Page 1 of 5

An Alternative Optical Method for Acoustic Resonance Detection in HID Lamps

Walter Kaiser Ricardo Paulino Marques Alexander Fernandez Correa

Escola Politecnica da Universidade de Silo Paulo Av. Prof. Luciano Gualberto, trav. 3, no. 158

CEP 05508-900 Silo Paulo SP BRAZIL E-mail: kaiser@lac.usp.br

Abstract- Acoustic resonances are observed in high-pressure discharge lamps operated with ac input modulated power frequencies in the kHz range. This paper describes an optical acoustic resonance detection method for HID lamps using computer controlled webcams and image processing software. Quality indexes are proposed to evaluate lamp performance and experimental results are presented.

Keywords-Acoustic resonance, Optical detection, HID lamps.

I. INTRODUCTION

In spite of the advantages of electronic ballasts, the operation of HID lamps in high frequency remains limited by an unstable and harmful phenomenon called "acoustic resonance" (AR). Theoretically, it originates from pressure wave propagation in the discharge enclosure with reflexes on the walls from which a standing wave will result that causes arc deformation and light fluctuations. The AR resonance frequencies are numerous and vary according to the power injected, the geometry and pressure of the discharge tube, the composition of the gas, the lamp age and model, and even the manufacturing batch.

The common explanation of the physical background for acoustic resonance phenomena is that when a HID lamp is operated with periodic power, the current is modulated and the intensity of the discharge changes with the same frequency as the power. Any increase of the discharge intensity increases the pressure of the filling gas inside the arc tube. In the same manner, a decrement of the discharge intensity decreases the pressure. In other words, the periodic input power and the subsequent energy exchange by elastic collisions between charged particles and neutral gas are the source of pressure perturbation. The fluctuation of the pressure, which is originated in the vicinity of the discharge, propagates through the gaseous medium inside the arc tube. This propagation represents a traveling longitudinal wave with the characteristically behavior of sound (acoustic) waves [1]. Based on the theory of acoustic streaming, a plausible theory for the physical causes for the excitation of acoustic instabilities and the temporal response of the discharge has been proposed [I].

If the power frequency is at or close to an eigenfrequency of the arc discharge tube, traveling pressure waves will appear and distort the arc discharge path [2-5]. These waves reflect

against the discharge tube walls and at certain frequencies standing pressure waves, called acoustic resonance occur.

Acoustic resonance with sufficient acoustic energy may cause undesired effects in HID lamps. Such effects range from a nearly imperceptible arc movement to extreme displacement of the discharge causing flicker, lamp voltage rise and even cracking of the discharge tube [6]. These effects are extremely dynamic and unpredictable; one or two cycles at the appropriate frequency can be sufficient to extinguish the arc. The critical frequency values depend on distance between electrodes, tube geometry and gas composition and pressure. Also, lamp ageing leads to changes in lamp resonant frequencies since filling gases and lamp electrodes change with time. Theoretically, the eigenfrequencies of the lamp discharge tube can be predicted by solving the acoustic wave equation with mass conservation equation, momentum conservation equation, energy conservation equation, thermodynamic equation and the equation of state [6]. The system equations are nonlinear and require a time consuming numerical solution that is not a trivial task since there are uncertainties in parameters that determine the speed of sound around the discharge tube.

AR can exhibit a hysteresis that changes the resonance windows systematically when the supply frequency initially increases and then decreases [1].

II. ACOUSTIC RESONANCE DETECTION METHODS

Designers of electronic ballasts have been interested in determining the frequencies of destabilizing resonances to be avoided in high-pressure lamps. There are basically three AR detection mechanisms: acoustic emissions measurement [4], electrical measurements (lamp voltage, current or impedance) [7] and optical detection of arc displacements or disturbances [8].

III. ACOUSTIC RESONANCE DETECTION METHOD

In this paper the AR detection will be optically using the experimental apparatus described in [8].

The arc deformation is measured with the lamp in a quadrangular chamber with two webcams on perpendicular planes to obtain a three-dimensional rendering (see Fig. 1). Light is filtered by a neutral density optic filter with a gain of 111024.

978-1-4244-9500-9/11/$26.00 © 2011 IEEE

Figure 1. Measurement setup.

A class D converter operating at 300 kHz provides current.A programmable waveform generator synthesizes the lamp current waveform and a DSP (Digital Signal Processor) provides three level PWM command signals for class D converter MOSFETs. A LC filter at converter output recomposes the desired lamp current waveform. A manual ignitor starts the lamp and is bypassed at normal operation. Lamp current and voltage are measured to determine the the arc resistance and lamp power to ensure operation at nominal power conditions. The measuring system set up is fully automated by a PC, using the software package Matlab.

IV. QUALITY INDEXES

Three quality indexes, based on the acquired images, are proposed to assess different operational aspects for each lamp. A general equation for these indexes is as follows.

e q=l- - . emax

The generic index q is based on the relations between errors e and emax which may have different meanings for each case. It is assumed that for an arbitrarily chosen best case, e = 0 and then q = 1. It is also assumed that for an arbitrarily chosen worst case, e = emax and so q = O. This allows a sort of qualitative approach to the indexes and is intended to facilitate the comparison of essentially very different measures.

A. Arc Quality Index 1

The first Arc Quality Index 1 (hence AQI1) has its focus on how straight an arc is, so only its central axis is used in the index calculation.

The best case is assumed to be an arc whose central axis is perfectly straight, as shown in Fig.2 (the vertical lines are the cross sections where the arc parameters are calculated).

fI II II IIII \I_I_I_I_I_I_I_I_I_J I·: I'-:I: '���_

Figure 2. Straight arc

Notice that for this index, the arc position is disregarded (no matter if an arc is in the tube center or nearer the walls, if it is straight along the tube axis its AQI1 would be 1). The worst

Page 2 of 5

case conceivable, assuming that there is in fact an arc, would be a zigzagging arc, somehow like in the picture of Fig. 3, which shows one possible arc configuration that would result in a null AQI1.

Figure 3. Worst case arc

The index is in the manner of a standard deviation for the measured arc, and its calculation is very simple. The maximal arc error is given by

d emax = 2' (1)

where d is the arc diameter (measured in pixels from the acquired images).

The arc error (in pixels) is given by

L�l .J (Xi)2 + (Yi)2 e = ---"-=--'------- (2) n

where n is the number of cross sections used (n = 40 was

used in the essays), and Xi , Yi ' are the arc distances along

cross section i from the arc central line to the mean arc line (not necessarily in the tube center).

Finally, the index is calculated as

e AQI1 = 1- - , emax

with e and emax given by (2) and (1).

(3)

This index has some important characteristics and limitations.

1. The index completely disregards arc width (for that see AQlz in the sequel).

2. Since the mean arc line is used, the fact of an arc being located in the tube center or near the wall is disregarded (only its shape affects the index).

3. Several different arcs may have the same index (which is unavoidable, no matter what index is conceived).

4. The number of cross sections fine tunes this index. The greater the number of them, potentially more accurate is the obtained index. Apart from this, the index should not be affected by the choice of n.

B. Arc Quality Index 2

Arc Quality Index 2 (AQlz) has its focus on how regular the arc width is, so only its inferred cross section area is used.

The arc axis is rectified, and the resulting 3D arc model is compared with a cylinder having the same volume (as in the diagram of Fig. 4.

978-1-4244-9500-9/11/$26.00 © 2011 IEEE

Page 3 of 5

Figure 4. Calculation procedure for AQlz

The errors are calculated as the quadratic errors between volumes per arc length. For the worst case, arc absence is assumed (i.e. null volume), while the best case is a perfectly cylindrical estimated arc.

The mean arc radius is given by

f= L�lrxi·rYi n

where rXi and rYi are the elliptical cross section semi­diameters. Notice that a circle of radius f has the same area as the cross section.

The error can be calculated as

Lf=l!rxi' rYi - f2 ! e = ---=.....;:;..-----

n while the worst case is given by

emax = f2

The index is then calculated as

e AQI2 = 1- - ,

em ax

with e and em ax given by (5) and (4).

(4)

(5)

(6)

Some important characteristics and limitations for this index are as follows.

1. The index completely disregards the arc axis (for that see AQI1 above).

2. Several different arcs may have the same index (which is unavoidable, no matter what index is conceived).

3. The worst and best cases are arbitrary choices. For this particular index, a negative value may be obtained depending on the choices made.

4. As with AQI1, the number of cross sections fine tunes this index.

C. Intensity Index This index, denoted by LumIl is based on the intensities of

each pixel of the acquired images of the tube (as in the example of Fig. 5).

Each pixel has an intensity varying from 0 (pitch black) to 1 (saturated white), and this index is given by the mean

between the mean intensity values for both images. This is equivalent, although simpler than using the general equation above. The worst case assumes there is no arc, while the best case assumes an arc occupying the whole tube, which is arguably exaggerated. For the images of Fig. 5, the intensities are 0.3036 for the x-plane and 0.2673 for the y-plane, resulting in LumIl = 0.5(0.3036 + 0.2673) = 0.2855.

x-plane y-plane

Figure 5. Acquired images for HPS lamp operating at 3.9kHz

V. SPECTRAL INDEXES

These indexes are based on the acquired spectra, and use as reference the spectrum for 60Hz operation. Two indexes are proposed.

A. Spectral Quality Index I

This index, denoted by SQI1 , compares the RMS error between the spectrum for a given operation frequency with the reference spectrum, as illustrated in Fig. 6.

CIl

O/l .5 C ::l o ()

/ reference spectrum

wavelength

Figure 6. Illustration of SQll calculation (gray area between curves)

For the best case, e = 0 (the 60Hz spectrum). The worst case assumes arc extinction ( emax is the area under the reference spectrum curve). The index is then given by the general formula

e SQI1 = 1- -- ,

emax

978-1-4244-9500-9/11/$26.00 © 2011 IEEE

with e and emax as above.

Notice that negative values may be obtained for this index in the case of an intense spectrum.

B. Spectral Intensity Index This index, denoted by SIll, is given by the area under the

spectrum curve, normalized by the value for 60Hz operation, and therefore does not follow the general formula. Although its value is always positive, it may be greater than one if the light intensity at a given operation frequency is greater than at 60Hz.

This index is comparable to the intensity index Lum!l, but unlike that index, which weighs the light emitted throughout the whole discharge tube, the spectral intensity index uses data acquired at a single point (roughly at the tube geometric center). While Lum!l is sensitive to changes in emission caused by differences in the arc 'size', SIll is basically sensitive only to changes in the 'quality' of the light emitted. In this respect, these two indexes provide complementary, rather than similar, information.

VI. EXPERIMENTAL RESULTS

In this section are presented results for two lamps: a 70W Osram NAV-E Lamp (hereinafter HPS lamp) and a 70W Osram Powerstar (hereinafter Me-Ha lamp). In both cases power was kept constant (at approximately nW) for different operation frequencies in the range from 1 kHz to approximately 10kHz. To keep power constant for every measurement, a careful adjustment is mandatory.

A. HPSLamp Figures 7-13 present the results for the HPS lamp.

80

� ,L������������������, O f(kHz)

Figure 7. Lamp power (approx. nW) for HPS lamp

f(kHz)

Figure 8. Lamp impedance (HPS lamp)

r:�r if :1 07,����7-�7-�7-�7-�7-�7-����,o f(kHz)

Page 4 of 5

Figure 9. Arc Quality Index I (AQ!l) for HPS lamp

0: [ . . . . . . . . 1

�::�

g-

1 2 3 4 5 6 7 8 9 10 f(kHz)

Figure 10. Arc Quality Index 2 (AQ!z) for HPS lamp

0.96

0.94

0.92

0 .• ,'--�---o-�----,:-���----:-�----:-�-----=�-----=�-----:�-:',o f(kHz)

Figure 11. Spectral Quality Index 1 (SQl1) for HPS lamp

0.5

O

O�

I�i i i i i i i i �

1 0

0:

0.35

. O.31'-----�2���3 ��4 ��5��6��7��8��.�-----J'o

f(kHz)

Figure 12. Intensity Index (Lum!l) for HPS lamp

'.5�������������������

05,7-�7-�7-�7-���7-�7-�7-���--:',O

f(kHz)

Figure 13. Spectral Intensity Index (SIll) for HPS lamp

B. Me-Ha Lamp Figures 14-20 present the results for the Me-Ha lamp.

Notice that the highest frequency that could be achieved was 8.8kHz. Above that, arc extinction occurred too quickly, not allowing measurements to be performed.

OOr-�.-�.-�.-�.-�'-�'-�'-�'-��

80

��,�----':-�----':-�----:-�----:-�-----=�-----=�-----:�-----:�---:',·O f(kHz)

Figure 14. Lamp power (approx. nW) for Me-Ha lamp

978-1-4244-9500-9/11/$26.00 © 2011 IEEE

Page 5 of 5

�

,00,---.---.---,----,---,---,----,---.---.

90

f(kHz)

Figure I S. Lamp impedance (Me-Ha lamp)

0.98

0.92

0.9,'------':---�--��---:---�---=---�--�---:',O.

f(kHz)

Figure 16. Arc Quality Index I (AQI1) for Me-Ha lamp

0.6 5

0.5

0.4 5

0 4 ,:------:----::------:----�-----':---�------::------:-------!,0· f(kHz)

Figure 17. Arc Quality Index 2 (AQI2) for Me-Ha lamp

0.98

0.94

0.92

0.9,'------':---�--��---:---�---=---�-----':----:',o f(kHz)

Figure 18. Spectral Quality Index I (SQI1) for Me-Ha lamp

'0 f(kHz)

Figure 19. Intensity Index (LumIl) for Me-Ha lamp

, �,-----':---�----:-----�5--�--�,----:----::----�,0 f(kHz)

Figure 20. Spectral Intensity Index (SIll) for Me-Ha lamp

VII. COMMENTS AND CONCLUSIONS

The HPS lamp presents evident arc degradation around 3.9kHz (see Fig. 5) as can be seen from the indexes of Figs. 9 and 10. This is reflected in the lamp impedance, as can be seen in Fig. 8. Figure 11 shows that the lamp spectrum remains almost unaltered for the whole frequency range. Light intensity fluctuates along the frequencies, as can be seen in Figs. 12 and 13. The similarity between these curves, in spite of the methodological differences between the indexes, suggests that the intensity fluctuations are not caused by arc distortion or encroachment, but reflect changes on the emission of the arc itself.

The Me-Ha lamp does not present such evident behavior, but Fig. 16 shows a remarkable decline in arc quality when approaching the frequency range associated with arc extinction, although no similar trend is observed in Fig. 17. As in the previous case, there are no significant alterations in the lamp spectrum (see Fig. 18), while the intensity indexes (see Figs. 19 and 20) show very similar behaviors.

For the HPS lamp, acoustic resonance can be clearly seen at an operation frequency of approximately 3.9kHz. Its effects include arc degradation (Figs. 9 and 10) and a remarkable increase in lamp impedance (Fig. 8). The Me-Ha lamp seems to approach acoustic resonance at high frequencies, but the effect is so intense (remark the degradation in arc quality for higher frequencies shown in Fig. 16) that arc extinction prevented further measurements.

The methodology presented here, as shown by the results above, is a viable tool to detect, quantify (although with the aid of qualitative and somewhat arbitrary indexes) and qualify resonance types or modes.

REFERENCES

[ I ] Afshar, F., "The Theory o f Acoustic Resonance and Acoustic Instability in HID Lamps", LEUKOS, vol 5, no.l, pp. 26-38, July 2008.

[2] Witting, H., "Acoustic resonances in cylindrical high-pressure arc discharges", Journal of Applied Physics, vol. 49, no.5, pp. 2680-2683, 1978.

[3] Schafer, R., Stormberg, H. P., "Investigations of the fundamental longitudinal acoustic resonance of high-pressure discharge lamps", Journal of Applied Physics, vol. 53, no.5, pp. 3476-3489,1982.

[4] Stormberg, H. P., Schaefer, R., "Excitation of acoustic instabilities in discharge lamps with pulsed supply voltage". Lighting Research and Technology, v.15, n.3, p.127-132, May 1983

[5] Denneman,1. W., "Acoustic resonances in high frequency operated low wattage metal halide lamps", Philips Journal of Research, vol. 38, no. 415, pp. 263 - 272, 1983.

[6] Morse, P. M., Ingard, K. U., Theoretical Acoustics, McGraw-Hill Book Company, 1968.

[7] Siess egger, B.; Guenther, K.; Gueldner, H.; Hirschmann, G., "Characterization of acoustic resonances in HID lamps based on relative impedance difference with an automated measuring station", Power Electronics Specialists Conference, 2008. pp 1898 - 1904, June 2008.

[8] Kaiser, W., Marques, R.P., Correa, A.F., "An Alternative Optical Method for Acoustic Resonance Detection in HID Lamps", 43th IEEE lAS Annual Meeting Conference, pp 1-6, 2009.

978-1-4244-9500-9/11/$26.00 © 2011 IEEE