# Design of an Isolated Bidirectional Symmetric Resonant Converter

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Circuit Structure and Operation Analysis

#### 2.1. Circuit Structure

_{DC_Grid}to battery port V

_{Bat}, and reverse discharging mode marks the power transfer reversely. With the usage of the symmetric resonant scheme, the power switches can achieve soft switching in either direction of power transfer and thus reduce the switching losses and EMI. Figure 2 illustrates the voltage gain curves of the traditional LLC resonant converter; the reverse-mode voltage gain is limited to be less than 1.

#### 2.2. Description of Operating Range

#### 2.3. Description of Operating Range

_{DC_Grid}supplies energy via power switches Q

_{1}, Q

_{2}, Q

_{3}, and Q

_{4}; it passes from the transformer primary side to the secondary side and thus is rectified by the intrinsic diodes D

_{B5}, D

_{B6}, D

_{B7}, and D

_{B8}to charge the battery V

_{Bat}. By adjusting the switching frequency, the output voltage and output power are controlled accordingly. The trigger signals of Q

_{1}–Q

_{4}are a pair of symmetric square waves with each being around a 50% duty ratio. With Q

_{1}and Q

_{4}being a group and Q

_{2}and Q

_{3}being another, the trigger signals of Q

_{1}and Q

_{2}are displaced by 180°, and an appropriate dead time is introduced therein. Due to the symmetric feature, the reverse discharging mode will apply the same operation. Therefore, only the forward mode operating in Region II is used to describe the operating principle. Figure 5 illustrates the important theoretic waveforms. For simplifying the analysis, the following assumptions must be made:

- The circuit operates in the steady state.
- Only intrinsic diode D
_{B}and parasitic capacitance C_{OSS}are taken into account with others being ignored. - The effect of the parasitic capacitances C
_{OSS1}–C_{OSS8}is neglected. - All devices are ideal.
- The output capacitances C
_{DC_Grid}and C_{Bat}are large enough to look upon V_{DC_Grid}and V_{Bat}as the ideal voltage source.

#### 2.3.1. Stage I [t_{1} < t ≤ t_{2}]

_{1}, Q

_{2}, Q

_{3}, and Q

_{4}are all cut off. At the secondary side, D

_{B5}and D

_{B8}conduct, while D

_{B6}and D

_{B7}remain cut off. At the primary side, the resonant current i

_{Lr1}passes through D

_{B1}and D

_{B4}to keep the resonant current flow and prevent the devices from voltage spike damage. In addition, the circuit is ready for the ZVS of Q

_{1}and Q

_{4}. At t = t

_{2}, as gate signals v

_{GS1}and v

_{GS4}turn from low level to high, the next stage follows.

#### 2.3.2. Stage II [t_{2} < t ≤ t_{3}]

_{1}–Q

_{4}remain at the cut-off state. The intrinsic diodes D

_{B5}and D

_{B8}keep on conducting while D

_{B6}and D

_{B7}remain at the cut-off state. The resonant current i

_{Lr1}flows via intrinsic diodes D

_{B1}and D

_{B4}to retain the conduction loop. As the power switch turns on at the end at t = t

_{3}, the ZVS is realized, whereas due to the magnetizing inductor L

_{m}being clamped by the output voltage V

_{Bat}and the secondary resonant capacitor voltage V

_{Cr2}, L

_{m}is absent from resonating, and thus i

_{Lm}keeps on rising linearly. At t = t

_{3}, resonant current i

_{Lr1}approaches 0, and this stage ends.

#### 2.3.3. Stage III [t_{3} < t ≤ t_{4}]

_{1}and Q

_{4}turn on at t = t

_{3}and achieve ZVS while Q

_{2}and Q

_{3}remain at the cut-off state. In this stage, V

_{DC_Grid}passes the energy through C

_{r1}, L

_{r1}, C

_{r2}, and L

_{r2}, and it delivers the energy to the battery side via the isolated transformer. After being rectified by intrinsic diodes D

_{B5}and D

_{B8}, the energy charges the battery, whereas L

_{m}is absent from resonating due to the magnetizing inductor L

_{m}being clamped by the output voltage V

_{Bat}and the secondary resonant capacitor voltage V

_{Cr2}, and thus i

_{Lm}keeps on rising linearly. At t = t

_{4}, i

_{Lr1}equals i

_{Lm}, and this stage terminates. In the meantime, current i

_{DB5,8}falls to 0, and thus ZVS is achieved.

#### 2.3.4. Stage IV [t_{4} < t ≤ t_{5}]

_{1}and Q

_{4}remain conducting while Q

_{2}and Q

_{3}remain at the cut-off state. As i

_{Lr1}equals i

_{Lm}at t = t

_{4}, the transformer is decoupled, and electromagnetic induction takes a break. The secondary side bridge is temporarily disabled without current flow. The D

_{B5}and D

_{B8}is naturally cut off and gets ready for ZCS. In this mode, the transformer does not transfer energy to the load, and the magnetizing inductor L

_{m}is not clamped by the output voltage V

_{Bat}and the secondary resonant capacitor voltage V

_{Cr2}. The magnetizing inductor L

_{m}, L

_{r1}, and C

_{r1}constitute a resonant circuit while L

_{r2}and C

_{r2}are idle. As the gating signals v

_{GS1}and v

_{GS4}turn from high to low at t = t

_{5}, Q

_{1}and Q

_{4}cut off, and this stage ends.

#### 2.3.5. Stage V [t_{5} < t ≤ t_{6}]

_{1}and Q

_{4}are cut off at t = t

_{5}while Q

_{2}, Q

_{3}still remain at the cut-off state. This exactly marks the dead time region with resonant current i

_{Lr1}charging the parasitic capacitors C

_{OSS1}and C

_{OSS4}as well as helping C

_{OSS2}and C

_{OSS3}to discharge. In the secondary side, D

_{B6}and D

_{B7}conduct, and D

_{B5}and D

_{B8}cut off. When the voltages on C

_{OSS2}and C

_{OSS3}are discharged to 0 and simultaneously C

_{OSS1}and C

_{OSS4}are charged to V

_{DC_Grid}, this stage terminates.

## 3. Equivalent Circuit and Mathematic Formulation

_{DC_Grid_}

_{FHA}is the fundamental component of the square voltage waveform at the primary side. V

_{oe}is the fundamental component of the square voltage waveform of the resonant tank and transformer. The resonant capacitance at the primary side, resonant inductance at the primary side, magnetizing inductance, resonant capacitance at the secondary side, and resonant capacitance at the secondary side are designated as C

_{r1}, L

_{r1}, L

_{m}, C

_{r2}′, and L

_{r2}′, respectively. Moreover, power equivalent load resistance R

_{oe}is the AC load resistance of the energy storage battery referred to the primary side and is expressed as (1).

_{Bat}is the equivalent resistance of battery pack. For obtaining the transfer function of voltage gain, the Laplace transform of the ratio between the output voltage and the input voltage is derived as follows.

_{x}, and based on basic circuit theory, (2) is obtained.

_{1}(s), Z

_{2}(s), Z

_{3}(s), and Z

_{4}(s) are the Laplace forms of Z

_{1}, Z

_{2}, Z

_{3}, and Z

_{4}, respectively, looking from different positions, and are as expressed by (3).

_{s}is the switching frequency of power switches; f

_{r1_F}is the first resonant frequency; f

_{n_F}is the ratio of f

_{s}and f

_{r1_F}, referred to as normalized frequency; Q

_{1}represents quality factor; k

_{1}is the ratio of L

_{m}and L

_{r1}; g

_{1}and m

_{1}represent the resonant capacitor ratio and resonant inductance ratio, respectively, with reference to the primary side. These are written as follows:

_{r1}and L

_{r1}are expressed as (6) and (7).

_{n_R}, Q

_{2}, k

_{2}, g

_{2}, and m

_{2}are defined below.

## 4. The Design Procedure of Circuit Component Parameters

- It must have a wide voltage range.
- There must be soft switching of power switches.
- Cost and size should be reduced under high frequency operation.

#### 4.1. Step 1: Determining the Specification of Converter

#### 4.2. Step 2: Calculating the Transformer Turn Ratio

#### 4.3. Step 3: Calculating the Maximum and the Minimum Voltage Gains of Forward Mode

#### 4.4. Step 4: Selecting Parameters of Q_{1}, k_{1}, g_{1}, and m_{1} to Meet the Forward Voltage Gain Requirement

_{1}, g

_{1}, and m

_{1}being fixed and the forward mode quality factor Q

_{1}being adjusted. It clearly shows that the voltage gain curve is not a monotonic one and Q

_{1}with 0.6–2 cannot realize the maximum and minimum gain requirement. Moreover, if Q

_{1}= 0.4, the operating range of switching frequency is too wide and will result in longer response time. Therefore, a value of Q

_{1}= 0.2 is suitable for the forward charging mode. With the same consideration, the selection of k

_{1}, g

_{1}, and m

_{1}is to meet the maximum and minimum gain as the primary priority.

_{1}= 0.2, k

_{1}= 3.5, g

_{1}= 1, and m

_{1}= 1, as shown in Figure 11.

#### 4.5. Step 5: Checking the Maximum and the Minimum Gains of the Forward Charging Mode

_{1}, k

_{1}, g

_{1}, and m

_{1}. As the conditions are met, the design can go on to the next step.

#### 4.6. Step 6: Calculating the Resonant Device Parameters

_{1}, k

_{1}, g

_{1}, and m

_{1}are determined, the parameters of the associated resonant devices with device parameters R

_{oe}, C

_{r1}, L

_{r1}, L

_{m}, C

_{r2}, and L

_{r2}can be obtained by (14) to (19).

#### 4.7. Step 7: Calculating the Maximum and the Minimum Voltage Gains of Reverse Mode

#### 4.8. Step 8: Using the Resonant Device Parameters of Step 6 to Reversely Obtain the Parameters Q_{2}, k_{2}, g_{2}, and m_{2} of the Reverse Discharging Mode

_{2}, k

_{2}, g

_{2}, and m

_{2}of the reverse discharging mode.

#### 4.9. Step 9: Checking the Maximum and the Minimum Gains of the Reverse Charging Mode

_{1}, k

_{1}, g

_{1}, and m

_{1}recursively until the voltage gains of both forward and backward mode meet the requirements.

#### 4.10. Step 10: Determining the Maximum and Minimum Operating Frequencies of the Forward and Reverse Charging Modes

_{s_max_Forward}and f

_{s_min_Forward}) and reverse (f

_{s_max_Reverse}and f

_{s_min_Reverse}) charging modes can be calculated.

#### 4.11. Step 11: Determining the Duration of Dead Time (t_{dead})

_{OSS}being equal to 55 pF are used, and thus the ZVS is easily accomplished. By using (22), the required dead time can be attained.

## 5. The Structure of the Digital Signal Control System

#### 5.1. Control Strategy

_{b_ref}being 95% of the upper limit battery voltage and I

_{b_ref}being the reference current signal according to the battery charging current. When the battery is charged in the constant-current mode, the analog-to-digital converter (ADC) of the DSP will fetch the output signal I

_{b}and compare it with the reference current signal I

_{b_ref}to obtain the difference. With the compensation by a Proportional integrator (PI) controller and modulation by a frequency modulation generator (FM generator), a frequency modulated pulse-width modulation (PWM) is achieved to accomplish the constant current control.

#### 5.2. The Step Response Test of the Charging Current

## 6. The Measurements and Operating Efficiency Analysis

_{r1}= 59.9 µH, Lr2 = 41.6 µH, L

_{m}= 209.65 µH, C

_{r1}= 42.29 nF, and C

_{r2}= 60.9 nF. Owing to the winding transformer’s windings and resonant inductor being handmade, there definitely exists some differences from the calculated ones. Indeed, the transformer magnetizing inductance L

_{m}was measured to be 219.85 µH, and the primary and secondly leakage inductances are L

_{lk1}= 6 µH and L

_{lk2}= 4 µH, respectively. Moreover, two resonant inductances are L

_{r1}= 55.2 µH and L

_{r2}= 40.36 µH. The resonant capacitors are connected in parallel; it not only can divert the current flow, but it also can reduce the current stress of each capacitor and decrease equivalent series resistance (ESR) loss with C

_{r1}= 41.4 nF and C

_{r2}= 53.7 nF.

_{1}–Q

_{8}) to promote the converter’s performance.

#### 6.1. Critical Measurements for the Forward Charging Mode

_{GS3}, v

_{DS3}, and i

_{DS3}in the cases where V

_{DC_Grid}= 400 V and charging battery voltages are V

_{Bat}= 280 V and V

_{Bat}= 403 V respectively. It is obvious that there appears a reverse current i

_{DS3}inside the power switch both in Figure 16a,b which helps remove the energy on the parasitic capacitance and rapidly decline V

_{DS3}to 0V, thus achieving ZVS.

_{DB7}and i

_{DB7}in the cases where V

_{DC_Grid}= 400 V and charging battery voltages are V

_{Bat}= 280 V and V

_{Bat}= 403 V, respectively. By observing Figure 17a, the diode current i

_{DB7}has not fallen to 0 A prior to the cut-off of diode D

_{B7}and thus leads to diode ZCS failure. Figure 17b shows that the diode current i

_{DB7}has reached 0 A before diode D

_{B7}turns off and thus succeeds in the ZCS of D

_{B7}. It is worth noting that the oscillation of v

_{DB7}at the switching instant resulted from the resonance of parasitic capacitance and resonant inductance.

#### 6.2. Critical Measurements for the Reverse Discharging Mode

_{GS8}, v

_{DS8}, and i

_{DS8}in the cases where the discharging battery voltages are V

_{Bat}= 280 V and V

_{Bat}= 403 V, respectively, and V

_{DC_Grid}= 400 V. It is obvious that there appears a reverse current i

_{DS8}inside the power switch both in Figure 18a,b, which helps remove the energy on the parasitic capacitance and rapidly decline v

_{DS8}to 0 V, thus achieving ZVS.

_{DB4}and i

_{DB4}in the cases where the discharging battery voltages are V

_{Bat}= 280 V and 403 V, respectively, and the DC grid voltage V

_{DC_Grid}= 400 V. By observing Figure 19a, the diode current i

_{DB4}has fallen to 0 A prior to the cut-off of diode D

_{B4}and thus leads to diode ZCS being successful. It is worth noting that there appears oscillation of v

_{DB4}at the switching instant, which resulted from the resonance of parasitic capacitance and the secondary resonant inductance. Due to the resonant converter working at Region I, Figure 19b shows that the diode current i

_{DB4}has not reached 0 A before diode D

_{B4}turns off and thus fails in ZCS of D

_{B4}.

#### 6.3. Efficiency Plots for Forward Mode and Reverse Mode

_{Bat}being 280, 340, and 403 V and charging currents ranging from 0.5 to 2.5 A. This reveals that the maximum conversion efficiency is 91.96% at the lowest battery voltage 280 V, and the maximum conversion efficiency is 93.25% at the highest battery voltage 403 V. The maximal efficiency of 93.67% appears in the case of the 340 V battery voltage because it gets near to the resonant point, and the total impedance is nearly 0. In the forward charging mode, the voltage of DC grid is 400 V, and the designed resonant frequency is around 100 kHz at the 340 V battery voltage, thus getting higher efficiency due to the switching instants of the turn-on and cut-off being near the zero-crossing point. When the discharging current is low, although possessing both ZVS and ZCS, the effect is not obvious due to low current. As the current rises to 1.5A, the efficiency at battery voltage 403 V apparently surpasses that with 280 V battery voltage.

_{Bat}being 280, 340, and 403 V and discharging currents ranging from 0.5 to 2.5 A. In the reverse discharging mode, the voltage of DC grid is 400 V as well. For low battery voltage level, it needs more voltage gain to fulfill DC grid charging and operates in the Region II due to low operating frequency. At different voltage levels of the battery, low battery voltage conditions need more current to discharge the constant voltage DC grid to achieve the identical power level and thus experience more relative power loss. In the case of a 280 V battery voltage, despite the converter operating in Region II and possessing ZCS on the rectifier side, its power loss rate is relatively higher. Operating at a 340 V battery voltage, even though the converter works near the resonant frequency and possesses the advantage of ZVS and ZCS, the conversion efficiency is better than that of the 403 V battery voltage due to more discharging current being needed for the identical power conversion. In fact, when the battery voltage is 403 V and operates at high frequency in Region I with only a ZVS mechanism, it achieves similar efficiency with that of 340 V. This reveals that the maximum conversion efficiency is 91.3% at the lowest discharging voltage 280 V, and the maximum conversion efficiency is 94.6% at the highest discharging voltage 403 V.

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Ma, Z.; Pesaran, A.; Gevorgian, V.; Gwinner, D.; Kramer, W. Energy storage, renewable power generation, and the grid: NREL capabilities help to develop and test energy-storage technologies. IEEE Electrif. Mag.
**2015**, 3, 30–40. [Google Scholar] [CrossRef] - Babokany, A.S.; Jabbari, M.; Shahgholian, G.; Mahdavian, M. A review of bidirectional dual active bridge converter. In Proceedings of the 9th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology; Institute of Electrical and Electronics Engineers (IEEE), Phetchaburi, Thailand, 16–18 May 2012; pp. 1–4. [Google Scholar]
- Tytelmaier, K.; Husev, O.; Veligorskyi, O.; Yershov, R. A review of non-isolated bidirectional dc-dc converters for energy storage systems. In Proceedings of the 2nd International Young Scientists Forum on Applied Physics and Engineering (YSF), Kharkiv, Ukraine, 10–14 October 2016; pp. 22–28. [Google Scholar]
- Zhao, B.; Yu, Q.; Sun, W. Bidirectional full-bridge DC-DC converters with dual phase-shifting control and its backflow power characteristic analysis. In Proceedings of the Chinese Society of Electrical Engineering, Bejing, China, 25 April 2012; pp. 43–50. [Google Scholar]
- Zhao, B.; Song, Q.; Liu, W. Efficiency Characterization and Optimization of Isolated Bidirectional DC–DC Converter Based on Dual-Phase-Shift Control for DC Distribution Application. IEEE Trans. Power Electron.
**2013**, 28, 1711–1727. [Google Scholar] [CrossRef] - Zhao, B.; Song, Q.; Liu, W.; Sun, Y. Overview of dual-active-bridge isolated bidirectional DC–DC converter for high-frequency-link power-conversion system. IEEE Trans. Power Electron.
**2013**, 29, 4091–4106. [Google Scholar] [CrossRef] - Li, W.; Zhao, H.; Kan, T.; Mi, C. Inter-operability considerations of the double-sided LCC compensated wireless charger for electric vehicle and plug-in hybrid electric vehicle applications. In Proceedings of the IEEE PELS Workshop on Emerging Technologies: Wireless Power (2015 WoW), Daejeon, Korea, 5–6 June 2015; pp. 1–6. [Google Scholar]
- Shafiei, N.; Saket, M.A.; Ordonez, M. Time domain analysis of LLC resonant converters in the boost mode for battery charger applications. In Proceedings of the IEEE Energy Conversion Congress and Exposition (ECCE), Cincinnati, OH, USA, 1–5 October 2017; pp. 4157–4162. [Google Scholar]
- Liu, C.; Wang, J.; Colombage, K.; Gould, C.; Sen, B. A CLLC resonant converter based bidirectional EV charger with maximum efficiency tracking. In Proceedings of the 8th IET International Conference on Power Electronics, Machines and Drives (PEMD 2016), Glasgow, UK, 19–21 April 2016; pp. 1–6. [Google Scholar]
- Dalala, Z.; Zahid, Z.U.; Saadeh, O.; Lai, J.S.J. Modeling and controller design of a bidirectional resonant converter battery charger. IEEE Access
**2018**, 6, 23338–23350. [Google Scholar] [CrossRef] - Pledl, G.; Tauer, M.; Buecherl, D. Theory of operation, design procedure and simulation of a bidirectional LLC resonant converter for vehicular applications. In Proceedings of the IEEE Vehicle Power and Propulsion Conference, Lille, France, 1–3 September 2010; pp. 1–5. [Google Scholar]
- Chen, W.; Rong, P.; Lu, Z. Snubberless bidirectional DC–DC converter with new CLLC resonant tank featuring minimized switching loss. IEEE Trans. Ind. Electron.
**2010**, 57, 3075–3086. [Google Scholar] [CrossRef] - Lv, Z.; Yan, X.; Fang, Y.; Sun, L. Mode analysis and optimum design of bidirectional CLLC resonant converter for high-frequency isolation of DC distribution systems. In Proceedings of the IEEE Energy Conversion Congress and Exposition (ECCE), Montreal, QC, Canada, 20–24 September 2015; pp. 1513–1520. [Google Scholar]
- Tan, K.; Yu, R.; Guo, S.; Huang, A.Q. Optimal design methodology of bidirectional LLC resonant DC/DC converter for solid state transformer application. In Proceedings of the 40th IEEE Annual Conference of the IEEE Industrial Electronics Society, Dallas, TX, USA, 29 October–1 November 2014; pp. 1657–1664. [Google Scholar]
- Jiang, T.; Zhang, J.; Wu, X.; Sheng, K.; Wang, Y. A Bidirectional LLC resonant converter with automatic forward and backward mode transition. IEEE Trans. Power Electron.
**2015**, 30, 757–770. [Google Scholar] [CrossRef] - Zhang, J.; Liu, J.; Yang, J.; Zhao, N.; Wang, Y.; Zheng, T.Q. An LLC-LC type bidirectional control strategy for an LLC resonant converter in power electronic traction transformer. IEEE Trans. Ind. Electron.
**2018**, 65, 8595–8604. [Google Scholar] [CrossRef] - Zong, S.; Fan, G.; Yang, X. Double Voltage Rectification Modulation for Bidirectional DC/DC Resonant Converters for Wide Voltage Range Operation. IEEE Trans. Power Electron.
**2018**, 34, 6510–6521. [Google Scholar] [CrossRef] - Song, J.; Yang, D.; Zhang, C.; Duan, B. Hybrid control method for CLLLC resonant converter with Low output voltage ripple. IFAC PapersOnLine
**2018**, 51, 680–684. [Google Scholar] [CrossRef] - Texas Instruments Power Supply Design Seminar. Designing an LLC Resonant Half-Bridge Power Converter; Texas Instruments Power Supply Design Seminar: Dallas, TX, USA, 2019. [Google Scholar]
- Ditze, S. Steady-state analysis of the bidirectional CLLLC resonant converter in time domain. In Proceedings of the IEEE 36th International Telecommunications Energy Conference (INTELEC), Vancouver, BC, Canada, 28 September–2 October 2014; pp. 1–9. [Google Scholar]
- Lu, B.; Liu, W.; Liang, Y.; Lee, F.; van Wyk, J. Optimal design methodology for LLC resonant converter. In Proceedings of the 21st Annual IEEE Applied Power Electronics Conference and Exposition, APEC’06, Dallas, TX, USA, 19–23 March 2006; pp. 533–538. [Google Scholar]
- Luo, S.J. Implementation of a Dual-Active-Bridge Bidirectional Isolated DC to DC Converter in Home Area Network. Master’s Thesis, Department of Electrical Engineering, National Sun Yat-Sen University, Kaohsiung City, Taiwan, 2012. [Google Scholar]
- Liang, J.C. Contactless Li-Mn Battery Charger with Intelligent Control. Master’s Thesis, Department of Electrical Engineering, National Central University, Taoyuan City, Taiwan, 2014. [Google Scholar]

**Figure 1.**The proposed isolated bidirectional symmetric resonant converter with dual active full bridge.

**Figure 3.**Voltage gain profile in the forward mode of the proposed bidirectional symmetric resonant converter.

**Figure 6.**The conduction path of each stage in Region II: (

**a**) Stage I conduction path; (

**b**) Stage II conduction path; (

**c**) Stage III conduction path; (

**d**) Stage IV conduction path; (

**e**) Stage V conduction path.

**Figure 15.**The voltage state under abrupt load current fluctuation: (

**a**) load current changes from 1.5 A to 2.5 A; (

**b**) load current changes from 2.5 A to 1.5 A.

**Figure 16.**Waveforms of v

_{GS3}, v

_{DS3}, and i

_{DS3}with two battery voltages: (

**a**) V

_{Bat}= 280 V; (

**b**) V

_{Bat}= 403 V.

**Figure 17.**Waveforms of v

_{DB7}and i

_{DB7}with two battery voltages: (

**a**) V

_{Bat}= 280 V; (

**b**) V

_{Bat}= 403 V.

**Figure 18.**Waveforms of v

_{GS8}, v

_{DS8}, and i

_{DS8}with two discharging battery voltages: (

**a**) V

_{Bat}= 280 V; (

**b**) V

_{Bat}= 403 V.

**Figure 19.**Waveforms of v

_{DB4}and i

_{DB4}with two discharging battery voltages: (

**a**) V

_{Bat}= 280 V; (

**b**) V

_{Bat}= 403 V.

Parameters | Specifications |
---|---|

DC grid voltage V_{DC_Grid} | 400 V |

Battery port voltage V_{Bat} | 280–403 V |

Max. conversion power P | 1000 W |

Series resonant frequency f_{r1} | 100 kHz |

Power switching range f_{s} | 70–150 kHz |

Device Symbol | Quantity |
---|---|

Transformer turn ratio N_{P}:N_{S} | 1.2:1 |

Magnetizing inductance L_{m} | 219.85 µH |

Resonant inductance L_{r1}(including primary leakage inductance) | 61.2 µH |

Resonant inductance L_{r2}(including secondary leakage inductance) | 44.36 µH |

Resonant capacitance (primary) C_{r1} | 41.4 nF |

Resonant capacitance (secondary) C_{r2} | 53.7 nF |

DC grid capacitor tank C_{DC_Grid} | 540 µF |

Battery capacitor tank C_{Bat} | 540 µF |

Power switches Q_{1}–Q_{8} | C2M0160120D |

Trigger controller | TMS320F28335 |

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## Share and Cite

**MDPI and ACS Style**

Yan, Y.-H.; Cheng, H.-L.; Chan, S.-Y.; Chen, Y.-D.; Chang, Y.-N.
Design of an Isolated Bidirectional Symmetric Resonant Converter. *Appl. Sci.* **2020**, *10*, 8144.
https://doi.org/10.3390/app10228144

**AMA Style**

Yan Y-H, Cheng H-L, Chan S-Y, Chen Y-D, Chang Y-N.
Design of an Isolated Bidirectional Symmetric Resonant Converter. *Applied Sciences*. 2020; 10(22):8144.
https://doi.org/10.3390/app10228144

**Chicago/Turabian Style**

Yan, Yih-Her, Hung-Liang Cheng, Shun-Yu Chan, Yu-Da Chen, and Yong-Nong Chang.
2020. "Design of an Isolated Bidirectional Symmetric Resonant Converter" *Applied Sciences* 10, no. 22: 8144.
https://doi.org/10.3390/app10228144