Microphone Thermal Agitation Noise

Received 1 October 1971 5.9

Microphone Thermal Agitation Noise

HARRY F. OLSO•

RCA Laboratories, Princeton, New Jersey 08540

In electrodynamic microphones there are two major sources of thermal agitation noise, namely, the electromotive force due to the thermal agitation of the electrons in the conductor and the electromotive force produced by the motion of the diaphragm due to the thermal agitation of the molecules impinging upon the diaphragm. In commercial microphones, the thermal acoustic noise is far below the thermal electric noise. Therefore, in order to detect the thermal-acoustic noise, a special high-sensitivity ribbon velocity microphone was designed and built. The presence of the thermal acoustic noise was detected and measured in the microphone. The theoretical and experimental data correspond for both the thermal electric noise and the thermal acoustic noise.

INTRODUCTION

The lower amplitude level of sound transmission is usually determined by the amplitude level of the noise in the sound reproducing system. There are many sources of noise in a sound reproducing system. One ex- ample is the sound pickup system, consisting of the studio and the microphone. In general, the ambient noise level in the studio determines the noise level of

a sound pickup system. However, the purpose of this paper is to examine the thermal agitation noise in a electrodynamic type of microphone. Specifically, the purpose of this paper is to examine the thermal electric

noise and thermal acoustic noise in a ribbon-type velocity microphone.

I. NOISE IN A SOUND PICKUP SYSTEM

The sources of noise in the sound pickup system employing a vacuum tube as the first amplifying element are depicted in Fig. 1. The sources of noise are as fol- lows: the ambient noise in the studio; the thermal acoustic noise due to the random sound pressures upon the diaphragm due to the thermal agitation of the air molecules impinging upon the diaphragm of the microphone; the thermal mechanical noise due to the thermal

i I AMBIENT I THERMAL THERMAL ACOUSTIC I ACOUSTIC I ELECTRIC NOISE I NOISE lAND THERMAL

I I MECHANICAL I NOISE

i I • i i I I i I I I

Air I A•R I RIBBON I

STUDIO I I I

MICROPHONE

BARKHAUSEN SHOT EFFECT AND THERMAL AND FLICKER

ELECTRIC NOISE .EFFECT NOISE

LINE

' I I TRANSFORMERS

I I

I

I I

I I I I !

I

I

I -•

THERMAL ELECTRIC

NOISE

I

VACUUM TUBE ! REACTOR AND RESISTOR

AMPLIFIER

Fzo. 1. Sources of noise in a sound pickup system employing a ribbon-type microphone and a vacuum tube amplifier.

The Journal of the Acoustical Society of America 425

Redistribution subject to ASA license or copyright; see http://acousticalsociety.org/content/terms. Download to IP: 129.120.242.61 On: Sat, 22 Nov 2014

04:56:08

H. F. OLSON

i I AMBIENT I THERMAL THERMAL ACOUSTIC I ACOUSTIC I ELECTRIC NOISE NOISE lAND THERMAL

[ I MECHANICAL

I I NOSEj I I I I I I I I I I

BARKHAUSEN AND THERMAL

ELECTRIC NOISE

LINE

I RIBBON TRANSFORMERS I

STUDIO I MICROPHONE I I I

SHOT EFFECT AND THERMAL

NOISE

TRANSISTOR

THERMAL ELECTRIC

NOISE

- D

RESISTORS

AMPLIFIER

FIG. 2. Sources of noise in a sound pickup system employing a ribbon-type microphone and a transistor amplifier.

agitation of the atoms or molecules of the metallic or plastic diaphragm; the thermal electric noise due to the thermal agitation of the electrons in the conductor of the microphone; the noise due to the Barkhausen effect in the core of the transformer; the noise due to the shot effect, flicker effect, and other electronic phenomena in the vacuum tube; and the noise due to the thermal electronic noise resulting from thermal agitation of the electrons in the resistance of the plate inductor and the biasing resistor.

The sources of noise in the sound pickup system employing a field effect transistor as the first amplifying element are shown in Fig. 2. The various noises are the same except that the transistor in Fig. 2 is substituted for the vacuum tube of Fig. 1. The noises in the transistor are due to shot effect, thermal noise, and other electronic phenomena.

II. TRIODE VACUUM TUBE AMPLIFIER

The circuit diagram of the triode vacuum tube amplifier is shown in Fig. 3. For audio applications the triode vacuum tube exhibits the lowest noise of all the

tube types. The RCA 12AY7 triode vacuum tube was selected as a particularly low-noise triode for audio ap-

plications. Batteries were used for the heater and plate supply to eliminate hum of ac supplies. The voltage amplification of the amplifier shown in Fig. 3 is 30. The vacuum tube amplifier exhibits uniform response to within a fraction of a decibel from 30 to 15 000 Hz.

The vacuum tube noise for the frequency range 5000- 15 000 Hz referred to the 250-•2 line is 1.4 abvolts.

III. FIELD EFFECT TRANSISTOR AMPLIFIER

The circuit diagram of the field effect transistor amplifier is shown in Fig. 4. The RCA 3N154 field effect transistor was selected because it presents a very large input impedance suitable for coupling to the high impedance of the "step up" transformer. The voltage amplification of the amplifier shown in Fig. 4 is 10. The transistor amplifier exhibits uniform response to within a fraction of a decibel from 30 to 15 000 Hz. The

transistor noise for the frequency range 5000-15 000 Hz referred to the 250-•2 line is 4.3 abvolts.

The ratio of gain to noise is higher in the vacuum tube amplifier than in the transistor amplifier. However, the step up ratio of the transformer could be higher in the case of the transistor. Under these conditions the effective noise would be about the same for the vacuum

12AY7

_ _

!

FIG. 3. Schematic circuit diagram of a triode vacuum tube amplifier with a line-to-grid input transformer.

426 Volume 51 Number 2 (Part 1) 1972

3NI54

FIG. 4. Schematic circuit diagram of a field effect transistor amplifier with a line-to-gate input transformer:


04:56:08

MICROPHONE THERMAL AGITATION NOISE

ALNICO

FIG. 5. Face and side views of the high-sensitivity ribbon-type velocity microphone.

POLE

SECTION

A-A'

A I

ARMCO

ALNICO

PERMENDUR

RIBBON

ERMINAL

FACE VIEW SIDE VIEW

tube and transistor. Unfortunately, such a transformer is not commercially available.

IV. MICROPHONE

In the most sensitive commercially available electrodynamic microphones, the electromotive force due to the thermal electric noise in the conductor is very much greater than the electromotive force due to the thermal acoustic noise produced by the random pressures of the molecules impinging upn the diaphragm. In the ribbon- type microphone, the ribbon acts as both the conductor and diaphragm. Therefore, this microphone provided the most favorable system for high sensitivity and the resultant possibility of detecting the thermal acoustic noise due to the random pressures produced by the molecules impinging upon the ribbon. Accordingly, a high-sensitivity velocity microphone was designed.

The special design of high-sensitivity ribbon-type velocity microphone is shown in Fig. 5. A photograph of the high-sensitivity ribbon-type velocity microphone is shown in Fig. 6. The acoustical system, the electrical system, and the acoustical network of the microphone shown in Figs. 5 and 6 are shown in Fig. 7.

The acoustic impedance frequency characteristics of the acoustic elements of the microphone of Figs. 5, 6, and 7 are shown in Fig. 8. The difference in pressure between the two sides of the ribbon as a function of the

frequency is shown in Fig. 8. The electromotive force generated by the motion

of the ribbon is given by

e=Bt2, (1)

where e is open-circuit generated voltage, in abvolts; B is flux density in the air gap, in gauss; 1 is length of the



04:56:08

H. F. OLSON

Fro. 6. Photo-

graph of the high- sensitivity ribbon- type velocity microphone.

ribbon, in centimeters; and 2 is velocity of the ribbon, in centimeters/sec.

The velocity of the ribbon is given by

(2)

where Ap is difference in sound pressure between the two sides of the ribbon, in microbars, S is area of the ribbon, in square centimeters; and z,t is total acoustic impedance of the acoustic elements of the vibrating system, in acoustical ohms. The acoustic impedance of the elements of the vibrating system and the difference in sound pressure between the sides of the ribbon are shown in Fig. 8.

From Eqs. 1 and 2, the electromotive force developed by the ribbon is given by

e= B1/xp/Sz, z. (3)

The open-circuit voltage characteristic developed by the ribbon can be computed from Eq. 3 and the data of Fig. 8.

The measured open-circuit voltage frequency characteristic of the microphone depicted in Figs. 5 and 6 is shown in Fig. 9. The measured open-circuit voltage and the open-circuit voltage computed from Eq. 3 are in close agreement.

V. EQUIPMENT FOR THERMAL NOISE EXPERIMENT

The arrangement of the apparatus for measuring the electromotive force generated in the ribbon by the thermal electric noise and the electromotive force generated by the motion of the ribbon due to the random

TERMINAL

RIBBON / /

M s rAs'- -•

A' FRONT VIEW

POLE

M• rA•

P• M 2 rA2 P•

MR

SECTION A - A'

ACOUSTICAL SYSTEM

VT

TRANS LINE A

r•, ZE__•.• • • ELECTRICAL SYSTEM

r'Ei

EQUIVALENT ELECTRICAL

CIRCUIT

Ms rAS

P,

ACOUSTICAL NETWORK

Fro. 7. The acoustical system, acoustical network, electrical system, and equivalent electrical circuit of the electrical system of a ribbon-type velocity microphone In the acoustical system and acoustical network: p• and p•. are sound pressures on the two sides of the ribbon; M• and M•. are inertances due to the mass of the air load on the two sides of the ribbon; r• and r•. are acoustical resistances of the acoustical radiation on the two sides of the ribbon; Ms and r•s are inertance and acoustical resistance of the slits between the ribbon and the pole pieces; Ma and C•a are inertance and acoustical capacitance of the ribbon; z•. is acoustical impedance due to the electrical system. In the equivalent electrical circuit: rm is electrical resistance of the ribbon; zs•. is electrical impedance presented to the ribbon by the electrical load of the electrical system; zs• is electrical impedance due to the acoustical system.

428 Volume 51 Number 2 (Part l) 1972


04:56:08


100

10 10

::) 0,1 0 0,1

O.Ol o ,Ol

o.ool ooool io ioo iooo ioooo

FREOUENCY IN Hz

FTG. 8. The acoustical impedance characteristics of the ribbon-type velocity microphone shoxvn in Fig. 5. XAR' the positive and negative acoustical reactances due to the inertance and acoustical capacitance of the ribbon; XAA' acoustical reactance of the air load; r•' acoustical resistance due to the air load; xE•' the positive and negative acoustical reactances due to the electrical system; r•E' acoustical resistance due to the electrical system and air viscosity losses;/Xp/p' ratio of the difference in sound pressure between the two sides of the ribbon and the free-field sound pressure.

force produced by the impinging molecules upon the ribbon is shown in Fig. 10.

Sections II and III show that the ratio of the amplification to self-noise is much greater in the triode vacuum tube amplifier. Therefore, this triode vacuum tube amplifier was selected for the first stage.

The first stage of amplification is followed by a Bal- lantine decade amplifier with a gain of 40 dB. The next

element is the SKL active-type low- and high-pass filters. The frequency response characteristic of the SKL filter for the frequency range 5000-15 000 Hz is shown in Fig. 11. The gain of the SKL filter system in the passband is unity.

The voltage output of the system is measured by means of a Ballantine electronic voltmeter. The high- sensitivity velocity microphone was placed inside of a

3O

25

•20

w

a: 0

-5

-I0

IO 2 IO 3 IO 4 FREOUENCY IN Hz

Fro. 9. The open circuit voltage as a function of the frequency for the ribbon-type velocity microphone of Figs. 5 and 6. The voltage characteristic depicted is at the output of a ribbon-to-line transformer with an impedance step-up ratio of 1000:1.0 dB-- 10 -4 V/t•bar.



04:56:08

H. F. OLSON

STEEL PLATE

/ VACUUM

GUAGE

CENCO HYVAC VACUUM PUMP

WOOD COVER

GLASS BELL JAR

MICROPHONE

RUBBER SUSPENSION

TRIODE

AMPLIFIER

CABLE

BALLANTINE VOLTMETER

BALLANTINE --

'/ L.P. HP.

Fro. 10. Schematic diagram depicting the equipment used in the microphone thermal noise experiment.

bell jar that could be evacuated by means of the Cenco Hyvac vacuum pump.

VI. AMBIEI•IT ACOUSTIC l•1OISE

The ambient noise in the anechoic room is 6 dB over

the frequency range 5000-15 000 Hz. The measured

acoustic shielding of the bell jar under atmospheric pressure is 38 dB. The measured acoustic shielding of the wood box is 12 dB. This makes a total acoustic

shielding of 50 dB over the frequency range of 5000- 15 000 Hz. The ambient noise level at the microphone is therefore --44 dB. This is a sound pressure of 1.2

-5

-3O

-35

_.o/ , I' , I z 3 4 •, e 759 I 2 •, 4 5 6

IOOO IO ooo 60 ooo FREOUENCY IN Hz

430 Volume 51 Number 2•(Part 1) 1972

Fro. 11. The frequency response characteristic of the SKL filter with high-pass setting of 5000 Hz and a low-pass setting of 15 000 Hz.


04:56:08


FiG. 12. The significant noise levels involved in the measurement of the microphone thermal noise.

ODB

AMBLE N T MICROPHONE VACUUM ACOU S TIC THERMA L TUBE

NOISE AT THE ACOUSTIC AMPLIFIER MICRO PHONE NOISE NOISE

/ -7.6DB

L2DB

MICROPHONE THERMAL ELECTRIC

NOISE

-22DB

X 10 -6 ubar. The ambient acoustic noise is well below the thermal electric noise and the thermal acoustic

noise.

VII. INSIGNIFICANT NOISES

The thermal mechanical noise due to the thermal

agitation of the atoms in the aluminum ribbon is far below the thermal acoustic noise.

The noise due to the Barkhausen effect in the core of

the two transformers shown in Fig. 9 is manifested in the leakage reactance. This noise is far below the thermal acoustic noise.

Employing the vacuum tube amplifier of Fig. 3, with batteries for the heater and plate supply, the noise in the vacuum tube is due to the flicker and shot effect.

Since the frequency range to be considered is above 5000 Hz, the flicker effect is negligible. The main noise is therefore the shot noise. The shot noise is well below the thermal acoustic noise.

Following the triode vacuum tube amplifier, the noise in the Ballantine decade amplifier is well below the noise of the triode amplifier as manifested at the point of measurement.

To summarize:in the system of Fig. 9, by employing the microphone of Figs. 5 and 6, the significant noises will be the thermal electric noise in the ribbon and

thermal acoustic noise upon the ribbon.

VIII. THERMAL NOISE EXPERIMENT

Employing the equipment depicted in Fig. 9 evacuated the bell jar. With the bell jar evacuated, the noise is due to the thermal electric noise generated in the ribbon circuit, since the thermal acoustic noise does not exist under these conditions. The electric resistance con- sists of the ribbon and the transformer. The electric

resistance of the ribbon is 0.2 a and the transformer, both primary and secondary, referred to the low side is 0.05 •2.

The thermal electric noise electromotive force •,2

generated in a resistor due to random motion of the

-4 2 DB

free electrons is

e = [-4K rrg(f•- f•)-I •, (4)

where e is voltage, in abvolts; K is Boltzmann's constant, 1.374X10 -•6 erg/degree Kelvin; T is absolute temperature, in degrees; rE is electrical resistance, in abohms; and f2--fi is frequency range, in hertz. The reason for using cgs electromagnetic units is to provide a direct analogy of Eq. 4 with Eq. 5.

With the system evacuated, the thermal electric noise voltage was measured by means of the Ballantine voltmeter. The measured noise voltage referred to the 250-• line was 20.5 abvolts. This voltage was translated back to the ribbon. Employing this voltage, the electric resistance of the ribbon was computed from Eq. 4. The result was 0.26 •2 as compared to 0.25 •2 as measured from direct current measurement of the resistance by means of a bridge.

Following the analogy a with thermal electric noise, the thermal acoustic noise pressure generated in an acoustical resistance is given by

p = [4K Try. (f2-- f•)]«, (5)

where p is sound pressure, in microbars; K is Boltz- mann's constant, 1.374X10 -•6 erg/degree Kelvin, T is absolute temperature, in degrees; r A is acoustical resistance, in acoustical ohms; and f•--f• is frequency range, in hertz.

With the system under atmospheric pressure, the noise voltage was measured by means oi• the Ballantine voltmeter. There are two sources of noise, namely, the thermal electric noise in the resistance of the ribbon circuit and the thermal acoustic noise caused by molecules impinging upon the ribbon. The total measured thermal noise voltage referred to the 250-•2 line was 21.8 abvolts. The relation between the noises can be

expressed as

eT• = eE•q-eEA 2 , (6)

where eT• is total thermal noise voltage, in abvolts; eE• is thermal electric noise voltage, in abvolts; and eE• is thermal acoustic noise voltage, in abvolts.



04:56:08

H. F. OLSON

Since the thermal electric noise voltage e•s was determined with the bell jar evacuated, the thermal acoustic noise voltage e•A can be determined from Eq. 6. The measured thermal acoustic noise voltage at the 250-12 line determined from Eq. 6 was 7.4 abvolts. When eEA has been established, the sound pressure can be determined from the microphone sensitivity characteristic of Fig. 7. The sound pressure due to thermal acoustic noise determined by this means was 8.3X 10 -5 ubar. The sound pressure due to acoustic thermal noise 4 computed from Eq. 5 using the value of the acoustic radiation resistance rA• of Fig. 7 was 7.5X10 -5 ubar.

The agreement between the measured sound pressure due to thermal acoustic noise and the theoretical

thermal acoustic noise pressure is within the experimental errors and the errors in allocating the proper constants in determining the value of the acoustical radiation resistance rA•.

IX. SUMMARY

A summary of the significant noises involved in this experiment for the frequency range of 5000-15 000 Hz is shown in Fig. 12. The reference sound level of 0 dB is 0.0002 ubar. The measurement conditions were made with an ambient noise level of --42 dB at the micro-

phone. This noise level was extrapolated from the measured ambient noise level outside the two shields sur-

rounding the microphone and the transmission'loss introduced by the two shields. The measured thermal acoustic noise of the microphone was --7.6 dB. The measured microphone thermal electric noise of the microphone was equivalent to 1.2 dB. The measured vacuum tube noise was --22 dB. The data of Fig. 12 show that the ambient acoustic noise and the vacuum

tube noise are sufficiently low so that the measurements

of the thermal acoustic noise and thermal electric noise

are not affected by these noises. The total thermal noise of the microphone corre-

sponds to a sound-pressure level of 1.7 dB. In general, the recommendations are that the noise in a studio

should not excede an NC (noise criteria) of 20. This is equivalent to a noise level of 30 dBA. In other words, a microphone could be 25 dB less sensitive than the microphone described in this paper and still not be the limitation on noise. Therefore, a microphone need not be the limitation on noise.

X. CONCLUSION

The thermal electric noise generated in the ribbon of a ribbon-type velocity microphone due to the thermal agitation of the electrons in the ribbon conductor has been measured. The results agree with the theoretically predicted electric noise. The thermal acoustic noise due to the random sound pressures produced by the thermal agitation of the air molecules impinging upon the ribbon acting as a diaphragm in a velocity microphone has been measured. The results agree with the theoretically predicted acoustic noise.

1 J. B. Johnson, "Thermal Agitation of Electricity in Conduc- tors," Phys. Rev. 32, No. 1, 97 (1928).

•' H. Nyquist, "Thermal Agitation of Electronic Charge in Con- ductors," Phys. Rev. 32, No. 1, 110 (1928).

3 L. J. Sivian and S. D. White, "On Minimum Audible Sound Fields," J. Acoust. Soc. Amer. 4, 288 (1933).

4 F. V. Hunt, "Thermal Noise in the Acoustic Medium," in American Institute of Physics Handbook (McGraw-Hill, New York, N.Y., 1963), 2nd ed. Sec. 3c-11, pp. 3-56. The specific basis for the derivations of Eq. 3c-97,b for the thermal noise pressure in air in this article and Eq. 5 of this paper differ in some degree. In- cluding the directivity of the microphone, since all directions are equally probable, the effective noise pressure employing Eq. 3c-97b turns out to be 8X 10 -5 •bar, which is indeed very close to 7.5X10 -5 •bar derived from Eq. 5 in this paper.

432 Volume 51 Number 2 (Part 1) 1972


04:56:08

Documents

Microphone Thermal Agitation Noise