Design of a digitally-controlled LLC resonant converter

Jia-Wei huang1, Shun-Chung Wang 2 and Yi-Hua Liu1 1National Taiwan University of Science and Technology, Taipei, Taiwan, R.O.C.

2 Lunghwa University of Science and Technology, Taoyuan County, Taiwan, R.O.C.

Abstract. Nowadays, liquid crystal display (LCD) panels are widely used in applications such as monitors, notebooks and televisions. In large scale LCD TV (>30”), the power supply typically requires an output power ranges from 200 W to 600 W. Generally, a half-bridge LLC resonant converter with zero voltage switching (ZVS) capability is utilized as the DC/DC power stage. In this paper, the design of a digitally-controlled LLC resonant converter is presented. The LLC resonant topology allows for ZVS of the main switches, thereby dramatically lowering switching losses and boosting efficiency. A digital signal controller (dsPIC30F2020) from Microchip corp. is utilized as the digital controller of the LLC resonant converter. In order to design the compensation circuit correctly, the large-signal and small-signal model of the utilized LLC converter is also derived in this paper using the phasor transformation method. Finally, experimental results are presented to validate the correctness of the proposed system.

Keywords: LLC resonant converter, digital control, phasor transformation

1. Introduction Nowadays, liquid crystal display (LCD) panels are widely used in applications such as monitors,

notebooks and televisions [1]-[2]. In large scale LCD TV (>30”), the power supply typically requires an output power ranges from 200 W to 600 W. As the screen area increases, the power required for the 24-Vdc rail continues to rise until it is no longer practical to implement the SMPS using a flyback topology. As a result, a variety of higher-power topologies, including the half bridge LLC topology, has been considered to achieve high efficiency in a compact space with low-EMI generation [3]-[4].

In this paper, the design of a digitally-controlled LLC resonant converter is presented. The LLC resonant topology allows for ZVS of the main switches, thereby dramatically lowering switching losses and boosting efficiency. A digital signal controller (dsPIC30F2020) from Microchip corp. is utilized as the digital controller of the LLC resonant converter. Digital power also provides intelligent adaptability and flexibility to satisfy any complex power requirement with the straightforward ability to monitor, process and adapt to system conditions [5]. In order to design the compensation circuit correctly, the large-signal and small-signal model of the utilized LLC converter is also derived in this paper using the phasor transformation method [6]-[7]. Finally, experimental results are presented to validate the correctness of the proposed system. The measured efficiency of the whole system achieved 87 %.

2. Hardware Description Fig. 1 shows the circuit configuration of the proposed digitalized LLC resonant converter. From Fig. 1,

the whole hardware system can be divided into two major parts: LLC resonant converter DC/DC power stage and digital controller. Detailed descriptions about each part will be given in the following subsections.

2.1. LLC resonant converter The half-bridge LLC resonant topology is utilized in this paper to convert the output voltage of power

factor corrector front stage (typically 400 V) into voltages needed to supply the functional blocks such as backlighting, microprocessor and interfacing circuits, etc. LLC resonant converter is widely used in consumer applications such as LCD TVs or plasma display panels with output power level ranges from 200 W up to 600 W. The advantages of LLC converter include:

• ZVS capability over the entire load range

2011 International Conference on Information and Electronics Engineering IPCSIT vol.6 (2011) © (2011) IACSIT Press, Singapore

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• Lower electromagnetic interference (EMI) • Zero current turnoff of the secondary diodes • No increased component count comparing to conventional half bridge topology. From Fig. 1, the primary side of the LLC converter is a half-bridge configuration. The secondary side is

a center-tapped rectifier followed by a capacitive filter. Switches S1 and S2 are both driven by 50 % duty cycle gating signals, with a small amount of dead time introduced between the consecutive transitions. The circuit has three passive components, Lr, Cr and Lm, where Lm is the magnetizing inductance that acts as a shunt inductor, Lr is the series resonant inductor, and Cr is the resonant capacitor.

Fig. 2 shows the typical waveforms of the presented LLC resonant converter. From Fig. 2, the operation of half of switching cycle can be divided into four modes.

(1) Mode 1 (t0 < t < t1)：at t=t0, S1 turned on. During this mode, output rectifier diode D1 conduct. The transformer voltage is clamped at Vo. Lm is linearly charged with output voltage, so it doesn’t participate resonant during this period and p outV n V= ⋅ . The current Lri and Lmi increases. The energy flows through the resonant tank and transformer and to the load. This mode ends when Lri current is the same as Lmi current. Output current reach zero.

(2) Mode 2 (t1 < t < t2)：at t=t1, , the two inductor current Lri and Lmi are equal. Output current reaches zero. Both output rectifier diodes D1 and D2 is reverse biased. Transformer secondary voltage is lower than output voltage. Output is separated from transformer. During this period, since output is separated from primary, Lm is freed to participate resonant. This mode ends when S1 is turned off.

(3) Mode 3 (t2 < t < t3)：at t=t2, S1 is turned off. During this mode, S1 and S2 are both off. The resonant current Lri charges (discharges) the parasitic capacitance 1ossC ( 2ossC ) of the power switches. When the voltage across 1ossC equals Vin, the body diode of S2 is turned on.

(4) Mode 4 (t3 < t < t4)：The body diode of S2 is turned on in previous mode, which creates a ZVS condition for S2. Gate signal of S2 should be applied during this mode. When S2 is turned on, Lri decreases and this will force secondary diode D2 conduct and iout begin to increase. Also, from this moment, transformer sees output voltage on the secondary side. Lm is clamped with constant voltage p outV n V= − ⋅ , so it doesn’t participate resonant during this period.

For next half cycle, the operation is same as analyzed above and is omitted here.

2.2. Digital controller In this paper, the dsPIC30F2020 digital signal controller (DSC) from Microchip corp. is used to control

the presented LLC resonant converter. The proposed digital power supply offers a new freedom for users to control the power output of the LCD power supply according to the power requirement, this leads to an energy economy. When compared to an analog one, digital control boasts several advantages such as

• the possibility for implementing sophisticated control laws • allows the designer to modify the control strategy without significant hardware modifications • higher tolerance to signal noise and the complete absence of ageing effects or thermal drifts • the possibility to provide man to machine interface (MMI) The digital controller utilized in this paper is a conventional PID controller; the digital control algorithm

can be designed as:

0 1 2( ) ( 1) ( ) ( 1) ( 2)u n u n K e n K e n K e n= − + ⋅ + ⋅ − + ⋅ − (1) where E(n) is the error signal and U(n) is the input signal. It should be noted that the LLC converter works with variable frequency control. This implies that

power flow can be controlled by changing the operating frequency of the converter in such a way that a reduced power demand from the load produces a frequency rise, while an increased power demand causes a frequency reduction. Unlike the conventional PWM control strategies in which the duty cycle is the control variable. For LLC converter, the control variable is the switching frequency. Therefore, for the presented digital controller, the output of PID controller should be fed into the Period register of the utilized PWM

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module while the PDC (duty cycle) register should be set as half the value of that in Period register to obtain 50 % duty cycle.

Fig. 1 Circuit configuration of the digitalized LLC resonant converter

Fig. 2 Typical waveforms of LLC Resonant Converter

3. Small-signal Model of the LLC Resonant Converter In order to design the parameters (Kp, Ki and Kd) of the compensation circuit, a small-signal model

should first be obtained. In this paper, the phasor transformation method as presented in [6] is utilized. In [6], a modified phasor transform as shown in Eq. (2) can be used to apply to variable frequency operation.

( )( ) Re[ ( ) ]sj t dtx t x t e ω∫= (2)

where ( )x t is the time-varying phasor corresponding to x(t), which presents the amplitude of x(t), and ( )s tω is time-varying instantaneous frequency. Using Eq. (2), the phasor equations for resistor, inductor and

capacitor can be derived respectively. Using the same technique, the phasor presentation of a general switching network and a rectifier with a transformer can also be obtained. Since the LLC resonant converter only consists the above-mentioned parts, the large signal and small signal models of the LLC resonant converter can be obtained and are presented in Fig. 3. Using this small-signal model, the transfer function can be derived and the compensation circuit can be designed accordingly. Fig. 4 shows the open loop and close loop bode plot of the presented system. From the close loop bode plot, the cut-off frequency is 20 kHz and the phase-margin is 55.8 degree. The obtained compensation circuit parameters can be described as

2

0

(1 )(1 )( )

(1 )

z

zc c

p

ssG s G s

ωω

ω

+ += ×

+

343.31 105.34 11.89 10 I

P DKs K K s

s s−×≈ + + × = + + (3)

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(a) Large signal model (b) Small-signal model

Fig. 3 Large and small signal model of LLC Resonant Converter

(a) Open loop (b) Close loop

Fig. 4 Open loop and close loop bode plot of the utilized LLC Resonant Converter

4. Experimental Results In order to verify the correctness of the proposed system, some experiments are carried out. Due to

limited space, only selected waveforms are displayed in this section. The specification of the presented prototype system is

1) Input voltage: 400 Vdc 2) Output voltage: 24 Vdc 3) Output current: 14.6 A (350 W) Fig. 5 shows the measured key waveforms of the proposed LLC converter. From Fig. 15, the proposed

system operates in LLC resonant mode correctly. Fig. 6 shows the measured efficiency of the proposed LLC converter. From Fig. 6, the efficiency of the proposed LLC is higher than 87 %. Fig. 7 shows the photo of the proposed system.

(a) light load (3 A) (b) full load (14.6 A)

(VGS：10 V/div, VDS：500 V/div, Vp：500 V/div, ir：2 A/div, Time：10 μs/div) Fig. 5 Measure key waveforms of the proposed LLC converter

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Fig. 6 Measured efficiency of the proposed LLC converter

Fig. 7 Photo of the proposed system

5. Conclusion In this paper, the design of a digitalized LLC resonant converter is presented. Detailed description of the

LLC resonant converter stage and the digital controller is presented. Since the LLC converter works with variable frequency control, the design consideration of implementing frequency control using commercially available microcontroller is also presented. In order to design the compensation circuit correctly, the large-signal and small-signal model of the utilized LLC converter is also derived in this paper using the phasor transformation method. According to the experimental results, the efficiency of the proposed LLC converter is higher than 87 % for the whole load range.

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[2] H. J. Chiu, S. J. Cheng, “LED Backlight Driving System for Large-Scale LCD Panels,” IEEE Trans. on Industrial Electronics, vol. 54, no. 5, Oct. 2007, pp. 2751-2760.

[3] F. Krismer and J. W. Kolar, “Accurate small-signal model for the digital control of an automotive bidirectional dual active bridge,” IEEE Trans. on Power Electronics, VOL. 24, NO. 12, pp. 2756-2768, Dec. 2009.

[4] M. M. Peretz and S. Ben-Yaakov, “Digital control of resonant converters: resolution effects on limit cycles,” IEEE Trans on Power Electronics, VOL. 25, NO. 6, pp. 1652-1661, Jun. 2010.

[5] Yan-Fei Liu; Meyer, E.; Xiaodong Liu, “Recent Developments in Digital Control Strategies for DC/DC Switching Power Converters,” IEEE Transactions on Power Electronics, VOL. 24, NO. 11, pp. 2567-2577, Nov. 2009.

[6] J. Tian, J. Petzoldt, T. Reimann, M. Scherf, G. Deboy, M.Maerz, G.Berger, “Envelope Model for Resonant Converters and Application in LLC Converters,” 2007 European Conference on Power Electronics and Applications, pp.1-7, 2007.

[7] J. Tian, J. Petzoldt, T. Reimann, M. Scherf, G. Berger, “Modelling of asymmetrical pulse width modulation with frequency tracking control using phasor transformation for half-bridge series resonant induction cookers,” 11th European Conference on Power Electronics and Applications (EPE), September, 2005, Dresden, Germany.

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