# Modeling Push–Pull Converter for Efficiency Improvement

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Power Losses of Push–Pull Converter

_{IN}stands for input power, P

_{OUT}represents output power, and P

_{LOSS}covers total power losses in the converter. Clearly, the efficiency can be easily derived from (1) if we know how to calculate total power losses.

_{LOSS}can be expressed as:

_{COND}—conduction losses, P

_{FIXED}—fixed losses, W

_{TOT}—total energy consumed during one period. Average dynamic power losses can be represented as P

_{DYN}= W

_{TOT}·f

_{sw}. Clearly, the dynamic losses directly depend on switching frequency f

_{sw}. On the other end, controller power supply current and leakage currents contribute to fixed losses. They are negligible in comparison to conduction and dynamic losses and, therefore, can be excluded from further analysis.

_{ON}(when turned on). The model also includes the transistor input capacitance C

_{ISS}. Diode (forward-biased) is modeled using constant voltage source V

_{D}and resistance R

_{D}.

_{C,ESR}(equivalent series resistance of the output filter capacitance). Similarly, inductor equivalent series resistance (R

_{L,ESR}) accounts for its conduction losses. In addition, we consider inductor core power losses. Finally, the supply circuit is modeled as a series of resistance R

_{GEN}and voltage generators, where R

_{GEN}represents converter supply circuit losses. In [23], an analytical expression is given for R

_{GEN}for the case when the supply circuit consists of AC generator and single-phase or three-phase rectifier.

_{SW,eff}, I

_{D,eff}, I

_{C,eff}, I

_{IN,eff}represent effective values of currents through switch, diode, output capacitor and converter input, respectively. I

_{D,avg}is average diode current. P

_{L,COND}and P

_{TR,COND}are conduction losses in inductor and transformer windings, respectively. P

_{CLAMP}is power dissipation of the limiting circuit of the rectifier output.

_{L,ESRL,DC}represents inductor equivalent serial resistance for DC current. The second term in (4) accounts for power losses in the winding due to the skin and proximity effects, where R

_{L,ESR,AC}denotes inductor resistance for the AC current I

_{1L,EFF}at the switching frequency.

_{L,ESR,AC}is given by the following Equation [25]:

_{DC,m}represents resistance of the m

^{th}layer for DC current

_{m}number of turns in the m

^{th}layer, l

_{m,turn}one turn wire length, and A

_{W}is the wire cross-sectional area. Moreover, ξ from (6) is characterized as

_{SEC}is voltage amplitude on transformer’s secondary winding.

_{ISS}is power loss in transistor gate, P

_{SW}is power loss during switching, P

_{BRIDGE}is power loss in rectifier, P

_{L,CORE}is dynamic power loss in inductor core, P

_{TR,CORE}is dynamic power loss in transformer core, P

_{SW,SNUB}is power loss in snubber circuit of the switch, and P

_{SEC,SNUB}is power loss in snubber circuit of the transformer’s secondary winding. We note here that, in the case of push–pull converter, if snubber circuit is used on the transformer’s secondary winding, then limiting circuit is not used and vice versa.

_{G}is total charge in the gate and V

_{CG}is supply voltage of gate control circuit.

_{vr}and t

_{vf}are rising and falling time of the output voltage, respectively. Factor k is between 1/6 and 1/2 [27]. Rising and falling times can be calculated using the equations from [16]:

_{G (SW)}represents gate charge at the switching point, which can be expressed with the following equation:

_{SP,ON}and V

_{SP,OFF}are voltages at the switching points. The values of these voltages can be retrieved from the gate charge diagram from the MOSFET specifications. Alternatively, they can be calculated approximately with equations:

_{G}represents gate threshold voltage, and g

_{m}stands for MOSFET transconductance.

_{OSS}. However, the authors in [17] proved that they are already expressed in (13).

_{SEC}-secondary voltage, t

_{rr}-diode recovery time, Q

_{r}-pn junction accumulated charge. The losses in (21) are present only when the converter operates in CCM. Given that the diode current is zero when transistor turns on, we can conclude that these losses are zero in DCM.

_{CORE}represents volume of the inductor core, k, α, and β are coefficients of the core material (retrieved from the specifications), and ΔB stands for the maximum induction in the core.

_{P}is number of turns in primary winding.

_{L}) is calculated using the equation:

_{SN}is capacitance of the snubber circuit.

_{L,eff}, in CCM operating mode of the converter, can be derived from the waveform shown in Figure 3a:

_{L,avg}= I

_{LOAD}. Effective currents through the secondary winding and switch are expressed as:

_{PRI}

_{,max}) and minimum (I

_{PRI}

_{,min}) currents are given as follows:

_{L,eff}) we obtain

_{1}is defined as

#### 2.2. Experimental Setup of Push–Pull Converter

- DC input voltage V
_{IN}= 30–58 V; - DC output voltage V
_{OUT}= 300 V (0–100% load); - maximum output power P
_{OUT}= 500 W; - switching frequency f
_{sw}= 10–100 kHz.

_{p}/2) of AWG 13 wire, while the secondary winding consists of 84 turns of AWG 17 wire. The inductor winding contains 79 turns of AWG 21 wire, which makes total wire length of 2.86 m and inductance of about 1 mH. Capacitance of the filter capacitor at the input of the converter is around 10 mF with the equivalent serial resistance of around 0.015 Ω. Output filter capacitor of the push–pull converter has capacitance of 220 µF with the equivalent serial resistance of around 0.25 Ω. We used MOSFET IRFP250 as a switch, and bridge rectifier was realized with MUR1560 diodes. A controller part of the push–pull converter is implemented using PIC24FJ64GA002 microcontroller. For measuring efficiency of the converter, HUMUSOFT MF624 acquisition card featuring MATLAB Simulink with Real-Time Windows Target was used. Power measurement error is 1%. Resistor, 75 Ω, and MOSFET were used to simulate the variable load of the converter. The wind turbine with PM generator is emulated using HP 6674 A DC power supply. The generator resistance (R

_{gen}) is not modeled and, therefore, it is not considered in simulation and experimental results.

## 3. Results

_{DS}), which is used to model transistor on state. In datasheet, two values are usually given: typical (R

_{DS,TYP}) and maximum (R

_{DS,MAX}) value. Given the above, we performed simulations for two distinct scenarios: best case, (e.g., using R

_{DS,TYP}) and worst case, (e.g., using R

_{DS,MAX}) with respect to the converter efficiency.

## 4. Discussion

_{100k}) and the maximum measured energy efficiency (η

_{opt}). Additionally, we calculated and presented the total power losses of the converter. On the other end, based on Figure 8, Figure 9 and Figure 10, the maximum efficiency is obtained at lower frequencies. Table 5 also shows improvement in terms of power losses for the case when the converter operates using the optimal switching frequency comparing to the case when the maximum switching frequency is used. Obviously, it should be kept in mind that one must not arbitrarily decrease the switching frequency as it may compromise the designed working conditions.

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Abbreviations

List of abbreviations | |

AC | Alternating current |

AWG | American wire gauge |

CCM | Continuous current mode |

DC | Direct current |

DCM | Discontinuous current mode |

ESR | Equivalent series resistance |

MOSFET | Metal oxide semiconductor field effect transistor |

PM | Permanent magnet |

SPICE | Simulation Program with Integrated Circuit Emphasis |

List of symbols | |

A_{W} | Wire cross-sectional area |

C_{ISS} | MOSFET input capacitance |

C_{OSS} | Output capacitance |

C_{SN} | Capacitance of the snubber circuit |

d | Wire diameter |

f_{sw} | Switching frequency |

g_{m} | MOSFET transconductance |

I_{C,eff} | Effective value of the current through output capacitor |

I_{D,avg} | Average diode current |

I_{D,eff} | Effective value of the diode current |

I_{IN,eff} | Effective value of the converter input current |

I_{L,avg} | Average inductor current |

I_{L,eff} | Effective inductor current |

I_{LOAD} | Load current |

I_{PRI}_{,max} | Primary winding maximum current |

I_{PRI}_{,min} | Primary winding minimum current |

I_{SW,eff} | Effective value of the current through switch |

I_{1L,EFF} | Effective value of the inductor’s current first harmonic |

l_{m,turn} | One turn wire length |

m | Number of layers of the inductor winding |

N_{m} | Number of turns in the m^{th} layer |

N_{P} | Number of turns in primary winding |

n | Transformer’s turns ratio |

P_{BRIDGE} | Power loss in rectifier |

P_{COND} | Conduction losses |

P_{CLAMP} | Power dissipation of the limiting circuit of the rectifier output |

P_{FIXED} | Fixed losses |

P_{IN} | Input power |

P_{ISS} | Power loss in transistor gate, |

P_{L,COND} | Conduction losses in inductor |

P_{L,CORE} | Dynamic power loss in inductor core |

P_{LOSS} | Total power losses |

P_{OUT} | Output power |

P_{SW} | Power loss during switching |

P_{TR,COND} | Conduction losses in transformer windings |

P_{TR,CORE} | Dynamic power loss in transformer core |

P_{SEC,SNUB} | Power loss in snubber circuit of the transformer’s secondary winding |

P_{SW,SNUB} | Power loss in snubber circuit of the switch |

Q_{G} | Total charge in the gate |

Q_{G (SW)} | Gate charge at the switching point |

Q_{r} | Pn junction accumulated charge |

R_{C,ESR} | Equivalent series resistance of the output filter capacitance |

R_{D} | Diode resistance in on state |

R_{DC,m} | Resistance of the m^{th} layer for DC current |

R_{DS,MAX} | Maximum value of drain–source resistance |

R_{DS,TYP} | Typical value of drain–source resistance |

R_{GEN} | Resistance of the generator |

R_{L,ESR} | Inductor equivalent series resistance |

R_{L,ESR,AC} | Inductor resistance for the AC current |

R_{L,ESRL,DC} | Inductor’s equivalent serial resistance for DC current |

R_{ON} | MOSFET resistance in on state |

t_{rr} | Diode recovery time |

t_{vf} | Falling time of the output voltage |

t_{vr} | Rising time of the output voltage |

V_{CG} | Supply voltage of gate control circuit |

V_{CORE} | Volume of the inductor core |

V_{D} | Diode voltage in on state |

V_{G} | Gate threshold voltage |

V_{IN} | DC input voltage |

V_{OUT} | DC output voltage |

V_{SEC} | Voltage amplitude on transformer’s secondary winding |

V_{SP,ON} | Voltages at the switching on point |

V_{SP,OFF} | Voltages at the switching off point |

W_{TOT} | Total energy consumed |

ΔB | Maximum induction in the core |

Δi_{L} | Inductor current change |

δ | Skin depth |

η | Energy efficiency |

ρ | Resistivity of the wire |

## References

- Wu, Q.; Wang, Q.; Xu, J.; Xu, Z. Active-clamped ZVS current-fed push–pull isolated dc/dc converter for renewable energy conversion applications. IET Power Electron.
**2018**, 11, 373–381. [Google Scholar] [CrossRef] - Bose, B. Modelling of Microinverter and PushPull Flyback Converter for SPV Application. In Proceedings of the 2020 8th International Conference on Reliability, Infocom Technologies and Optimization (Trends and Future Directions) (ICRITO), Noida, India, 4–5 June 2020; pp. 458–462. [Google Scholar] [CrossRef]
- Das, M.; Agarwal, V. Design and Analysis of a High-Efficiency DC–DC Converter With Soft Switching Capability for Renewable Energy Applications Requiring High Voltage Gain. IEEE Trans. Ind. Electron.
**2016**, 63, 2936–2944. [Google Scholar] [CrossRef] - Gu, A.; Sun, W.; Zhang, G.; Chen, S.; Wang, Y.; Yang, L.; Zhang, Y. Boost-type push–pull converter with reduced switches. J. Power Electron.
**2020**, 20, 645–656. [Google Scholar] [CrossRef] - Junior, M.E.T.S.; Freitas, L.C.G. Power Electronics for Modern Sustainable Power Systems: Distributed Generation, Microgrids and Smart Grids—A Review. Sustainability
**2022**, 14, 3597. [Google Scholar] [CrossRef] - Mangkalajan, S.; Ekkaravarodome, C.; Sukanna, S.; Jirasereeamongkul, K.; Higuchi, K. Design of Digital Robust Control of A2DOF with Push-Pull Convert for Renewable Energy Application. In Proceedings of the 2019 16th International Conference on Electrical Engineering/Electronics, Computer, Telecommunications and Information Technology (ECTI-CON), Pattaya, Thailand, 10–13 July 2019; pp. 537–540. [Google Scholar] [CrossRef]
- Joseph, P.K.; Devaraj, E. Design of hybrid forward boost converter for renewable energy powered electric vehicle charging applications. IET Power Electron.
**2019**, 12, 2015–2021. [Google Scholar] [CrossRef] - Sunarno, E.; Sudiharto, I.; Nugraha, S.D.; Qudsi, O.A.; Eviningsih, R.P.; Raharja, L.P.S.; Arifin, I.F. A Simple And Implementation of Interleaved Boost Converter For Renewable Energy. In Proceedings of the 2018 International Conference on Sustainable Energy Engineering and Application (ICSEEA), Tangerang, Indonesia, 1–2 November 2018; pp. 75–80. [Google Scholar] [CrossRef]
- Abhishek, M.; Reddy, K.S.; Shanthini, C.; Devi, V.S.K. Comparative Analysis of Boost and Quadratic Boost Converter for Wind Energy Conversion System. In Proceedings of the 2022 International Conference on Electronics and Renewable Systems (ICEARS), Tuticorin, India, 16–18 March 2022; pp. 283–287. [Google Scholar] [CrossRef]
- Forouzesh, M.; Siwakoti, Y.P.; Gorji, S.A.; Blaabjerg, F.; Lehman, B. Step-Up DC–DC Converters: A Comprehensive Review of Voltage-Boosting Techniques, Topologies, and Applications. IEEE Trans. Power Electron.
**2017**, 32, 9143–9178. [Google Scholar] [CrossRef] - Nugraha, S.D.; Qudsi, O.A.; Yanaratri, D.S.; Sunarno, E.; Sudiharto, I. MPPT-current fed push pull converter for DC bus source on solar home application. In Proceedings of the 2017 2nd International conferences on Information Technology, Information Systems and Electrical Engineering (ICITISEE), Yogyakarta, Indonesia, 1–2 November 2017; pp. 378–383. [Google Scholar] [CrossRef]
- Tarzamni, H.; Babaei, E.; Esmaeelnia, F.P.; Dehghanian, P.; Tohidi, S.; Sharifian, M.B.B. Analysis and Reliability Evaluation of a High Step-Up Soft Switching Push–Pull DC–DC Converter. IEEE Trans. Reliab.
**2019**, 69, 1376–1386. [Google Scholar] [CrossRef] - Hassan, T.-U.; Abbassi, R.; Jerbi, H.; Mehmood, K.; Tahir, M.; Cheema, K.; Elavarasan, R.; Ali, F.; Khan, I. A Novel Algorithm for MPPT of an Isolated PV System Using Push Pull Converter with Fuzzy Logic Controller. Energies
**2020**, 13, 4007. [Google Scholar] [CrossRef] - Maksimovic, D.; Stankovic, A.M.; Thottuvelil, V.J.; Verghese, G.C. Modeling and simulation of power electronic converters. Proc. IEEE
**2001**, 89, 898–912. [Google Scholar] [CrossRef] - Aloisi, W.; Palumbo, G. Efficiency model of boost dc-dc PWM converters. Int. J. Circuit Theory Appl.
**2005**, 33, 419–432. [Google Scholar] [CrossRef] - Sven, F.; Nagy, B. Buck/Boost Converter Modeling and Simulation for Performance Optimization. In Proceedings of the 22nd IASTED Internation-al Conference on Modelling and Simulation (MS 2011), Canada, Calgary, 4–6 July 2011; pp. 1–8. [Google Scholar]
- Xiong, Y.; Sun, S.; Jia, H.; Shea, P.; Shen, Z.J. New Physical Insights on Power MOSFET Switching Losses. IEEE Trans. Power Electron.
**2009**, 24, 525–531. [Google Scholar] [CrossRef] - Salima, K.; Achour, B. Efficiency Model of DC/DC PWM Converter Photovoltaic Applications. In Proceedings of the Global Conference on Re-newables and Energy Efficiency for Desert Regions and Exhibition, GCREEDER 2009, Amman, Jordan, 31 March–2 April 2009; pp. 1–5. [Google Scholar]
- Ayachit, A.; Kazimierczuk, M.K. Averaged Small-Signal Model of PWM DC-DC Converters in CCM Including Switching Power Loss. IEEE Trans. Circuits Syst. II Express Briefs
**2018**, 66, 262–266. [Google Scholar] [CrossRef] - Yao, L.; Li, D.; Liu, L. An improved power loss model of full-bridge converter under light load condition. PLoS ONE
**2018**, 13, e0208239. [Google Scholar] [CrossRef] - Lai, Y.-S.; Su, Z.-J. New Integrated Control Technique for Two-Stage Server Power to Improve Efficiency Under the Light-Load Condition. IEEE Trans. Ind. Electron.
**2015**, 62, 6944–6954. [Google Scholar] [CrossRef] - Zhao, L.; Li, H.; Liu, Y.; Li, Z. High Efficiency Variable-Frequency Full-Bridge Converter with a Load Adaptive Control Method Based on the Loss Model. Energies
**2015**, 8, 2647–2673. [Google Scholar] [CrossRef] [Green Version] - Ivanovic, Z.; Blanusa, B.; Knezic, M. Analytical power losses model of boost rectifier. IET Power Electron.
**2014**, 7, 2093–2102. [Google Scholar] [CrossRef] - Kondrath, N.; Kazimierczuk, M. Inductor winding loss owing to skin and proximity effects including harmonics in non-isolated pulse-width modulated dc–dc converters operating in continuous conduction mode. IET Power Electron.
**2010**, 3, 989–1000. [Google Scholar] [CrossRef] - Nan, X.; Sullivan, C. An improved calculation of proximity-effect loss in high-frequency windings of round conductors. In Proceedings of the IEEE 34th Annual Conference on Power Electronics Specialist, 2003. PESC ‘03, Acapulco, Mexico, 15–19 June 2003. [Google Scholar] [CrossRef]
- Jon, K. Synchronous Buck MOSFET Loss Calculation with Excel Model; Fairchild Semiconductor Publication: 2006. Available online: https://www.overclock.net/attachments/an-6005-pdf.270912/ (accessed on 3 April 2022).
- Wilson, E. Mosfet Current Source Gate Drivers, Switching Loss Modeling and Frequency Dithering Control for MHz Switching Frequency DC-DC Converters. Ph.D. Thesis, Queen’s University, Kingston, ON, Canada, February 2008. [Google Scholar]
- Van den Bossche, A.; Valchev, V.C. Modeling Ferrite Core Losses in Power Electronics. International Review of Electrical Engineering. 2006, pp. 14–22. Available online: https://biblio.ugent.be/publication/373054/file/459940 (accessed on 3 April 2022).
- Li, J.; Abdallah, T.; Sullivan, C. Improved calculation of core loss with nonsinusoidal waveforms. In Proceedings of the Conference Record of the 2001 IEEE Industry Applications Conference. 36th IAS Annual Meeting (Cat. No.01CH37248), Chicago, IL, USA, 7 August 2002; Volume 4, pp. 2203–2210. [Google Scholar] [CrossRef]

**Figure 3.**Characteristic voltage and current waveforms for push–pull converter: (

**a**) CCM operation mode, (

**b**) DCM operating mode.

**Figure 8.**Comparison of simulation and experimental results for the push–pull converter efficiency with input power of 500 W.

**Figure 9.**Comparison of simulation and experimental results for the push–pull converter efficiency with input power of 300 W.

**Figure 10.**Comparison of simulation and experimental results for the push–pull converter efficiency with input power of 150 W.

Characteristic | Proposed Model | SPICE | Ref. [15] | Ref. [18] | Ref. [19] | Ref. [20] | Ref. [21] | Ref. [22] |
---|---|---|---|---|---|---|---|---|

Converter type | Push–pull | Any | Boost | Boost | Boost | Full bridge | Full bridge | Full bridge |

Operating mode | CCM, DCM | CCM, DCM | CCM, DCM | CCM, DCM | CCM | CCM | CCM | CCM, DCM |

Diode dynamic losses | Yes | Yes | No | No | No | Yes | No | Yes |

MOSFET dynamic losses | Yes | Yes | Yes | No | Yes | Yes | Yes | Yes |

Skin effect | Yes | No | No | No | No | Yes | No | No |

Proximity effect | Yes | No | No | No | No | No | No | No |

Transformer/Inductor core | Yes | Yes | No | No | No | Yes | Yes | Yes |

Snubber circuit | Yes | Yes | No | No | No | No | No | No |

Gate driver | Yes | Yes | No | No | No | No | No | No |

Capacitor ESR | Yes | Yes | Yes | No | Yes | Yes | No | No |

Time-consuming | No | Yes | No | No | No | No | No | No |

Convergence issues | No | Yes | No | No | No | No | No | No |

P_{IN} (W) | 150 | 300 | 500 | |||
---|---|---|---|---|---|---|

f_{sw} (kHz) | 10 | 100 | 10 | 100 | 10 | 100 |

P_{COND} (W) | 11.22 | 15.23 | 43.37 | 30.41 | 93.74 | 71.04 |

P_{COND}/P_{LOSS} (%) | (91%) | (72.4%) | (92.4%) | (70%) | (93.2%) | (73.7%) |

P_{DYN} (W) | 1.11 | 5.82 | 3.59 | 13.06 | 6.82 | 25.35 |

P_{DYN}/P_{LOSS} (%) | (9%) | (27.6%) | (7.6%) | (30%) | (6.8%) | (26.3%) |

P_{LOSS} (W) | 12.33 | 21.05 | 46.96 | 43.47 | 100.55 | 96.39 |

η_{model} (%) | (91.9%) | (91.1%) | (84.4%) | (85.6%) | (79.9%) | (80.7%) |

η_{exper} (%) | (85.3%) | (86.3%) | (80.5%) | (83.4%) | (73.1%) | (78.2%) |

|η_{model}–η_{exper}| (%) | (6.47%) | (4.75%) | (3.9%) | (2.2%) | (6.8%) | (2.5%) |

P_{COND}/f_{sw} (kHz) | 10 | 100 |
---|---|---|

P_{MOSFET} (W) | 24.8 | 13.54 |

P_{BRIDGE} (W) | 1.92 | 1.79 |

P_{INDUCTOR} (W) | 0.18 | 0.12 |

P_{C ESR} (W) | 2.59 | 1.33 |

P_{TRANS} (W) | 0.55 | 0.3 |

P_{CLAMP} (W) | 13.33 | 13.33 |

P_{COND_TOT} (W) | 43.37 | 30.41 |

P_{DYN}/f_{sw} (kHz) | 10 | 100 |
---|---|---|

P_{MOSFET} (W) | 0.40 | 3.00 |

P_{BRIDGE} (W) | 0.00 | 3.60 |

P_{INDUCTOR} (W) | 0.83 | 4.23 |

P_{TRANS} (W) | 2.00 | 0.07 |

P_{SNUBBER} (W) | 0.36 | 2.16 |

P_{DYN_TOT} (W) | 3.59 | 13.06 |

Efficiency, P_{LOSS} | P_{IN} = 150 W | P_{IN} = 300 W | P_{IN} = 500 W |
---|---|---|---|

η_{100k} (%) | (86.26%) | (83.43%) | (78.22%) |

P_{LOSS}|_{100k} (W) | 20.61 | 49.71 | 108.9 |

η_{opt} (%) | (88.90%) | (86.71%) | (82.59%) |

P_{LOSS}|_{opt} (W) | 16.65 | 39.87 | 87.05 |

P_{LOSS}|_{100k}–P_{LOSS}|_{opt} | 3.96 | 9.84 | 21.85 |

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**MDPI and ACS Style**

Ivanovic, Z.; Knezic, M.
Modeling Push–Pull Converter for Efficiency Improvement. *Electronics* **2022**, *11*, 2713.
https://doi.org/10.3390/electronics11172713

**AMA Style**

Ivanovic Z, Knezic M.
Modeling Push–Pull Converter for Efficiency Improvement. *Electronics*. 2022; 11(17):2713.
https://doi.org/10.3390/electronics11172713

**Chicago/Turabian Style**

Ivanovic, Zeljko, and Mladen Knezic.
2022. "Modeling Push–Pull Converter for Efficiency Improvement" *Electronics* 11, no. 17: 2713.
https://doi.org/10.3390/electronics11172713