Novel Design of LLC Resonant Converter with Peak Gain Adjustment

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DOI:_{10.12928/TELKOMNIKA.v14i4.3306} ₁₂₄₂

Novel Design of LLC Resonant Converter with Peak

Gain Adjustment

P. Kowstubha*1, K. Krishnaveni2, K. Ramesh Reddy3 1,2

Department of Electrical and Electronics Engineering, Chaitanya Bharathi Institute of Technology, Hyderabad, India

Department of Electrical and Electronics Engineering, G.Narayanamma Institute of Technology and Science, Hyderabad, India

*Corresponding author, e-mail: kowstubha.p@gmail.com1, krishnaveni2k12.rvr@gmail.com2, kollirameshreddy@yahoo.com3

Abstract

The main benefits of a half-bridge LLC resonant DC/DC converter that uses two inductors (LL) and a capacitor (C) over the other load resonant converters are its less circulating currents, larger bandwidth for Zero Voltage Switching (ZVS) and limited tuning of operating frequency for controlled output. LLC resonant DC/DC converter is identified as a widely adopted topology in server and telecom power system applications because of its higher efficiency, flexibility and reliability. This paper proposes a novel design procedure using peak gain adjustment for a design example of 400V/12V-5A LLC resonant DC/DC converter used in server based applications. An experimental set up of the converter for the specifications mentioned is built and evaluated with the power switch traded as FSFR 2100 IC of Texas Instruments in closed loop configuration. The experimental results have exhibited an improved efficiency of 94% with the novel design proposed for the converter.

Keywords: LLC resonant DC/DC converter, Fundamental Harmonic Approximation, zero-voltage switching, MOSFETS

1. Introduction

High efficiency and high power density for any power converter can be achieved by forcing Pulse Width Modulated (PWM) converters to operate at high frequency. But, at high frequencies the occurrence of switching losses are huge. Therefore, a new topology called resonant converter topology has come in to existence. These converters process the power in a sinusoidal manner and the switching devices are soft commutated [1-2]. The switching losses and noise leading Electro Magnetic Interference (EMI) can be drastically reduced in these converters [3-8].

The main benefits of a LLC resonant DC/DC converter over the other load resonant converters are its less circulating currents, larger bandwidth for Zero Voltage Switching (ZVS) and limited tuning of operating frequency for controlled output. This converter is identified as a widely adopted topology in server and telecom power systems applications due to its higher efficiency, flexibility and reliability. Figure 1 shows the schematic of half-bridge LLC resonant DC/DC converter with Lm as magnetizing inductance, Lr as series resonant inductance and Cr as resonant capacitor. The operation of LLC resonant DC/DC converter consisting of three stages called a square wave generator, a resonant network and a diode rectifier network is explained with the help of Figure1 [9, 10].

The square wave generator produces a square wave voltage (Va) at phase node by driving the switches S1 and S2 alternatively with 50% duty cycle with a small dead time introduced between the consecutive transitions. The resonant network filters the higher harmonic currents and allows only sinusoidal current to flow through it even though a square wave voltage is applied to it. So the current through the inductance Lr lags the voltage applied (Va) and allows the MOSFETs to be turned on with zero-voltage leading to the reduction of turn-on loss. The rectifier network produces DC voltage by rectifying the AC current with rectifier diodes and a capacitor filter.

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Figure 1. Schematic of half bridge LLC resonant DC/DC converter

The existing design procedures in choosing the L-C components usually provide boundaries or ranges of the values, but are not explicit about determining the parameters [11-14]. This paper provides a detailed mathematical modeling and design procedure for a half-bridge LLC resonant DC/DC converter using an unique analytical tool, called Fundamental Harmonic Approximation (FHA). A novel design procedure using peak gain adjustment is proposed for a design example of 400V/12V-5A used in server based applications. An experimental set up of the converter for the specifications mentioned is built and evaluated with the power switch traded as FSFR 2100IC of Texas Instruments in closed loop configuration. The experimental results has proved an improved efficiency of 94% with the novel design proposed for the converter.

2. Research Method

As a part of research methodology, modeling of the LLC resonant DC/DC converter is developed with FHA and later a novel design procedure using peak gain adjustment for the converter is discussed in this section.

2.1. Modeling of the Converter with FHA

It is typical to operate the converter around the resonant frequency (fo) that yields the circulating current in the resonant tank as a pure sinusoidal current with single frequency. An approximation single fundamental harmonic of the square wave could be considered at phase node (Va) of Figure 1. The assumptions made in this Fundamental Harmonic Approximation (FHA) method are:

1. Represent the input square-wave voltage and current with their fundamental components. 2. Neglect the effect of output capacitor and the transformer’s secondary-side leakage

inductance

3. Refer all secondary-side variables to the primary side.

4. Represent the referred secondary voltage and secondary current with their fundamental components.

An equivalent circuit of Figure 1 with these assumptions can be obtained as a model of half bridge LLC resonant DC/DC converter as shown in Figure 2 used in the modeling and designing the converter. A nonlinear and non sinusoidal circuit of Figure2(a) is transformed into a linear and sinusoidal circuit of Figure 2(b). In this circuit of Figure 2(b), the AC resonant tank is excited by an effective sinusoidal input source driving an equivalent resistive load.

In Figure 2(b), both input (Vge) and output (Voe) are in sinusoidal form with the frequency of fundamental component of square-wave (Vsq) voltage, generated by switching S1 and S2. Before going to the design of the converter, the electrical variables and their relationships are obtained by considering Figure 2(b) are presented as follows.

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(a) Non linear non sinusoidal circuit (b) Linear sinusoidal circuit Figure 2. Model of half bridge LLC resonant DC/DC converter converter

The fundamental voltage of square-wave voltage (Vsq) on the input side is:

V t _π V sin πf t (1)

It’s RMS value is given as:

V √_π V (2)

Since Vso is approximated as a square wave, the fundamental output side voltage is:

V t _π n V sin πf t φ (3)

Where φV is the phase difference between Voe and Vge, and its RMS output voltage is:

V √_π n V (4)

The fundamental component of current corresponding to Voe.

i t π I sin πf t φ (5)

Where φi is the phase angle between ioe and voe, and its RMS output current is:

I π_√ I (6)

Then the AC equivalent load resistance, Re can be calculated as:

R _π _π R (7)

The angular frequency is:

ω πf (8)

And can be simplified as:

ω ω πf (9)

The capacitive and inductive reactance of Cr, Lr, and Lm, respectively, are:

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The RMS magnetizing current is:

I _ω √_π _ω (10)

The circulating current in the series resonant circuit is:

I I I (11)

With these relationships of electrical variables, voltage-gain function is developed. 2.1.1. Voltage-Gain Function

The relationship between input and output voltages is described by their ratio or gain:

M _/ _/ (12)

As described earlier, the DC input voltage and output voltage are converted into switching mode, and then Equation (12) can be approximated as the ratio of the bipolar square-wave voltage (Vso) to the uni-polar square-wave voltage (Vsq):

M (13)

The AC voltage ratio, M g-AC can be approximated by using the fundamental components, Vge and Voe to respectively replace Vsq and Vso in equation above.

M n V

V / M

M _ (14)

To simplify the notation, Mg will be used here in place of Mg -AC. From Figure 2(b), the relationship between Voe and Vge can be expressed with the electrical parameters Lr, Lm, Cr, and Re. Then the input-to- output voltage-gain or voltage-transfer function becomes:

M _|| ||

ω ||

ω || ω _ω (15)

Where j √ .

Equation (15) gives the relation between input voltage (Vin) and output voltage (Vo) established in connection with Mg for LLC-circuit parameters. Further on simplification, Equation (15) can be written as:

V M (16)

That is output voltage can be determined after Mg, n, and Vin are known. 2.1.2. Normalized Format of Voltage-Gain Function

The voltage- gain function of Equation (15) is expressed with absolute values. It could be convenient to express this equation in a normalized format so as to design the converter parameters. Therefore series resonant frequency (f0) can be selected as the base for normalization and the normalized frequency is given as:

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f (17) Further, an inductance ratio can be defined as:

β (18) The quality factor is defined as:

(19) Notice that fn, β, and Qe are constants. The normalized voltage-gain function can be given as:

M _β β _β (20)

The relationship between input and output voltages can also be obtained from Equation (21).

V M M f ,β, Q (21)

Where, V V 2.1.3. DC Characteristics

The voltage gain (M), obtained through (FHA) [15] as in Equation (21) can be rewritten as:

M β

β (22)

Where,

R π R

(Usually less than f0)

Where Re is the equivalent resistance of load and rectifier stage, f0 and fp are the two resonant frequencies. Figure 3 represents the DC characteristics of LLC resonant DC/DC converter. It is the graph between DC voltage gains of the converter and the normalized switching frequency for different values of quality factor. The two resonant frequencies are determined by the components Lr, Cr, Lm, and load condition. As load increases, the resonant frequency shifts towards higher frequency as observed in Figure 3.

The inferences drawn from the above DC characteristics are:

1. Maximum gain varies along with the variations of load suitable for buck and boost types

2. Regulation can be achieved around resonant frequency. Operational zone can be divided as ZCS and ZVS.

Since MOSFETs are used for the converter, ZVS is preferred and the operating range should be between fp and f0 frequencies.

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Figure 3. DC Characteristic of LLC resonant DC/DC converter.

2.2. Design Procedure

To design the parameter values of LLC resonant DC/DC converter, a voltage-transfer function as given in Equation (22) and the DC Characteristics as shown in Figure 3 are considered. In this paper, a novel design method based on peak gain adjustment provides the optimal set of L-C parameters that minimizes the power losses and meets the gain requirement. According to this, the peak gain point is the key parameter involved in a converter design as it indicates the max gain capability and the lower limit of the switching frequency.In this novel design of resonant tank, set the peak gain in such a way that the converter reaches its peak gain under the full load and minimum switching frequency condition and at the same time ensure that this peak value is equal to the required gain for the minimum input voltage. Therefore this procedure requires solving the peak gain of the LLC resonant DC/DC converter being operated in the below-resonance region, derived from inspection maximum gain adjustment.

Now from Equation (22) it is clear that there are two resonant frequencies that are existing in the converter. One is determined by Lr and Cr, while the other is determined by Lr , Lm and Cr. Now once again by considering Figure 3 as well as the gain Equation (22) for different values of Q with β=4, fo=100kHz.The following observations are made.

1. The gain characteristics are almost independent of the load when the switching frequency is around the resonant frequency, fo .

2. The bandwidth of the LLC resonant converter is limited by the peak gain (attainable maximum gain), which exists between fp and fo..

3. As Q decreases (i.e as load decreases), the peak gain frequency moves to fp and higher peak gain is obtained. Meanwhile, as Q increases (i.e as load increases), the peak gain frequency moves to fo and the peak gain drops; thus, the full load condition should be the worst case for the resonant network design.

As per the observations made, a novel design procedure is demonstrated with an example having following design specifications as given in Table 1 used for server based applications.The input to the converter is supplied from Power Factor Correction (PFC) pre-regulator.

Table 1. Design Specifications of LLC resonant converter

Specifications and Parameters Values

DC-Bus voltage range(VDC) 300V-400V(output of PFC stage)

Output voltage(V0) and current(I0) 12V and 5A

Hold-up time requirement 20ms (50Hz line freq.)

DC link capacitor of PFC output 100μF

Resonant frequency 100kHz

Turns ratio of transformer 18:1

Maximum required voltage gain 1.25

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The different procedural steps carried out to determine the circuit parameters are given below. Step-1:

With the estimated efficiency (η) of 92%, the maximum input power is given as:

P _η

Since the maximum input voltage would be the nominal PFC output voltage and therefore the minimum input voltage considering the hold-up time requirement is given as:

V V

Where V0PFC is the nominal PFC output voltage, THU is a hold-up time, and CDL is the DC link bulk capacitor.

Step-2:

As observed in Equation (22), the gain at f0is a function of β(β =Lm/Lr) and is chosen as 4 which results in a voltage gain of 1.1~1.3 at the resonant frequency (f0).

Voltage gain for the nominal PFC output voltage is obtained as:

M _ββ @f f

Which is the minimum gain because the nominal PFC output voltage is the maximum input voltage. Now the maximum voltage gain is given as:

M M

Step-3:

The transformer turns ratio is given as:

n M

Where VF is the secondary-side rectifier diode voltage drop. Step-4:

With the transformer turns ratio obtained from Step-3,the equivalent load resistance is obtained as:

R _π R

Step-5:

With βvalue chosen in step-2 read proper Qvalue from the peak gain curves in Figure 3 that allows enough peak gain. Once the Qvalue is determined, the resonant parameters are obtained as:

C _π

L _π

L βL

Now all above mentioned procedural steps have been evaluated and final resonant network design is summarized in Table 2.

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Table 2. Designed Values of LLC Resonant DC/DC Converter

Parameter Designed Values

Lm 1924µH

Lr 481 µH

Cr 5.26nF

f0 100kHz

Β 4

Q 0.48

M @f0 1.15

Minimum frequency 75kHZ

3. Experimental Results and Analysis

For the proposed design, an experimental set up of LLC resonant DC/DC converter based on design specification given in Table 1 has been built and evaluated on test bench in closed loop configuration. Figure 4 shows the experimental set up of a LLC resonant DC/DC converter for a maximum output power of 60W.

Figure 4. Experimental set up of a LLC resonant DC/DC converter

This set up utilizes a half-bridge power switch traded as FSFR2100 of Texas Instruments. The rectifier diodes are implemented with MUR160 power diodes. For practical design, low equivalent series resistance (ESR) and high frequency capacitors are used both on main input and output buses. An integrated transformer is implemented by EER 3542 core with sectional bobbin having a turns ratio of n = 18:1. The integrated transformer is built in such a way that the leakage inductance is used as a series inductor (Lr) and the magnetizing inductance is used as a shunt inductor (Lm). Litz wire is used in wounding the no of turns of integrated transformer. To reduce turn-off losses, a small capacitor is to be connected in parallel with the power MOSFETs [16]. Load resistance is varied from 2.5Ω to infinite and the operating switching frequency range is tuned between 60 kHz and 100 kHz covering all modes of operation. The developed prototype is tested under different loads (0–5 A DC) and input voltage conditions (300–400V DC). The experimental results confirm high performance of designed wide-range converter and are discussed as follows.

Figure 5 and Figure 6, shows the primary and secondary side waveforms of LLC resonant DC/DC converter under no-load and full-load conditions with maximum and minimum input voltages. To measure drain to source voltage (VDS) and the capacitor voltage (VCr) as shown in Figure 5(a, b) and Figure 6(a, b), the probe of CRO is connected with ×10 multiplier. The results shown in Figure 5(c) and Figure 6(c) represent the DC output voltage both on no load and full load conditions. To measure, the primary side inductor current (iLr), a low wattage resistor is connected with the transformer primary, which itself acts as a load for the converter. So Instead of measuring the primary side inductor current (iLr), switching current of MOSFET 2 is sensed through current sensing pin CS of FSFR2100 IC with 2W Rsensing resistor, which is shown as R8 in the PCB layout of LLC resonant converter as given Figure 8 of Appendix. From Figure 5(i) and Figure 6(i) switch current waveform, it is clear that on no-load the current sensed is negligible, whereas on full-load a reasonable current is sensed.

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(a) (b)

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Figure 5. LLC resonant DC/DC converter waveforms under no-load condition Io= 10µA, Vo=12V when Vin =400V (a) Primary-side VDS voltage and Switching current through MOSFET 2, (b)

Primary-side resonant capacitor voltage(VCr), (c) Secondary load voltage(V0)waveforms

(a) (b)

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Figure 6. LLC resonant DC/DC converter waveforms under full-load condition Io= 5A, Vo=12V when Vin =300V (a) Primary-side VDS voltage and Switching current through MOSFET 2, (b)

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As illustrated in Figure 6(a) on full-load condition, for wide input voltage and wide dynamic load variation ranges, the MOSFETs turn on switching losses are almost zero and can be neglected due to ZVS operation. Therefore, because of this soft commutation, the frequency can be increased for reducing the passive components sizes. During hold-up time, the converter has to reduce switching frequency to boost up voltage gain and this is observed through Figure 6(a), and is given as 66 kHZ. In the set up, the modulation of frequency is done by FSFR 2100IC, which is enabled through an isolation opto-coupler based on load/line variations to regulate output voltage during hold up time. An efficiency of 94% is observed at full load condition. Figure7 represents a flat efficiency curve at Vin=400V and Vin=300V for different load conditions. An efficiency of 94% is observed at full load condition.

Figure 7. Measured efficiency graphs at different input voltages for different load conditions

From Figure 7, it is clear that under light loads, the efficiency is reduced, due to the increase of switching frequency and reactive power, occurred in the constant output voltage applications of the LLC resonant DC/DC converter.

4. Conclusion

A unique analytical tool, called Fundamental Harmonic Approximation (FHA) is discussed for the mathematical modeling and design of half-bridge LLC resonant DC/DC converter. A novel design procedure using peak gain adjustment is proposed by considering a design example of 400V/12V-5A converter operating at 75 kHz used in server based applications. A prototype model of the converter for the specifications mentioned is built with the power switch traded as FSFR 2100 IC of Texas Instruments in closed loop configuration.

Acknowledgements

The authors wish to thank Chaitanya Bharathi Institute of Technology and G.Narayanamma Institute of Technology and Science authorities for permitting to publish.

References

[1] Muhammad H Rashid. Power Electronics-Circuits, Devices, and Application. 3rd edition. Pearson Education. 2004.

[2] Ned Mohan, Tore M Underland, William P Robbins. PowerElectronics-Converters, Application and Design. 3rd edition. John Wiley & Sons. 2003.

[3] Younghoon Cho. A Low Cost Single-Switch Bridgeless Boost PFC Converter. International Journal of Power Electronics and Drive System. 2014; 4(2): 256-264.

[4] M Facta, T Sutikno, Z Salam. The Application of FPGA in PWM Controlled Resonant Converter for an Ozone Generator. International Journal of Power Electronics and Drive System. 2013; 3(3): 336-343.

[5] WY Choi, JM Kwon. High–performance front-end rectifier system for telecommunication power supplies. Proc. Inst. Elect. Eng. 2006; 153(4): 473-482.

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[6] H de Groot, E Janseen, R Pagano, K Schetters. Design of a 1-MHz LLC resonant converter based on a DSP-Driven SOI Half-Bridge power MOS module. IEEE Trans. Power Electron. 2007; 22(6): 2307-2320.

[7] X Fang, H Hu, J Shen, I Batarseh. Operation mode analysis and peak gain approximation of the LLC resonant converter. IEEE Trans.Power Electron. 2012; 27(4): 1985-1995.

[8] JF Lazar, R Martinelli. Steady-state analysis of the LLC series resonant convereter. In Proc. IEEE Appl. Power Electron. Conf.Expo. 2001; 2: 728-735.

[9] B Yang, FC Lee, AJ Zhang, G Huang. LLC resonant converter for front end DC/DC conversion. In Proc. IEEE Appl. Power Elec. Conf. and Expo. 2002; 2: 1108-1112.

[10] Y Ye, C Yan, J Zeng, J Ying. A Novel Light Load Solution for LLC Series Resonant Converter. In Proc. IEEE Telecommunications Energy Conf. 2007: 61-64.

[11] C Zhao, X Wu, Z Qian. Design and comparision of two front end DC/DC converters: LLC resonant converter and soft-switched phase-shifted full-bridge converter with primary-side energy storage inductor. In Proc. 24th Annu.IEEE Appl. Power Electron. Conf. Expo. 2009: 1073-1077.

[12] MP Foster, CR Gould, AJ Gilbert, DA Stone, CM Bingham. Analysis of CLL voltage-output resonant converters using describing functions. IEEE Trans. Power Electron. 2008; 23(4): 1772-1781.

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[14] CM Bingham, YA Ang, MP Foster, DA Stone. Analysis and control of dual-output LCLC resonant converters with significant leakage inductance. IEEE Trans. Power Electron. 2008; 23(4): 1724-1732. [15] B Yang, FC Lee, AJ Zhang, G Huang. LLC resonant converter for front end DC/DC conversion. In

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Appendix

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Figure 3. DC Characteristic of LLC resonant DC/DC converter.

2.2. Design Procedure

1. The gain characteristics are almost independent of the load when the switching frequency is around the resonant frequency, fo .

2. The bandwidth of the LLC resonant converter is limited by the peak gain (attainable maximum gain), which exists between fp and fo..

Table 1. Design Specifications of LLC resonant converter Specifications and Parameters Values

DC-Bus voltage range(VDC) 300V-400V(output of PFC stage) Output voltage(V0) and current(I0) 12V and 5A

Hold-up time requirement 20ms (50Hz line freq.) DC link capacitor of PFC output 100μF

Resonant frequency 100kHz Turns ratio of transformer 18:1 Maximum required voltage gain 1.25 Equivalent load resistor 630Ω

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The different procedural steps carried out to determine the circuit parameters are given below. Step-1:

With the estimated efficiency (η) of 92%, the maximum input power is given as:

P _η

Since the maximum input voltage would be the nominal PFC output voltage and therefore the minimum input voltage considering the hold-up time requirement is given as:

V V

Where V0PFC is the nominal PFC output voltage, THU is a hold-up time, and CDL is the DC link bulk capacitor.

Step-2:

As observed in Equation (22), the gain at f0is a function of β(β =Lm/Lr) and is chosen as 4 which results in a voltage gain of 1.1~1.3 at the resonant frequency (f0).

Voltage gain for the nominal PFC output voltage is obtained as:

M _ββ @f f

Which is the minimum gain because the nominal PFC output voltage is the maximum input voltage. Now the maximum voltage gain is given as:

M M

Step-3:

The transformer turns ratio is given as:

n M

Where VF is the secondary-side rectifier diode voltage drop. Step-4:

With the transformer turns ratio obtained from Step-3,the equivalent load resistance is obtained as:

R _π R

Step-5:

With βvalue chosen in step-2 read proper Qvalue from the peak gain curves in Figure 3 that allows enough peak gain. Once the Qvalue is determined, the resonant parameters are obtained as:

C _π

L _π

L βL

Now all above mentioned procedural steps have been evaluated and final resonant network design is summarized in Table 2.

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Table 2. Designed Values of LLC Resonant DC/DC Converter Parameter Designed Values

Lm 1924µH

Lr 481 µH

Cr 5.26nF

f0 100kHz

Β 4 Q 0.48

M @f0 1.15

Minimum frequency 75kHZ

3. Experimental Results and Analysis

Figure 4. Experimental set up of a LLC resonant DC/DC converter

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(a) (b)

(c)

Figure 5. LLC resonant DC/DC converter waveforms under no-load condition Io= 10µA, Vo=12V when Vin =400V (a) Primary-side VDS voltage and Switching current through MOSFET 2, (b)

Primary-side resonant capacitor voltage(VCr), (c) Secondary load voltage(V0)waveforms

(a) (b)

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Figure 6. LLC resonant DC/DC converter waveforms under full-load condition Io= 5A, Vo=12V when Vin =300V (a) Primary-side VDS voltage and Switching current through MOSFET 2, (b)