13 earmold tubing, (7) plastic earhook, (8) case-to-earhook adapter, (9) plastic tubing (from receiver port to end of case-to-earhook adapter), (10) Knowles BK-1604 receiver, (11) shrimp aid case.

To predict the sound pressure in a typical hearing aid system, shown in Fig. 4, a new matrix for the combination of the tubes and test cavity was computed for each frequency.

ß Then the input voltage to the receiver, along with the sound pressure level at the microphone, was measured with the same apparatus used for the two-load method. Finally the load matrices, receiver parameters, and input voltage were utilized by a computer program to produce a prediction of output sound pressure level. Results are shown in Fig. 5.

The predicted values of SPL are within about 5 dB of the actual measurements from 100-6000 Hz. Phase also

compares quite closely except immediately around tube resonances.

One problem with this particular implementation is the tedium of making numerous measurements. Moreover, the programs for computing the load matrices require a consid- erable amount of time to run, since the computer we used performs only about 620 multiplications/s. To compute the

(b) FREQUENCY, kHz 120

6O

I t t I i i I 2 3 4 5

(C) FREQUENCY, kHz

= 10

• ..1 2. 3 4 .5 u.I -1

-20 a.

FREQUENCY, kHz

18øT

-90 -180

FREQUENCY, kHz

FIG. 5.(a) Measured SPLL for lead in Fig. 4.(b) Predicted SPLL. (c) Error in predicted SPL• (measured SPL•--predicted SPL•).

619 J. Acoust. Sec. Am., Vol. 75, No. 2, February 1984 Bade et al.' Use of a computer to model hearing aids 619


matrices for the loads used to find the receiver parameters requires about 40 min for 60 test frequencies, while measurements of voltage, current, and SPL take 2 h. Once these data are stored the parameters can be computed in 20 min. Com- putation time for the load matrices for a typical heating aid system is approximately 2• h. Prediction of sound pressure levels requires 15 min of computation time.

II. CONCLUSIONS

Although extensive effort is required to write the programs and make the measurements, once the parameters for several receivers and loads are available, SPL predictions can be made in a relatively short time. The measurements could be facilitated by automatic switching and by interfac- ing all of the measuring instruments directly with the computer. This system provides a powerful, reliable model which could be used for the development of better-fitting heating aids.

Postscript: Since the B•,sIc system that is available for our computer did not include Bessel and hyperbolic functions, or matrix operations on complex arrays, appropriate subroutines had to be developed for this project. Subroutines for Bessel functions of order 0 and 1 for complex arguments, hyperbolic functions of complex arguments, and matrix operations on complex arrays were developed. These program listings would be useful to the reader since the arithme- tic expressions are quite complicated. However, it is inap- propriate to include them in this short paper. A technical report is available from the publications office of CID. 4

1L. L. Beranek,,4coustics (McGraw-Hill, New York, 1954), Chaps. 3 and 5. 2A. S. Iberall, "Attenuation of oscillatory pressures in instrument lines," J. Res. Natl. Bur. Stand. 45, 85-108 (1950}.

3D. P. EgoIf and R. O. Leonard, "Experimental scheme for analyzing the dynamic behavior of electro-acoustic transducers," J. Acoust. Soc. Am. 62, 1013-1023 (1977).

4p. F. Bade, "Technical Report 1: The use of a personal computer to model the electroacoustics of hearing aids," Central Institute for the Deaf, St. Louis, MO (July, 1983)(unpublished).

620 J. Acoust. Sec. Am., Vol. 75, No. 2, February 1984 Bade et al.' Use of a computer to model hearing aids 620


use of a personal computer to model the electroacoustics of hearing aids

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