electrical impedance measurements of an electrothermal loudspeaker

5.8 Received 30 January !970

Electrical Impedance Measurements of an Electrothermal Loudspeaker

G. A. Russm.•.

Department of Mechanical and Aerospace Engineering, University of Massachusetts, Amherst, Massachusetts 01002

A simple configuration of electrothermal loudspeaker is described, which is capable of producing audible acoustic outputs, without the usual supplements of flame seeding, voltage transforming, or biasing. The acoustic levels are measured for various electrode positions and electrical driving signals. The input impedance of the flame is measured and found to be approximately equivalent to that of a parallel resistance- capacitance circuit.

INTRODUCTION

Historically, the ability of flames to accept and acoustically reproduce mechanical oscillatory signals has long been recognized. •.•' More recently, it has been demonstrated s that flames can also acoustically reproduce signals introduced electrically into the flame stream; hence, the phenomena has been appropriately referred to as an electrothermal loudspeaker. 4

Experimental results on electrothermal loudspeakers reported to date a.4 have been taken using audio ampli- fiers as the electrical-signal source. These tests have stepped up the amplifier output voltage through a transformer and biased the transformer secondary wind- ing with a dc voltage. Also, the flame was seeded with an ionizing salt in each experiment. Although no supporting sound-pressure-level (SPL) data is given, the implication in each of these references is that all three effects, i.e., seeding, transforming, and biasing, are needed to obtain audible acoustic-output levels.

However, during early attempts at setting up an electrothermal loudspeaker demonstration in our labora- tory, it was noticed that audible outputs could be generated by inserting one electrode in the flame, grounding the burner, and applying a voltage signal. This observation was interesting in terms of the absence of flame seeding, voltage transforming, and voltage biasing normally used and, as such, prompted the investigation described in this paper.

I. EXPERIMENTAL APPROACH

The electrode and burner configuration which gave the best results is shown in Fig. 1. The electrode used

1482 Volume 47 Number 6 (Part 1) 1970

was a tungsten welding rod 20-cm long with a 0.3-cm cross-sectional diameter. A Meeker burner with an

adjustable air inlet and 0.2-cm grids at the burner sur- face was used to hold a natural-gas flame. The gas flow was adjusted to hold a flame with a blue zone of approximately 0.5 cm. The voltage applied between the electrode and the grounded burner was taken directly from a Brtiel and Kjaer model 1024 sine-random generator. The generator was adjusted to provide a sinusoidal output with an output impedance of 6000 f•.

The sound generated by this configuration was measured at a distance of 0.3 m and a driving frequency of 200 Hz under approximately free-field conditions with the results shown in Fig. 2. The SPL values shown represent «-oct band filtered signals about a center frequency of 200 Hz.

The frequency-dependent nature of the flame impedance was investigated with the circuit shown in Fig. 3. The applied sinusoidal voltage was taken from a Brtiel and Kjaer model 1024 sine-random generator at a 6000-f• output impedance. The voltage drop across the 17542 resistor was measured with a Brtiel and Kjaer model 2603 voltmeter in order to determine the current

passing through the flame. The results are shown in the form of impedance versus frequency over a frequency range of 30-20 000 Hz in Fig. 4.

II. DISCUSSION

The «-oct band SPL data shown in Fig. 2 indicates a decrease in sound level, with decreasing signal level and increasing electrode separation. These trends are physically reasonable and agree with results obtained by

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ELECTROTHERMAL LOUDSPEAKER IMPEDANCE

-• FO'aCM ELECTRODE

.2 C•I

4.0 CM --•

o

BURNER

Fro. 1. Electrode and burner configuration.

Burchard) It should be noted, however, that the analytical expression for the absolute magnitude of the sound pressure derived by Burchard (Eq. 8 of Ref. 4) is not applicable to the data given here, because of the cylindrical asymmetry of the electrode configuration.

The input impedance of the flame as seen by the electrical driving circuit is given by the frequency- response characteristic of Fig. 4. A relatively good fit to the measured data is given by the solid line super- imposed on the plot. This solid line represents the asymtotes 5 of the amplitude-versus-frequency characteristic of a parallel RC circuit; i.e.,

Z= R/['i + RC (j•o) ].

65

55-

500

D

! i

50 100

APPLIED VOLTAGE, RMS VOLTS

Fro. 2. «-oct band filtered SPL readings at a 200-Hz driving frequency and oscillator impedance of 6000 f•.

VOLTMETER

OSCl

175 OHM

RESISTOR

'•___• D ELECTRODE, FLAME AND BURNER

FIG. 3. Frequency-response test circuit.

The simple first-order impedance characteristic is reasonable, since the resistance effect can be attributed to the flame conductance, and the capacitance effect can be attributed to the presence of the two electrode surfaces juxtaposed in the flame.

Assuming the input impedance of the flame to be analogous to a parallel resistance-capacitance RC circuit with the frequency response of Fig. 4 implies that the resistance is 106 f• and the capacitance (com- puted from the resistance and the break frequency) is 0.637X10 -9 F. This value of flame impedance is considerably larger than the 100-5000 f• reported by Burchard 4 for various configurations of seeded flames. This would imply that the addition of ionizing salts to the flame is an effective means of reducing the electrical input impedance of the flame. In addition, if the capacitance effect is assumed to be independent of the ion content in the flame, the increased flame conductance, due to flame seeding, would lower the RC time constant and make the frequency response flat over a proportionally larger band of frequencies. That is, the first-order impedance characteristic measured here for an unseeded flame would not be apparent for a seeded flame over the range of audio frequencies.

III. CONCLUSION

The electrical impedance of a particular configuration of electrothermal loudspeaker has been measured and found to follow that of a parallel RC circuit. The mea-

'•0 1100 11000 10000 FREQUENCY, HERTZ

o

-10 i.- t- O

-20"' '- --•o

-30• n-

-40 '• O

-50

Fro. 4. Measured-frequency-response characteristic with 4.0-cm electrode separation and 120 V.

The Journal of the Acoustical Society of America 1483


G. A. RUSSELL

sured impedance characteristic is reasonable in terms of the low conductance of the unseeded flame and the

capacitance effect of the electrodes. The measurements made should be of some aid in analyzing the electrothermal-loudspeaker effect and in planning future experiments, especially with unseeded flames.

x G. B. Brown, Proc. Phys. Soc. 47, 703 (1935). • E. N. daC. Andrade, Proc. Phys. Soc. 53, 229 (1941). a W. R. Babcock, K. L. Baker, and A. G. Cattaneo, "Musical

Flames," J. Acoust. Soc. Arner. 43, No. 6 (1968). 4 j. K. Burchard, "Preliminary Investigation of the Electro-

thermal Loudspeaker," Cornbust. Flame 13, No. 1 (1969). 5 R. H. Cannon, Jr., Dyna•nics of Physical Systems (McGraw-

Hill, New York, 1967).

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electrical impedance measurements of an electrothermal loudspeaker

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