Design and Analysis of Full Bridge LLC Resonant

Converter for Wireless Power Transfer Applications

Taif Mohamed, AbouelKassim Becetti, Sertac Bayhan

Electrical and Computer Engineering

Texas A&M University at Qatar

Doha, Qatar

Abstract—A promising resolution to the challenge of charging

electric vehicles is wireless power transfer. Using a core-less

transformer to achieve this goal, however, requires a highly

efficient power transfer system design as much of the loss in

efficiency will occur at the transformer. This team suggests the

use of the LLC resonant power converter to attain maximum

efficiency at this stage. This paper will explain the design and

analysis of such a converter and present the results of simulations

performed in MATLAB/Simulink. The proposed prototype

converts 100 V from the input DC link to an output of 24 V DC at

an efficiency of 95.6 %

Keywords—wireless power transfer; electric vehicles; LLC;

resonance

I. INTRODUCTION

A DC-to-DC power converter is an electronic circuit that converts voltage source of direct current into a desired regulated direct current output voltage. The input of this converter can be a battery or a rectified alternating current line voltage. This means that the converter input voltage can either be regulated or unregulated. Linear voltage regulators were the initial DC-to-DC power converters where the output voltage was to be less than the input voltage. This caused the efficiency to be limited due to the significant voltage drop across the active device. Therefore, the Pulse-width modulation technique was used in developing switching mode DC-to-DC power converters where efficiency is greatly improved by controlling the duty cycle and the switching frequency. Moreover, step-down or step-up operations can be achieved using PWM DC-to-DC power converters. However, the inability of PWM converters to operate efficiently at very high frequencies limits the size of reactive components in the converter circuit. As well as that, PWM rectangular voltage and current waveforms result in turn-on and turn-off losses that limit the operating frequency [1].

In search of converters capable of operating at higher frequencies, new converter topologies were developed that shaped sinusoidal current and voltage waveforms limiting switching losses. The main idea is to use a resonant circuit with a sufficiently high quality factor while operating the transistors and diodes under soft-switching conditions. This new type of DC-to-DC power converters is obtained by cascading a resonant DC-to-AC inverter and high-frequency rectifier and a high-frequency transformer can be inserted between the

inverter and the rectifier if isolation is required [2]. This paper demonstrates the approach taken in designing a resonant LLC converter for wireless power transmission. The LLC converter was chosen for its ability to increase the efficiency significantly due to zero voltage switching (ZVS) for the primary side switches and Zero Current Switching (ZCS) for the secondary side rectifiers [3], [4]. The design methodology will be discussed first where the chosen topology will be explained, and the calculations made for sizing the circuit components and choosing suitable parameters for the required mode of operation will be discussed. Subsequently, the design verification will be reviewed where the results obtained from the simulations conducted using the MATLAB application SIMULINK will be discussed as to verify the conformity and accuracy of the design. Moreover, the hardware design involved in controlling the transistors in the circuit will be elucidated. The paper then covers all the necessary steps taken in designing the resonant converter prior to the actual implementation of the device.

II. CONVERTER TOPOLOGY

The DC-to DC converter being proposed consists of a full bridge inverter whose input is the DC voltage, nominally of 100 V. Following it is the LLC resonant tank consisting of an external capacitor in series with the transformer’s leakage inductance on the primary side, all in parallel with the magnetizing inductance of the transformer. On the secondary side of the transformer is the full bridge rectifier that, in turn, feeds the resistive load that represents the electric vehicle’s battery with a capacitive filter connected in parallel. The aforementioned set up is illustrated in Fig. 1

Fig. 1. LLC full bridge converter topology [5] – [7]

The LLC converter topology being full-bridge includes four MOSFETs in the inverter section. This is where the DC input voltage is inverted into an AC signal. The series inductor (Lr) and parallel inductor (Lm) are taken to be the leakage and magnetizing inductances of the transformer to reduce the costs of the converter [8]-[13]. The proposed switching frequency is 100 kHz, to which the resonant frequency of the LLC tank was matched. This means that the transformer must be able to withstand such a high frequency for the sake of eliminating the current ripple at the battery. While the high switching frequency allows for the sizing of smaller resonant components, it also increases switching losses, but that is countered by operating in the resonant mode of the converter and designing for zero voltage switching. Zero voltage switching (ZVS) is made possible due to the energy stored in the magnetizing inductance of the transformer [5]. Effectively, the LLC converter topology was chosen for its high efficiency, low noise, and reliability [6].

III. SIMULATION METHODS

A. Gate Drives

Having a full bridge converter dictated the necessity for two different gate drive signals in order to operate the MOSFETs in pairs. In order to generate the gate signals, a field-programmable gate array (FPGA) was used in the process. A terasic DE0-Nano board shown in Fig. 2 below was programmed using Altera Quartus II software in Verilog.

Fig. 2. DE0-Nano board

The goal behind implementing the FPGA was to generate two PWM signals out of phase both at a frequency of 100 kHz. Basically, the FPGA was programmed to deliver two square-wave signals half a period apart with a duty cycle of 0.5. The code is running an infinite loop generating a square wave using the register variable that was defined. It is by defining two output variables that the FPGA was able to deliver the two required gate signals. Signal A was defined to be the exact same as the register signal and Signal B was defined to be the inverse of aforementioned signal A.

After writing the code and compiling it, it was vital to test the code and verify its conformity. Thus, the FPGA was pin-planned by assigning the “clk” to the on-board 50 MHz clock

oscillator whose pin number is R8 and the two output PWM signals were assigned to two pins in one of the expansion headers. These pins can provide a DC voltage signal of up to +5V. Regarding the reset input variable “rst_n”, it was assigned to a dip switch. This allows for the user to control the start of the operation by moving the switch from the DOWN position to the UPPER position.

After implementing this code and monitoring it using an oscilloscope, the output resembled the following model in Fig. 3 taken from Simulink.

Fig. 3. FPGA output behavior on Simulink

B. LLC Component Design

As previously mentioned, the LLC converter’s most essential components are the resonant inductor Lr, resonant capacitor Cr, and the parallel inductor, which is the transformer’s magnetizing inductor Lm. To operate in the desired resonant mode, these components are designed so that the resonant frequency is equal to the switching frequency. Because the ultimate goal is to step down the regulated voltage from 100 V to 24 V, the gain of each of the three stages is taken into consideration. The switching full bridge provides a gain of 1, and the transformer’s turn ratio (Ns/Np) will serve as the stepping down stage as it is chosen to be 24/100. Consequently, the most optimum design of the LLC tank will yield a gain of 1 to maintain the correct gain ratio.

The gain of the resonant tank can be rewritten as a function

of several parameters as in (1):

2_

2 2 2 2 2 2 2_

( ) ( 1)( , , )

( ) ( 1) ( 1) ( 1)

o ac xx

in ac x x x

V s F mK Q m F

V s m F F F m Q

K in (1) represents the gain of the resonant tanks, while Fx represents the normalized switching frequency. Equations (2) to (6) were obtained from an application note published by Infineon Technologies [5] and were utilized in the design process to determine the proper sizing of the converter’s elements.

/r r

ac

L CQ

R (2)

2

2 2

8 p

ac o

s

NR R

N (3)

sx

r

fF

f (4)

1

2r

r r

fL C

(5)

r m

r

L Lm

L

(6)

Q, known as the Quality factor, is affected by the load, in the sense that a higher value of Q corresponds to heavier loads. Rac is the reflected load resistance, which accounts for the load on the secondary side of the transformer. When the value of fr is matched to the switching frequency, the normalized frequency is equal to 1. Finally, m is the ratio of the total primary inductance to the resonant inductance.

The values of Q and m set the base for the rest of the values retrieved from this set of equations. The values of Q and m were obtained using iterative trials and simulations in MATLAB/Simulink. The entire converter was built in Simulink. In addition to the basic components of the converter, a basic PI controller was added to control the switching frequency of the gate drives.

The figure shows, from left to right, the input DC link of 100 V followed by the full bridge inverter made up of four MOSFETs operating alternatively. Next, the LLC resonant tank connects between the inverter and the full wave rectifier that comprises four diodes, also operating alternatively. Finally, the load is represented as a resistance in parallel with a capacitive filter that limits output voltage ripple.

IV. RESULTS AND DISCUSSION

After several iterations the values of Q and were chosen to be 3 and 16.3, respectively. The resultant approximated values for the circuit components are outlined in Table 1. Using these values, the waveforms of the output voltage, switching frequency and voltage and current on the primary side of the

Fig. 4. Output voltage (top) and switching frequency waveforms (bottom)

transformer were evaluated.

TABLE I. LLC COVERTER COMPONENT VALUES

Component Value

Lr 0.8 mH

Cr 3 nF

Lm 12 mH

A. Output Voltage and Switching Frequency

The fundamental aim of the simulation was to obtain a constant DC voltage at the load’s side when the input is the nominal value of 100 V. Due to the presence of the PI controller, this output was not directly attainable. Instead, the system experienced a transient response that later settled to a final value, given that the designed system was stable. This explains the oscillation observed in the waveforms of output voltage and switching frequency in Fig. 5. As a result, another complication was presented to the design parameters only to be resolved through further iterations. The result shown Fig. 5 was found to be the most suitable and stable of all the obtained results, which confirmed the credibility of our calculations. The resultant voltage, shown at the top of Fig. 5, exhibits some oscillation before it settles to the final value of 24 V, exactly as desired. This corresponds to an identical response for the switching frequency, which settled to a value of approximately 99.68 kHz. This is as close to 100 kHz as possible, as seen through the simulations.

B. Intermediate Voltage and Current Waveforms

Fig. 6 illustrates, from top to bottom, the current on the primary side of the transformer, the current through MOSFET2, the voltage across MOSFET2, and the current at the output of the full-wave rectifier, which is the output current. As expected, the current arriving at the primary side of

the transformer, flowing through the LLC tank components, is a pure AC waveform. The current is shared among the MOSFETs so that MOSFETs 1 and 4 are on simultaneously for one half cycle, and then MOSFETs 2 and 3 are turned on for the other half cycle. As predicted, the voltage drop across the MOSFET is zero in its conducting half cycle, and is equal to 100 V when it is off.

It was important for this design’s functionality to see that the current and voltage seen by the primary side of the transformer are in phase. This is because any phase delay between these two waveforms indicates is an effect of reactive elements in the circuit. Given that the maximum efficiency of

the LLC converter is attained at the condition of resonance, in which the impedance becomes purely resistive, the main goal of repetitive iterations after achieving the required output voltage became making these two waveforms in phase.

C. Efficiency

The efficiency of the presented LLC converter was calculated to be approximately 95.6 %. This result was computed by observing the final value that the output power, displayed in Fig. 7 as well as the value of the input power, which was found to be 33.79 W.

Fig. 5. Current at the transformer’s primary side (first), current through MOSFET2 (second), voltage across MOSFET2 (third), output current of the full-wave

rectifier (fourth).

Fig. 6. Output Power

V. ACKNOWLEDGMENT

This publication was made possible by UREP20-101-2-029

from the Qatar National Research Fund (a member of Qatar

Foundation). The statements made herein are solely the

responsibility of the authors.

VI. REFERENCES

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