THE PRIMARY motivation for using a low-frequency

3180 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 9, SEPTEMBER 2008 Digital Control of a Low-Frequency Square-Wave Electronic Ballast With Resonant Ignition F. Javier Díaz, Francisco J. Azcondo, Senior Member, IEEE, Rosario Casanueva, Member, IEEE, Christian Brañas, Member, IEEE, and Regan Zane, Senior Member, IEEE Abstract This paper proposes a two-stage low-frequency square-wave (LFSW) electronic ballast with digital control. The first stage of the ballast is a power factor correction (PFC) stage, and the second is a full-bridge (FB) converter used for both lamp ignition and LFSW drive. As a novelty for LFSW ballasts, ignition is achieved without an additional igniter circuit by operating the FB during start-up as a high-frequency resonant inverter. After ignition, the converter operates as an LFSW inverter to avoid exciting acoustic resonances by controlling the FB as a buck converter and regulating alternately positive or negative current to the lamp. Lamp power is regulated by adjusting the average current supplied by the PFC stage. Another contribution of this paper is to utilize digital control as a simple solution to achieve multimode control, including resonant lamp ignition, LFSW transitions, and lamp current and power regulation. Index Terms Acoustic resonance, digital control, dimming control, low-frequency square-wave (LFSW) converter, metal halide (MH) lamps, resonant ignition. I. INTRODUCTION THE PRIMARY motivation for using a low-frequency square-wave (LFSW) drive in electronic ballasts is to avoid the excitation of acoustic resonances in metal halide (MH) lamps. The MH lamp has become very popular as a practical light source for general and specific applications due to its high efficacy, compact design, and superior color rendering properties. LFSW electronic ballasts are an alternative to resonant converters and, theoretically, provide a definitive solution to prevent acoustic resonance, provided that the lamp power has no ac component. The frequencies at which acoustic resonances appear depend on the size of the arc tube, gas pressure, and its composition, and they may vary with the lamp aging. The elements that compose the gas enclosed in the vessel determine the lamp chromatic rendering; in this way, a more complete spectrum of the light source requires a more complex composition of the lamp gas that presents more resonant modes. Standard solutions for LFSW high-intensity discharge (HID) lamp drivers over 100 W require three power conversion stages plus a lamp igniter circuit, as shown in Fig. 1(a). The three converter stages include the following: 1) a power factor correction (PFC) stage [1], [2]; 2) a current-mode-controlled dc dc converter; and 3) a full-bridge (FB) inverter. The additional lamp igniter circuit is required to achieve a sufficiently high voltage for lamp ignition [3], [4]. A two-stage solution with an external igniter circuit is presented in [5] where the lamp current control provides the required system stability. The proposed two-stage solution with integrated lamp ignition is shown in Fig. 1(b). All three functions from Fig. 1(a) of stages 2 and 3 and the igniter circuit are integrated in a single FB stage. Lamp ignition is achieved without an additional igniter circuit by operating the FB during start-up as a high-frequency resonant inverter. After ignition, the converter operates as an LFSW inverter by controlling the FB as a buck converter and supplying alternately positive or negative current to the lamp. Lamp power is regulated by adjusting the average current supplied by the PFC stage [6]. A simple digital microcontroller is used to achieve multimode control, including resonant lamp ignition, LFSW transitions, and lamp current and power regulation. Sampled signals from a single current sense resistor R g are used in LFSW mode as inputs to two key control loops, as shown in Fig. 1(b). A fast proportional inner current control loop regulates the buck converter inductor current to provide stability to the lamp, and a slow power regulation loop maintains the steady-state lamp power. The operating modes of the converter and the controller are described in Section II, followed by design constraints and guidelines for the LC filter in the FB converter in Section III. Converter models and controller design are provided in Section IV. Experimental results are presented in Section V, demonstrating complete ballast system operation driving a 150-W MH lamp. Manuscript received February 8, 2008; revised June 17, 2008. First published July 9, 2008; last published August 29, 2008 (projected). This work was supported in part by the Spanish Government under project CICYT TEC2008-01753: Digital power processing for the control of gaseous discharges and in part by the National Science Foundation under project CAREER: Modeling, Control, and Design of Energy-Efficient Lighting Systems. F. J. Díaz, F. J. Azcondo, R. Casanueva, and C. Brañas are with the Department of Electronics Technology, Systems and Automation Engineering, University of Cantabria, 39005 Santander, Spain (e-mail: diazrf@unican.es; azcondof@unican.es; casanuer@unican.es; branasc@unican.es). R. Zane is with the Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO 80309-0425 USA (e-mail: regan.zane@ colorado.edu). Digital Object Identifier 10.1109/TIE.2008.927959 II. BALLAST AND CONTROLLER OPERATING MODES The inverter switching frequency is denominated f isw, and the square output voltage is symmetric, 50% positive and negative, in the different modes. The converter operation is summarized in the flowchart of the dspic30f2010 program in Fig. 2. The microcontroller program starts with the ignition sequence until the lamp turns on, and then, the converter is operated in resonant inverter mode during the warm-up time. Finally, it changes to LFSW mode with double loop control. The FB has two different operation modes. 0278-0046/$25.00 2008 IEEE

JAVIER DÍAZ et al.: DIGITAL CONTROL OF A LOW-FREQUENCY SQUARE-WAVE ELECTRONIC BALLAST 3181 Fig. 1. Square-wave electronic ballast. (a) Design with three stages. (b) Proposed design where stage 1 is a power factor corrector stage and stage 2 is an FB that works as a resonant or an LFSW inverter according to the state of the lamp. A. FB Converter Operation as Resonant Inverter The bridge converter, the inductor L, and the capacitor C form a parallel resonant inverter before the lamp ignition. During the ignition sequence, resonant inverter operation is obtained, and, in this mode, f isw is higher than the resonant frequency f o of the LC filter [see Fig. 1(b)] when the lamp is off, and it gradually approaches f o, where the voltage gain is high enough to produce the discharge. The microcontroller generates the transistor drive signals shown in Fig. 3. The lamp ignition occurs above the unloaded resonant frequency of the LC circuit f o =1/2π LC. (1) One benefit of sweeping the frequency for ignition is that the lamp voltage rate of rise is properly controlled, and as a result, the required overvoltage to achieve the ignition is reduced [7] [12]. Part of the lamp warm-up is also carried out using the highfrequency inverter mode and is achieved during resonant converter operation at constant lamp current. During ignition and warm-up, the duty cycle control is disabled, and the converter operates as a traditional FB resonant inverter. B. FB Converter Operation as LFSW Ballast After lamp ignition and warm-up, the control circuit enters in LFSW mode, where the bridge converter is driven alternately as a positive and negative buck converter (see Figs. 4 6). The buck converter switching frequency f sw =1/T f o is constant. Control signals of the FB transistors for the buck operation modes are defined in Fig. 4. In the LFSW mode, the duty cycle d = t on /T is regulated to control the inductor current i and stabilize the lamp current in the short term, and to regulate i g in the long term for power adjustment and dimming control if required. The inductor L and the capacitor C define the converter lowpass filter that limits the ac component of the lamp power below the level that can excite acoustic resonance. Current mode control is achieved by regulating the inductor current i, which is the PFC output current i g during dt, sensed by R g (see Figs. 5 and 6). The inductor current i circulates, as shown in Fig. 5, with the continuous line during dt time and the discontinuous line during (1 d)t time. In addition, Fig. 6 shows the positive buck (positive lamp current) and negative buck (negative lamp current) operation modes. Since the buck converter input current i g is pulsating, as showninfig.6,duringontime(dt ), the inductor current is sampled at R g (i ) and is multiplied by d to obtain the sampled average input current i g. The inner high-speed current loop provides the ballast action since it stabilizes the lamp current, which is assumed to be equal to the average inductor current i, resulting in high output impedance for the inverter. The outer power loop provides the current reference i ref to the inductor current loop to achieve the designed lamp power. The power

3182 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 9, SEPTEMBER 2008 Fig. 2. Control program flowchart. Fig. 3. FB transistor drive signals during start-up sequence and warm-up of the lamp. sample data is i g, provided that the PFC output voltage V g is considered constant (see Fig. 5). The power mode control does not necessitate high-speed performance [13] [15]. The generation of open-loop transitions from positive to negative current through the lamp and vice versa is proposed to achieve the maximum transition speed. In this way, there is Fig. 4. Control signals of the FB transistors. (a) For the positive lamp current (positive buck). (b) For the negative lamp current (negative buck). no reignition effect even at very low f isw. Since the duty cycle does not change, the transition response depends on the quality factor of the filter LC loaded with the lamp. The control circuit detects the end of the transition to retake the current and power mode control. III. LC FILTER DESIGN The LFSW converter operation generates an ac component whose amplitude in steady state at the fundamental (switching)

JAVIER DÍAZ et al.: DIGITAL CONTROL OF A LOW-FREQUENCY SQUARE-WAVE ELECTRONIC BALLAST 3183 Therefore, the resulting amplitude of the ac component of the lamp power at the switching frequency is ˆP ac,fsw = 2DV g ˆV ac,fsw G (jf sw ) R lamp. (5) To prevent the excitation of acoustic resonant modes, the limitation ˆP ac,fsw <kp lamp (6) is imposed. This limitation is based on the acoustic resonance studies in [16] and [17], where a typical value for the parameter k to prevent the excitation of acoustic resonance under any condition is k<5%. The requirement for the low-pass filter is then derived from Fig. 5. Input (i g) and inductor (i) current direction, in continuous line during dt time and in discontinuous line during (1 d)t time. (a) Positive buck. (b) Negative buck. 2DV g ˆVac,fsw G(jf sw <k (DV g) 2 + R lamp and, using (2), leads to ˆV 2 ac,fsw G(jf sw 2 R lamp = k (DV g) 2 R lamp (7) G(jf sw ) < kπd 4sin(Dπ). (8) Fig. 6. Steady-state current waveforms. Above: Inductor current. Below: PFC front-end output current. (a) Positive buck. (b) Negative buck. frequency is ˆV ac,fsw = 2V g sin(dπ). (2) π The low-pass filter gain at the switching frequency G(jf sw ) reduces the ac component of the lamp voltage, which generates ac power amplitude supplied to the lamp at twice the switching frequency. By using the fundamental approximation p lamp = [ DV g + ˆV ] 2 ac,fsw sin(ω sw t) G(jf sw ) (3) R lamp where the magnitude of the buck filter response at the switching frequency is given by G(jf sw ) = ( 1 ( fsw f o 1 ) ). (4) 2 2 ( ) 2 + 1 fsw Q 2 fo As an illustrative example, the LC filter design for a converter that drives a 150-W HID lamp is presented. Step 1) Collect input data. PFC output voltage, i.e., LFSW converter input voltage and lamp equivalent resistance data are collected. V g = 400 V, which is the common value for a boost-based PFC, and the equivalent lamp resistance ranges from R lamp,min =50Ω (new lamp) to R lamp,max = 150 Ω at the end of its lifetime. Step 2) Estimate the duty cycle. The required duty cycle to supply the rated lamp power is calculated. In this case, the duty cycle varies from D =0.22 (new lamp) to D =0.38 (old lamp). Step 3) Determine filter gain. For the specified k<5%, the filter gain is calculated resulting in G(jω sw ) < 37.4 db for D =0.22 and G(jω sw ) < 35.9 db for D =0.38. A practical solution for (8) considering the lamp lifetime is G(jω sw ) < 40 db leading to ω sw =10ω o. Step 4) Select the filter quality factor. Inductor and capacitor values are chosen to obtain the characteristic impedance Z = L C (9) which limits the resonant current during the ignition sequence, and a quality factor Q that results in a fast and nonoscillatory transient from positive to

3184 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 9, SEPTEMBER 2008 Fig. 7. Gain (in decibels) of the double-pole low-pass filter around f o for different R lamp s (50, 75, 100, and 150 Ω). Fig. 8. Block diagram of the proposed digital power control. negative buck converter and vice versa. The practical limit of the quality factor is Q max = R max. (10) Lω o Q max =1.2 is selected in order to limit the lowfrequency transient oscillations. Step 5) Select the switching frequency. A practical upper limit for the switching frequency is ω sw =2π 200 krad/s to avoid excessive switching losses, which results in ω o =2π 20 krad/s. Step 6) Calculate filter components. By using (10), L = 995 µh, and with (9), C =63.6 nf. A simulation of this case is shown in Fig. 7. IV. CONVERTER MODELING AND CONTROLLER DESIGN As aforementioned, the implementation of a suitable regulation of the lamp should solve the ballast performance in the short and long terms. The proposed solution is to use a fast current mode control that stabilizes the lamp arc and a slow power mode control that regulates the nominal lamp power and implements dimming control [18], [19], as shown in Fig. 8. Since i = i g during dt (on time), the inductor current can be captured at R g [see Fig. 1(b)] for the current loop. The power control variable is the average input current i g, which is calculated by multiplying the dc bus current sampled during the on time i by the duty cycle d, giving i g. By considering the buck converter and assuming that the ripple of the PFC output voltage V g is negligible, the averaged model equation is described by dv g ν Ts sl = i Ts (11) where the average inductor current i Ts is the variable to control to achieve the current mode control. The resulting averaged small-signal model is given by ˆdV g ˆν = î. (12) sl Equation (12) analyzes the effects of the perturbations of the duty cycle and output voltage on the inductor current i. The desired small-signal control transfer function from duty cycle to inductor current is derived introducing (13) in (12) and is given by z lamp ˆν = î (13) 1+sCz lamp G id (s) =î ˆd = V g z lamp 1+sCz lamp 1+s L z lamp + s 2 LC (14)

JAVIER DÍAZ et al.: DIGITAL CONTROL OF A LOW-FREQUENCY SQUARE-WAVE ELECTRONIC BALLAST 3185 Fig. 9. Experimental small-signal response with the frequency of 150-W HID lamp. The gain is in continuous line, and the phase is in dashed line. Fig. 10. phase. Estimated Bode plot of G id (s). Above: gain in decibels. Below: where z lamp is the lamp incremental impedance [20] [22]. The experimental small-signal response of 150-W HID lamp is shown in Fig. 9. The gain and phase of the transfer function given in (14) is shown in Fig. 10. This model, where a resistive load is considered, is valid in a rather restricted range of frequencies. The continuous averaged model results in a transfer function that fits the discrete model in a frequency range up to f sw /30 with no significant error in gain and phase. On the other hand, due to the lamp behavior, the frequency range where z lamp behaves as positive impedance is minimum [22]. For the case presented, it is considered that G id in (14) is valid from approximately 3 to 10 khz, i.e., between the dashed lines in Fig. 10, which is also the target frequency area to locate the crossover frequency of the current control loop gain. For the power mode control, it is considered that P lamp = η lfsw V g i g (15) i g = d i (16) Fig. 11. Top: measured input current ν sen = i gr g. Middle: input current i g. Bottom: transistor drive signal ν gs. where η lfsw is the efficiency of the LFSW converter, and the reference for the average inductor current i ref (see Fig. 2) is the variable under control for power mode operation. In Fig. 11, the transistor drive signal ν gs, the input current i g, and its sample R g i g = ν sen are shown. Provided that the buck converter is operating in continuous conduction mode with small i, one sample of i during dt is valid to obtain the average inductor current with a sufficiently small error. Controlled transition from positive to negative lamp current and vice versa may lead to a slow transient that might produce reignition, flickering effect, and low-frequency harmonics [23]. As an example, in [24], a pulsewidth modulation (PWM) controller modulates the output current with a square wave whose rising time is several times that of the buck converter switching period. In this paper, to achieve the fastest transient, an openloop transition is proposed. As L and C form a low-pass filter loaded with R lamp, the step response depends on the quality factor. If the quality factor Q is between 0.4 and 1.2 (see Fig. 7), the desired output voltage step response, around the critical damping, is obtained.

3186 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 9, SEPTEMBER 2008 Four operation modes are distinguished according to the type of the drive signals generated for the switches. A. Soft Start-Up Ignition Sequence Mode The frequency sweep from 100 to 23 khz is performed for the FB resonant inverter. When the lamp is off, the FB switches V g at a high frequency, the lamp voltage ν is sinusoidal, and the switching frequency f isw is reduced to approach f o until ν reaches the ignition voltage. In the case of hot restrike or simply when the ignition fails, the frequency sweep is restarted before excessive overvoltage is reached, and the sweep is repeated until the lamp ignition is achieved. The sweep is until 23 khz to avoid an output voltage higher than 1600 V during lamp start-up. B. Warm-Up Mode When the lamp ignition is detected, the circuit provides a fixed switching frequency slightly above the unloaded resonant frequency during a specified period. The warm-up time is 240 s for 150-W high pressure sodium (HPS) lamps and 30 s for 150-W MH lamps. The lamp ignition generates a signal that keeps f isw near and above f o during the lamp warm-up. If the ignition fails or a significant decrease in the input current is detected, the ignition sequence is repeated. C. LFSW: Positive and Negative Buck Modes After the lamp warm-up, f isw is shifted to a low frequency, and the lamp voltage becomes a square wave. Current and power mode controls are then activated to regulate the average inductor current and the average lamp power [25] [27]. The control circuit establishes an alternate operation of the FB inverter as a positive and negative buck converter with a frequency of 200 Hz. A dead time is included to assure safe operation. Positive and negative buck modes are achieved, generating the corresponding drive signal at f sw = 200 khz, as shown in Fig. 4. In positive and negative buck modes, the inductor current control and the power mode control are activated. An equivalent for the digital inductor current control loop gain T d in the continuous time domain is T d (s) =G c (e st 1 )H(s)G id (s)e st d (17) where G c (z) is the discrete-time compensator with z = e st 1, T 1 =2/f sw is the sampling period, and e st d represents the total delay of the controller from the input current sampling instant to the time of corresponding duty cycle actuation. The sample constant is H(s) =0.25. The sample frequency is set to half of the buck converter switching frequency, with sampling instants just prior to the end of the duty cycle. The gains of the input current A/D converter and DPWM modulator are assumed to be unity. Based on G id (s) given in (14), and as shown in Fig. 9, the inductor current loop requires a simple proportional compensator to stabilize the electrical discharge, achieving the required bandwidth. By assuming a total controller delay of Fig. 12. (a) Controlled system and (b) equivalent reduced controlled system. one sample t d = T and a desired loop gain crossover frequency of f c =5kHz, a suitable discrete-time compensator is given by G c (s) =k c =0.5. Discretization requires the verification that no limit cycling condition [28] [30] is produced or at least that one bit oscillation around the operation point causes minimum disturbances to the system, in this case lamp flickering. The resolution of the sampled current i is that one bit increment means I =10 ma, whereas the 10-b DPWM resolution is that one bit increment ( D) produces I =5 ma, i.e., P lamp = 433 mw over P lamp = 150 W. Therefore, the duty cycle resolution is higher than the analog-to-digital conversion. Integral action to achieve zero error is performed by the outer loop. On the other hand, the power loop requires a simple integrator to achieve zero error lamp power control. T 2 = 250 T 1 is the sampling time selected for this loop G p (s) =0.2 s +105. (18) s The controlled system is shown in Fig. 12(a) that is reduced to the equivalent system in Fig. 12(b), where G ip (s) in Fig. 13(b) is the transfer function of the inductor current loop G ip (s) = i i ref = [ ] Td (s)/h(s) 1+T d (s) (19) and T d is given in (17). A stability analysis of the current loop using the SISO design tool of MATLAB is shown in Fig. 13(a), whereas Fig. 13(b) shows the stability analysis of the power loop. Zero-order hold (ZOH) and bilinear transformation (BLT) were used to obtain the equivalent of G p (s) in the z domain, for the z-transform of the G p (s) to obtain G pzoh (z) and G pblt (z), respectively, G pzoh (z) =0.2 z (20) z 1 G pblt (z) =0.3 z 0.332. (21) z 1

JAVIER DÍAZ et al.: DIGITAL CONTROL OF A LOW-FREQUENCY SQUARE-WAVE ELECTRONIC BALLAST 3187 Fig. 13. Bode diagram and root locus of (a) the inductor current loop with the controller G c(s) and (b) power + current loop with controllers G c(s) and G p(s). In this case, G pzoh (z) is used as it is easier to implement by software than G pblt (z) with minimal error. The corresponding digital current control algorithm is given by d[n] =0.5(i [n] i ref ). (22) Moreover, the digital power control algorithm is given by i ref [n] =i ref [n 1] + 0.2e p [n] (23) where e p [n] is e p [n] =i g[n] i gref (24)

3188 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 9, SEPTEMBER 2008 Fig. 14. LFSW electronic ballast controlled by the microcontroller dspic30f2010. where i is the inductor current sample, i ref is the inductor current reference for current loop, i g is the input current sample, and i gref is the input current reference for power loop. i gref = P gref = P lamp (25) V g η lfsw V g where P gref and P lamp are the input and lamp target power, respectively, and η lfsw is the efficiency of the converter that is considered constant in control law. V. E XPERIMENTAL RESULTS The power stage is implemented according to the schematic shown in Fig. 14. Switches S1 and S3 are implemented using a new generation of insulated-gate bipolar transistors, HGTP12N60A4D, which have a good switching frequency performance with anti-parallel hyperfast diodes D1 and D3. In order to achieve high efficiency at a switching frequency of 200 khz, HEXFET Power MOSFETs, IRFP340, are adequate to implement S2 and S4 with antiparallel diodes D2 and D4. Gate drive signals are generated with two IR2110 drivers, and a dead time of 1 µs is selected for the inverter to prevent cross conduction between the upper and lower transistors. The inductor (1.3 mh) of the LC filter uses an E42 core size, material N27, and the capacitor is a 1600-V metallized polypropylene film, 47 nf [31]. The number of turns of the inductor L is calculated to prevent core saturation during the ignition sequence, where the flux density in the core is the maximum. On the other hand, the copper section is calculated according to the inductor current in steady state. Two types of lamps have been used to verify the ballast performance: 150-W MH lamp (SYLVANIA) HSI-TD Metalarc and 150-W HPS lamp (PHILIPS), whose nominal electrical parameters are V lamp = 100 V rms and I lamp =1.5 A rms. The digital control circuit is implemented in a dspic30f2010 whose clock frequency is 120 MHz. The dspic has peripheral Fig. 15. Digitally controlled ignition sequence and detail of the breakdown instant. Top: lamp voltage V lamp. Bottom: lamp current I lamp. capabilities, including six PWM outputs and ADC with 10-b resolution, 154-ns sample and hold time, and 2-µs conversion time. The value of the sense resistor is R g =0.5 Ω. Experimental results are given for a 150-W MH lamp and include the resonant lamp ignition sequence where a close to 1-kV ignition voltage is shown in Fig. 15 and a square wave operation is shown in Fig. 16. As comparative data, the typical ignition voltage is 4 kv for 150-W MH lamp and 2.7 kv for 150-W HPS lamps using peak ignition voltage. Overcurrent causes power spikes that make the instantaneous p lamp differ from the ideal constant value. The ac component of the lamp power is under the specified 5% [16], [17], and no acoustic resonances have been observed. Fig. 17 shows the lamp waveforms under dimming control when P lamp is reduced to 90 W. Transitions of the current through the lamp are shown in Fig. 18. Despite the low-frequency operation, in contrast to the case when the lamp is supplied through other low-frequency ballasts, fast transitions do not produce lamp reignition as is shown in the

JAVIER DÍAZ et al.: DIGITAL CONTROL OF A LOW-FREQUENCY SQUARE-WAVE ELECTRONIC BALLAST 3189 Fig. 16. Experimental waveforms in steady-state operation. Top: lamp voltage (Ch1) V lamp. Middle: lamp current (Ch2) I lamp. Bottom: lamp power (M1) P lamp. Fig. 19. Fast transition that does not produce lamp reignition. Horizontal axis: lamp voltage (Ch1) V lamp. Vertical axis: lamp current (Ch2) I lamp. Fig. 17. Experimental waveforms in steady state under dimming control operation. Top: lamp voltage (Ch1) V lamp. Middle: lamp current (Ch2) I lamp. Bottom: lamp power (M1) P lamp. Fig. 20. Transition from resonant to LFSW mode. Top: lamp voltage (Ch1: 100 V/div) and lamp current (Ch2: 2 A/div) I lamp, time/div: 40 ms. Bottom: zoom of lamp voltage (Ch1: 100 V/div) and lamp current (Ch2: 2 A/div) I lamp, time/div: 400 µs. Fig. 18. Transitions from (left) positive to negative and (right) negative to positive current through the lamp which depend on the quality factor of the filter. Top: lamp voltage (Ch1) V lamp. Middle: lamp current (Ch2) I lamp. Bottom: lamp power (M1) P lamp. measured i lamp versus ν lamp characteristic given in Fig. 19. The transition from resonant to LFSW mode is stable, as shown in Fig. 20. For the switching frequency utilized during the warmup time in the resonant converter mode, no acoustic resonances have been observed in the tested MH and HPS lamps. The Fig. 21. Experimental waveforms in steady-state operation. Top: sensed i g. Middle: t sh is a sample and hold time, and t c is a converter time. Bottom: transistor-driven signal. situation when the microcontroller takes the sample of input current is shown in Fig. 21. The sample and hold time required by the ADC to obtain correct data is only 154 ns. The possibility

3190 IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS, VOL. 55, NO. 9, SEPTEMBER 2008 Fig. 22. Experimental waveforms in steady-state operation under power loop of an old lamp. Top: lamp voltage (Ch1) V lamp. Middle: lamp current (Ch2) I lamp. Bottom: lamp power (M1) P lamp. Fig. 23. (a) Arc of the HPS lamp, in this case a straight line. (b) Arc of the MH lamp. of controlling the time where the sampling is produced enables noisy zones to be avoided, i.e., during the transistor switching. In order to verify the power loop control under load changes, as shown in Fig. 22, the lamp has been replaced by an old lamp. The arcs in HPS and MH lamps are shown in Fig. 23(a) and (b) respectively, where no arc distortion appears. The efficiency of the LFSW section measurement is around 92% and corresponds to a prototype that verifies the proposed new control technique and is not optimized for maximum efficiency. VI. CONCLUSION A new digitally controlled LFSW ballast using a single FB circuit for both low-frequency drive and resonant lamp ignition has been presented. One of the benefits of this electronic ballast is the reduction of components due to use of digital control and fewer power stages than similar ballasts. In this way, the proposed converter is a universal solution for different lamps of the same wattage (HPS and MH lamps). The digital control defines three operation modes: as a resonant inverter to achieve the lamp ignition and initiate the warm-up, and as a positive and negative buck converter during the LFSW operation mode. The buck converter operation is both inductor current controlled to stabilize the lamp operation in the short term (ballast action) and input power controlled to provide constant lamp power during the lamp lifetime (long term). The design of the LC filter assures a quality factor that limits the resonant current during the ignition and generates the fastest transitions of the LFSW around the critically damped behavior. Experimental results confirm the system stability with different lamp types and aging and that fast low-frequency transitions of the lamp current do not produce lamp reignition effects. No light arc distortion has been observed, and the lamp power is accurately established in nominal conditions and under dimming control operation. REFERENCES [1] S. Choi, K. Lee, and B. Cho, Design of fluorescent lamp ballast with PFC using a power piezoelectric transformer, IEEE Trans. Ind. Electron., vol. 52, no. 6, pp. 1573 1581, Dec. 2005. [2] F. J. Azcondo, C. Brañas, R. Casanueva, and S. Bracho, Power-modecontrolled power-factor corrector for electronic ballast, IEEE Trans. Ind. Electron., vol. 52, no. 1, pp. 56 65, Feb. 2005. [3] J. D. Paul and R. Redl, Electronic ballast for HID lamps, in Proc. APEC Professional Education Seminar, San Jose, CA, Mar. 5, 1996. [4] C. M. Huang, T. J. Liang, R. L. Lin, and J. F. Chen, Constant power control circuit for HID electronic ballast, in Conf. Rec. IEEE IAS Annu. Meeting, Oct. 2005, vol. 2, pp. 1193 1197. [5] M. Shen, Z. Qian, and F. Zheng, Design of a two-stage low-frequency square-wave electronic ballast for HID lamps, IEEE Trans. Ind. Appl., vol. 39, no. 2, pp. 424 430, Mar./Apr. 2003. [6] F. J. Diaz, F. J. Azcondo, C. Branas, R. Casanueva, and R. Zane, Control of low-frequency square-wave electronic ballast with resonant ignition using a dspic30f2010, in Proc. IEEE ISIE, Jun. 2007, pp. 3019 3024. [7] C. Brañas, F. J. Azcondo, and S. Bracho, Experimental study of HPS lamp ignition by using LC network resonance, in Proc. IEEE IECON, Nov. 2002, vol. 1, pp. 473 478. [8] R. Guo, Y. Yang, and Z. Quian, Investigation on the start-up of low wattage metal halide lamp controlled by low frequency square wave ballast, in Proc. IEEE IECON, Nov. 2005, pp. 815 819. [9] M. A. Dalla Costa and R. N. Do Prado, Lamp improved arrangement in the half-bridge topology, IEEE Trans. Ind. Electron., vol. 53, no. 5, pp. 1754 1756, Oct. 2006. [10] M. Doshi, J. Bian, R. Zane, and F. J. Azcondo, Low frequency architecture for multi-lamp CCFL systems with capacitive ignition, in Proc. IEEE APEC, Mar. 6 10, 2005, vol. 2, pp. 1072 1078. [11] J. Garcia Garcia, J. Cardesin, J. A. Martin-Ramos, M. A. Dalla-Costa, J. M. Lopera, and A. J. Calleja, Series igniters effects in metal halide lamps operation with high frequency ballasts: Study and minimization, IEEE Trans. Power Electron., vol. 22, no. 3, pp. 889 898, May 2007. [12] T. S. Cho, N. O. Kwon, Y. M. Kim, H. S. Kim, S. J. Kim, J. G. Kang, E. H. Choi, and G. Cho, Capacitive coupled electrodeless discharge backlight driven by square pulses, IEEE Trans. Plasma Sci., vol. 30, pt. 2, no. 5, pp. 2005 2009, Oct. 2002. [13] F. J. Azcondo, F. J. Díaz, R. Casanueva, and C. Brañas, Microcontroller power mode stabilized power factor correction stage for electronic ballast applied to metal halide lamps, in Proc. IEEE IECON, Nov. 2006, pp. 1733 1738. [14] C.-M. Huang, T.-J. Liang, R.-L. Lin, and J.-F. Chen, A novel constant power control circuit for HID electronic ballast, IEEE Trans. Power Electron., vol. 22, no. 3, pp. 854 862, May 2007. [15] F. J. Azcondo, F. J. Díaz, R. Casanueva, and C. Brañas, Microcontroller power mode stabilized power factor correction stage for high intensity discharge lamp electronic ballast, IEEE Trans. Power Electron., vol. 22, no. 3, pp. 845 853, May 2007. [16] W. Yan, Y. K. E. Ho, and S. Y. R. Hui, Investigation on methods of eliminating acoustic resonance in small wattage high-intensity-discharge (HID) lamps, in Conf. Rec. IEEE IAS Annu. Meeting, Oct. 2000, vol. 5, pp. 3399 3406.

JAVIER DÍAZ et al.: DIGITAL CONTROL OF A LOW-FREQUENCY SQUARE-WAVE ELECTRONIC BALLAST 3191 [17] J. Olsen and W. P. Moskowitz, Optical measurements of acoustic resonance frequencies in HID lamps, in Conf. Rec. IEEE IAS Annu. Meeting, Oct. 1997, vol. 3, pp. 2263 2269. [18] Y. Chen, W. Lin, and Y. Liu, Analysis and design of a dimmable electronic ballast controlled by a switch-controlled capacitor, IEEE Trans. Ind. Electron., vol. 52, no. 6, pp. 1564 1572, Dec. 2005. [19] C.-H. Lin, Digital-dimming controller with current spikes elimination technique for LCD backlight electronic ballast, IEEE Trans. Ind. Electron., vol. 53, no. 6, pp. 1881 1888, Dec. 2006. [20] M. A. Dalla Costa, J. M. Alonso, J. Ribas, J. Cardesín, and J. García, Small-signal characterization of acoustic resonances in low-wattage metal halide lamps, in Proc. IEEE PESC, Jun. 2005, pp. 1469 1475. [21] E. Deng and S. Cuk, Negative incremental impedance and stability of fluorescent lamps, in Proc. IEEE APEC, Feb. 1997, vol. 2, pp. 1050 1056. [22] J. Ribas, J. M. Alonso, A. J. Calleja, E. Lopez, J. Cardesin, J. Garcia, and M. Rico, Small signal dynamic characterization of HID lamps, in Conf. Rec. IEEE IAS Annu. Meeting, Oct. 2002, vol. 2, pp. 1489 1493. [23] M. Manana, A. Ortiz, C. Renedo, S. Perez, F. Delgado, F. J. Azcondo, F. J. Diaz, C. Brañas, and R. Casanueva, Comparison of flicker sensitivity in HPS lamps, in Proc. IEEE ISIE, Jun. 2007, pp. 3002 3007. [24] J. Ribas, J. M. Alonso, A. J. Calleja, E. López, J. Cardesín, J. García, and M. Rico, Arc stabilization in low-frequency square-wave electronic ballast for metal halide lamps, in Proc. IEEE APEC, Feb. 2003, pp. 1179 1184. [25] Y. Yin and R. Zane, Digital controller design for electronic ballasts with phase control, in Proc. IEEE PESC, Jun. 2004, vol. 3, pp. 1855 1860. [26] R. Lin and M. Yeh, Inductor phase feedback for phase-locked loop control of electronic ballasts, in Conf. Rec. IEEE IAS Annu. Meeting, Oct. 2005, vol. 4, pp. 2763 2769. [27] B. Bryant and M. K. Kazimierczuk, Voltage-loop power-stage transfer functions with MOSFET delay for boost PWM converter operating in CCM, IEEE Trans. Ind. Electron., vol. 54,no.1, pp.347 353,Feb. 2007. [28] I. K. Lee and B. H. Cho, A new control method for a low frequency inverter of MHD lamp ballasts with a synchronous rectifier, in Proc. IEEE APEC, Mar. 2005, pp. 1060 1064. [29] H. Peng, A. Prodic, E. Alarcon, and D. Maksimovic, Modeling of quantization effects in digitally controlled dc dc converters, IEEE Trans. Power Electron., vol. 22, no. 1, pp. 208 215, Jan. 2007. [30] D. H. J. van Casteren, M. A. M. Hendrix, and J. L. Duarte, Controlled HID lamp ballast interaction for low-frequency square-wave drivers, IEEE Trans. Power Electron., vol. 22, no. 3, pp. 780 788, May 2007. [31] C.-H. Lin, Y. Lu, H.-J. Chiu, and C.-L. Ou, Eliminating the temperature effect of piezoelectric transformer in backlight electronic ballast by applying the digital phase-locked-loop technique, IEEE Trans. Ind. Electron., vol. 54, no. 2, pp. 1024 1031, Apr. 2007. F. Javier Díaz was born in Torrelavega, Spain, in 1973. He received the M.S. degree in electrical and control engineering from the University of Cantabria, Santander, Spain, in 1998, where he is currently working toward the Ph.D. degree in electronics engineering. Since 1998, he has been an Assistant Professor with the Department of Electronics Technology, Systems and Automation Engineering, University of Cantabria. His research interests include design, modeling, and control of switch-mode power converters for discharge lamps and topologies for power factor correction applications. Francisco J. Azcondo (S 90 M 92 SM 00) was born in Santander, Spain, in 1965. He received the M.S. degree in electrical engineering from the Universidad Politécnica de Madrid, Madrid, Spain, in 1989, and the Ph.D. degree from the University of Cantabria, Santander, in 1993. From 1990 to 1995, he worked on the design of highly stable quartz crystal oscillators. Since 1995, he has been an Associate Professor with the Department of Electronics Technology, Systems and Automation Engineering, University of Cantabria. His research interests include switch-mode power converters and their control for discharge lamps, electrical discharge machining, and power factor correction applications. Rosario Casanueva (M 04) received the M.S. and Ph.D. degrees in physics from the University of Cantabria, Santander, Spain, in 1991 and 2004, respectively. From 1991 to 1993, she worked on the design of highly stable quartz crystal oscillators. Since 1993, she has been an Assistant Professor with the Department of Electronics Technology, Systems and Automation Engineering, University of Cantabria. Her research interests include digital and analog microelectronic circuit design, switch-mode power converters, resonant converters, and their control for electrical discharge machining and discharge lamp applications. Christian Brañas (M 03) received the M.S. degree in electronics engineering from the Instituto Superior Politécnico José A. Echeverría (ISPJAE), Havana, Cuba, in 1992, and the Ph.D. degree in electronics engineering from the University of Cantabria, Santander, Spain, in 2001. From 1992 to 1995, he was an Instructor Professor with the ISPJAE. Since 1995, he has been with the Department of Electronics Technology, Systems and Automation Engineering, University of Cantabria, where he is currently an Assistant Professor. His research interests include the design, modeling, and control of resonant inverters and switch-mode power supplies. Regan Zane (M 99 SM 07) received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Colorado, Boulder, in 1996, 1998, and 1999, respectively. From 1999 to 2001, he was a Senior Research Engineer with the GE Global Research Center, Niskayuna, NY. At GE, he developed custom integrated circuit controllers for power management in electronic ballasts and lighting systems. He joined the University of Colorado as a Faculty Member in 2001 and is currently an Associate Professor of electrical engineering with the Department of Electrical and Computer Engineering. At the university, he has ongoing research programs in energy-efficient lighting systems, adaptive and robust power management systems, and lowpower energy harvesting for wireless sensors.