A Behavioral SPICE Compatible Model of an Electrodeless Fluorescent Lamp
Sam Ben-Yaakov *1, Moshe Shvartsas 1 and Jim Lester 2
*
Corresponding author
1
Power Electronics Laboratory
Department of Electrical and Computer Engineering
Ben-Gurion University of the Negev
P. O. Box 653
Beer-Sheva 84105, ISRAEL
Phone: +972-8-646-1561; Fax: +972-8-647-2949;
Email: sby@ee.bgu.ac.il Website: bgu.ac.il/~pel
2Central Rearch & Services Laboratories驾驶证扣分周期
Fluorescent Systems Laboratory
金玉其外OSRAM SYLVANIA 71 Cherry Hill Dr. Beverly, MA 01915 USA Phone: 1-978-750-1605 FAX: 1-978-750-1790
EMAIL: jim.
Abstract- A behavioral, SPICE compatible, model was developed for an electrodeless fluorescent lamp (OSRAM SYLVANIA ICETRON/ENDURA 150W). The model emulates the static and dynamic behavior of the lamp
when driven at high frequency. The model was tested under various experimental conditions: at steady state for different power levels, with an AM modulated drive, and under transient changes. Good agreement was found between the simulation runs and experimental results. However, the effect of temperature on the lamp’s behavior may require a tighter fit of the m odel to the temperature dependence in cas where large changes in operating condition need to be simulated.
I. INTRODUCTION
Fluorescent lamps are simply constructed light sources
consisting of a glass vesl coated inside with light emitting
phosphor. Inside the vesl is a combination of inert gas and Mercury gas. During operation, the Mercury is energized and
produces UV, which activates the phosphor and produces light. In an electroded lamp, the Mercury is energized by the current delivered through the electrodes [1]. In an electrodeless lamp, power must be delivered to the lamp either inductively or capacitively. Most commercial electrodeless lighting products today u inductive coupling and low operating frequencies where power conversion is most efficient.
There are many shapes ud in electrodeless lamps [2, 3]. Each shape offers a different optical or efficiency advantage.
Some lamps are spherical in shape with the inductive coupling coil inside the lamp protected by a glass re-entrant cavity. Some spherical lamps have the coil surrounding the lamp. This paper will ex
amine the oval or racetrack shaped lamp shown in Fig. 1, which us two inductive coupling coils connected in parallel. The physics of this lamp has been
discusd in recent papers [4 - 7]. This paper will examine a
PSPICE circuit model for the lamp construction of Fig, 1, which can be ud in circuit simulations. The results can be applied to other electrodeless lamp shapes.
The objective of this study was to develop a SPICE compatible model that will exhibit two major electrical features of an electrodeless fluorescent lamp operated at HF: the dependence of the lamp's resistance on power level and its dynamic respon to changes in electrical excitation. Bad on an earlier methodology, which relies on experimental obrvations as well as some physics bad reasoning, a behavioral model was developed to emulate the electrical respon of the electrodeless fluorescent lamp.
Once developed, the model was calibrated against experimental data and then verified by independent measurements. II. THE BEHAVIORAL MODEL OF ELECTRODELESS FLUORESCENT LAMP
The propod model is bad on the assumption that the fundamental behavior of an electrodeless fluorescent lamp is similar to the b ehavior of a lamp with hot electrodes. The only difference being the way the electrical energy is coupled to the plasma. In the ca of the lamp with electrodes, coupling is via wires. In the ca of the electrodeless lamp of the ICETRON/ENDURA type, coupling is by magnetic induction. It was thus assumed that the model concept
developed earlier [8] will fit the ca of the electrodeless lamp.
As reported in an earlier study [9], the impedance of a fluorescent lamp operated at high frequency is, to a first order approximation, resistive. That is, at any given operation point, the current of the lamp’s arc tube can be expresd as: eq lamp
lamp R V I = (1)
winding
core
Primary Coupling core
Arc tube
BOTTOM VIEW
SIDE VIEW
Cold spot control
1. Physical ICETRON/ENDURA construction.
where:
I lamp – lamp current V lamp – lamp voltage
R eq – equivalent resistance of the lamp when driven at high frequency
However, the equivalent resistance R eq is a function of the operating point, namely, of the rms current of the lamp. This dependence can be easily obtained for a given lamp by measuring rms voltages and rms currents of the lamp over the modeled operating range [5, 10]. Bad on the sim
ple obrvations, the behavioral model can be developed by applying behavioral dependent voltage (or current) sources available in any modern electronic circuit simulators. The model (Fig. 2) describes the lamp as a dependent current source (G1) that emulates a variable resistance according to (1). The expression of the G1 function is the voltage across the lamp at any given point, divided by R eq which is expresd as a function of the rms current of the lamp:
(i(rms))
R V G eq lamp 1=
(2)
The output of the dependent voltage source E1 is proportional to the square of the lamp current (i(lamp) ).
2{i(lamp)}1E ≡
(3)
The resulting voltage signal {v(isq)} at node (isq) is then pasd through a low pass filter (R 1C 1, Fi
g. 2) to obtain its low frequency component. For frequencies f > 1/(2pR 1C 1) and for times t > R 1C 1 the average voltage on C 1 (node (p)) will be:
[]∫∫≡=T 0
T 0
2dt i(lamp)T
1
v(isq)dt T 1v(p)用水
(4)
where T is the time constant R 1C 1.
The filtered I rms is then obtained by E2 (node 'rms' in Fig. 2) as the square root of the average voltage across the capacitor C1 (node 'p'): The filtered I rms is then obtained by E2 (node 'rms' in Fig. 2) as the square root of the average voltage across the capacitor C1 (node 'p'):
v(p)2E ≡
(5)
Conquently, the voltage at node rms, v(rms) is equal to the numerical value of the rms current of the lamp. This voltage, is then ud in the expression of ))rms (v (R eq to calculate the lamp’s current by (1). The function ))rms (v (R eq is bad on a numerical fitting of R eq as a function of the lamp current. Various fitting templates have been ud in the past [8,10,11]; linear fitting as well as high order polynomial fitting. In this study we explored an exponential fitting that was found to yield a good match to the experimental data (Fig. 3).
Fig. 2. Propod fluorescent lamp model.
(b)
Fig. 3. Experimental curve fitting of the
ICETRON/ENDURA 150W. (a) V-A
curve. (b) Req.
III. EXPERIMENTAL SET UP
The experimental t up (Fig. 4a) was built around a parallel resonant inverter similar to the electrodeless lamp ballast described in [6]. It included a half bridge inverter (M1, M2), resonant network (L r , C r ) and a 50Ω resistor in parallel to a bi-directional switch (M3, M4). The switch was ud to inject a disturbance in the lamp’s current. That is, by shorting and releasing the 50Ω resistor, the lamp current was slightly modulated and the dynamic respon could be watched. An RC snubber (R sn, C s n) was placed around the switch to absorbed the spikes due to the hard switching. The lamp voltage was measured by extra windings on the toroid transformers ud to drive the electrodeless lamp (Lt1 and Lt2 of Fig. 4a) [4, 5]. The current of the lamp was measured by a current transformer that was built in hou (Fig. 4a), shunted by a 100Ω resistor (R sh ).
The simulation model (Fig. 4b) was made to follow as clo as possible the experimental t up. Ho
wever, in the interest of saving simulation run time, the inverter was replaced by a square-wave voltage source (V1+LIMIT) while the modulating bi-directional switch was replaced by an “ideal” switch (S1). The simulation model included 2 transformers (couples inductors) to drive the lamp, emulating the toroid drivers. The lamp was reprented by a dependent current source (G1 , connected between the nodes el1, el2) and the additional behavioral sources (E1 – E3) per the model of Fig. 2.
IV. MODEL CALIBRATION
The parameters of the model for the ICETRON/ENDURA 150W lamp were calibrated experimentally. The equivalent resistance of the lamp R eq was obtained by measuring voltages and currents of the lamp over a current range of 0.8A to 9 A. Typical results are shown in Figs. 3a,b. Several approaches were ud to fit the functional relationship between R eq and the lamp’s rms current. They include linear and polynomial fitting [8,10,11], table fitting (applying the ETABLE behavioral source of ORCAD), and an exponential curve fit. Best matching, over a large l amp current range, was obtained with an exponential fitting.
The numerical expression for the equivalent resistance of the ICETRON/ENDURA 150W lamp was found to be:
婴儿肌张力高的表现1.2499
lamp
eq
)
碳素厂(I
31.479
R−
=(6) The time constant R1C1 of the model (Fig. 2) was calibrated by exposing the lamp to a current transient. This was done by the experimental circuit of Fig. 4a against the simulation model of Fig. 4b. The time constant was found to be 75µs.
V. EXPERIMENTAL RESULTS
The degree of matching between the static experimental results and model simulation are shown in
Fig. 5 for the time domain signal, and in Fig. 6 for the static V-A curve. The dynamic respon was obrved by driving the modulating switch (M3, M4 of Fig. 4a, S1 of Fig 4b) at various frequencies. A typical respon of the lamp to the modulation is shown in Fig. 7. Figure 7b is a zoomed picture of the voltage and current disturbances.
Notice that when modulated, the incremental impedance ∆V lamp/∆I lamp is negative (∆V and ∆I in opposite phas). The magnitude of this incremental impedance was ud to calibrate the dynamic parameters of the model, that is the R int C int time constant (Fig. 4b). R int was kept at 1kΩ while C int was iterated to find the best fit against th e experimental data. It was found the a capacitance range of 75nF to 150nF yielded a good match. This corresponds to a time constant range of 75µs to150µs, corresponding to a bandwidth range of approximately 1kHz to 2kHz. The degree of matching between the simulation and experimental results is shown in Figs. 8-10 for the modulating frequency range of 300Hz to 20kHz.
The modulation experiments as well as the simulation
clearly show the (modulating) frequency dependence of the incremental impedance [8, 10, 11]. At 2kHz (Fig. 9), the incremental impedance is already slightly positive and becomes larger as the modulating frequency increas. The dependence of the incremental impedance on the modulating frequency, measured in this study, is summarized in Fig. 11. It is apparent from this summary that the 150nF value for C int is somewhat a better choice (corresponding to a time constant of about to150µs).
Notwithstanding the excellent match between the experimental data and the simulation results, it was obrved that the lamp’s parameters are temperature dependent. A cursory examination of this issue was carried out by repeating the V-A curve measurements while a fan cooled the lamp. The results (Fig. 12) show a rather large dependence on the surface temperature of the glass tube as perhaps would be expected considering the large surface area of the lamp.
VI. DISCUSSION AND CONCLUSIONS
The behavioral model developed through this study was found to faithfully emulate the static and dynamic behavior of the ICETRON/ENDURA electrodeless fluorescent lamp. The model emulates well the static behavior of the lamp both at nominal operating condition and under dimmed condition
s. The model also emulates well the negative incremental lamp impedance at a low modulating frequency and the positive impedance at a high modulating frequency The preliminary investigation of the temperature dependence of the lamp’s parameters shows that the lamp is rather nsitive to temperature. Conquently, the simulation model prented here is valid for the temperature condition that prevailed while the model was calibrated. By repeating the calibration over a number of temperature points, and making the parameters of the model temperature dependent, it would be possible to generate a univ ersal model that is valid over a given temperature range.
It is suggested that the propod model could be uful in the design pha of electronic ballasts for the electrodeless fluorescent lamp and in particular in the design of dimming and clod loop control for such systems. The model does not cover the process of ignition and some further calibration and fitting will be required to match the behavioral model to the physical lamp for wide temperature range applications.
REFERENCES
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London, 1971.
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[6] J. N. Lester and B. A. Alexandrovich, “Ballasting
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IES, vol. 29, no. 2, pp 89-99, Summer 2000.
[7] OSRAM SYLVANIA INC., “ICETRON, Fixture
Design Guide 100 Endicott St.,” Danvers, MA,
01923.
[8] S. Ben-Yaakov, M. Shvartsas, and S. Glozman,
”Static and dynamic of fluorescent lamps operating at
high frequency: Modeling and simulation,” IEEE
Applied Power Electronics Conference, APEC-99,
pp. 467-472, Dallas, 1999.
[9] E. E. Hammer, "High frequency characteristics of
fluorescent lamp up to 500kHz," Journal of the
Illuminating Engineering Society, pp. 52-61, Winter,
1987.
[10] M. Gulko and S. Ben-Yaakov, “Current-sourcing
parallel-resonance inverter (CS-PPRI): Theory and
application as a fluorescent lamp driver,” IEEE
Applied Power Electronics Conference, APEC-93,
pp. 411-417, San-Diego, 1993.
[11] S. Glozman and S. Ben-Yaakov, “Dynamic
interaction of high frequency electronic ballasts and
fluorescent lamps. IEEE Transactions on Industry
Applications, Vol. 37. 2001 pp. 1531 –1536, 2001.
+V
(a)
COUPLING = 1COUPLING = 1Rlamp(V(I_rms))
I(Viarc)*I(Viarc)白头发可以拔掉吗
浙江博物馆
(b)
Fig. 4. Experimental t-up ud to extract the dynamic parameter R 1C 1 of the lamp model (a), and the corresponding
lamp simulation model (b).
