An improved power loss model of full-bridge converter under light load condition

When the full-bridge converter works under the light load condition, the power efficiency obtained by the theoretical model is much different from that of the actual converter. Facing with this situation, an improved power loss model based on the typical power loss model is proposed. In this paper, the typical power loss model is called typical model for short and the improved power loss model is called proposed model for short. Firstly, the antiparallel freewheeling diodes at the arms of full-bridge circuit are taken into account. Every barrier junction capacitance of Schottky diode in the rectifier circuit is neglected. Then, the turning-off loss of full-bridge and the core loss of inductive components (the transformer and the filter inductor) in the typical model are compensated and modified by combining the theoretical values with the measured input current under the minimum and the maximum output current. In addition, it also corrects the equivalent resistance related to the conduction loss of converter. Eventually, the proposed model is established. The rise time and fall time of the midpoint voltage of two arms, and the fluctuation degree of the reverse bias voltage related to the Schottky rectifier diodes are regarded as the local indexes. The conduction time of the metal oxide semiconductor field effect transistor (MOSFET) in each switching period, and the power efficiency of converter are regarded as the global indexes. Based on the analyses, the local indexes are compared qualitatively, while the global indexes are compared quantitatively. It is found that the differences of the local indexes between the proposed model and the experiment are smaller than those between the typical model and the experiment. Meanwhile, the global indexes of the proposed model are closer to the experimental results. Therefore, it can be further demonstrated that the proposed model is more approximate to the actual converter than the typical model.


Introduction
DC-DC converters have been paid much attention to in recent years. They can be widely applied in many fields such as photovoltaic (PV) system, electric vehicle (EV) system, and so on. In the PV system, the maximum power point tracking (MPPT) methods are developed by the DC-DC converter. Regulating duty cycles of main switches is an effective way to realize the MPPT. Besides the conventional perturbation and observation method and the incremental a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 conductance method, some advanced MPPT algorithms have been successfully used. For example, an improved MPPT method combined with characteristics of solar cell arrays under the shadow condition has been proposed in [1]. In [2], a method without algorithm-specific parameters has been improved and it is also called natural cubic-spline-guided Jaya algorithm (S-Jaya). In [3], the nonsimplified single-diode model is used to determine the MPP. Curve fitting method is fully developed in the proposed real-time estimation of the MPP. In [4], the emulation of PV module is obtained according to the mathematical model of PV cell. Several characteristic curves of certain PV system and related MPPT methods can be achieved at the output terminals of proposed system. In the EV system, different energy storages are the source or load of DC-DC converter and power is converted by the converter. In [5], an interleaved-boost full-bridge DC-DC three-port converter is designed. The phase angle and duty cycle are variables in the modulation. The duty cycle is related to the power flow between two inputs and the phase angle is relevant to the output voltage. In [6], a three-phase rectifier, a three-phase inverter, and a dual-active bridge DC-DC converter are taken as a whole. Dynamic efficiency models of the whole are established so that the proposed varied dc-link voltage method can be effectively developed. In [7], a new bidirectional DC-DC converter is proposed and it is connected to the dual battery energy source and the DC-bus of different voltage levels.
Based on the hybrid model of converter, different modes of power flow can be regulated. Similarly, the DC-DC converter has been popular in the electric aircraft system. In [8], a fuel cell, a battery, and a supercapacitor are connected to the DC bus by the proposed quadruple active bridge converter. Furthermore, the energy sources and the power flow can be individually controlled by using multiple DC-DC converters. In the DC grid system, the DC-DC converter is also the main part of power transfer device. In [9], the modular multilevel converter is the investigated object and the switch-based model of insulated gate bipolar transistor (IGBT) is established. Transient performance of switches is reflected by the dynamic model which is based on the curve-fitting. Therefore, the power loss of converter can be analyzed and calculated. In [10], wind energy and solar energy are the two sources in the grid system. The voltage and frequency are regulated according to the droop characteristics of system. The practical conditions have been fully considered. Furthermore, both of the two energy blocks can achieve the MPPT. From what has been introduced above, it can be concluded that different DC-DC converters play important roles in many fields and their models can help researchers have knowledge of converters.
As the typical representative, full-bridge DC-DC converters with isolated transformer have been widely applied in the new energy generation, server power supply, and electric vehicles [11][12][13]. The work environment of the converters is becoming complex. As a kind of power conversion and transmission device, power efficiency is an important measurement index. Especially, under no more than 10% load, the efficiency has been paid much attention to. In order to study the improvement methods of power efficiency under the light load condition, many scholars rely on the approximate equivalent power loss models of full-bridge converters [14]. It is not difficult to find that there is a logical difference between the theoretical analyses and the actual results according to the appropriate power loss model, which can be taken as an effective and reasonable reference to improve power efficiency under light load. On the contrary, when the power loss model is not accurate, it will cause much large difference between the theoretical analyses and the actual results. Furthermore, it is not conducive to obtaining the methods of improving efficiency under light load.
The power loss is mainly resulted from the switching loss and the conduction loss when the full-bridge converter works under light load condition. Therefore, equivalent power loss model contains the two kinds of losses. Switching loss model mainly involves the IGBT or MOSFET at the arm of full-bridge, and the Schottky diode or MOSFET in the rectifier circuit. In [15], the nonlinear junction capacitances between the gate, drain, and source are taken into account in the equivalent model of MOSFET. Meanwhile, the parasitic inductance is also the consideration. Descriptions of state equation are given because the characteristics of MOSFET in the process of turning-on and turning-off are combined. In [16], the influence of load current on miller platform of MOSFET is considered in the equivalent model. Furthermore, the dead time of two bridges can be effectively adjusted. In [17], the thermodynamic model of switches at two bridges is established for the phase-shift full-bridge converter. The model is related to switching loss. In [18], the equivalent power loss model is obtained by converting the primary side and secondary side of transformer. The model of switches is approximately coped so that the range of zero-voltage switching (ZVS) for MOSFETs can be effectively analyzed. In [19], the voltage and current of IGBT are sampled and reconstructed in a specific way. Average switching loss model is obtained when the values of sample and reconstruction are simply calculated. In [20][21], the full-bridge converter contains the synchronous rectifier. Each junction capacitance between drain and source of MOSFET is taken as a linear capacitor in the model. Dead time of lagging bridge is regulated by load current. The difference between [20] and [21] is the current mode of filter inductor. The current works continuous mode so that filter inductor can be treated as a current source in [20]. Contrarily, the current works discontinuous mode and only the filter capacitor is regard as a voltage source in [21].
Conduction loss model mainly involves the core loss and copper loss of the inductive components. On the other hand, the conduction loss of switches can not be neglected. In [22], the leakage inductance, the excitation inductance, and the inter layer distributed capacitance are estimated according to the actual structure of isolated transformer in the power loss model. It can be used to analyze the core loss and copper loss of full-bridge converter. In [23], it is considered that the voltage generated at the midpoints between two arms of bridge is square wave rather than sine wave. Therefore, the modified Steinmetz equation is adopted when the core loss of transformer in the model is analyzed. In [24], the BH curve of isolated transformer is divided under the asymmetrical square wave excitation. Estimated core loss can be much close to the measured value based on the corrected core loss model. In [25], the BH curve of isolated transformer is fully used when the optimal phase shift angle of full-bridge converter is considered under light load. Furthermore, core loss model is optimized on the bases of revised Steinmetz equation. In [26], the space structure between the transformer and the synchronous rectifier is focused on so that the core loss and copper loss can be further clarified. Values of the leakage inductance and excitation inductance can be effectively obtained by combining with the operating points of LLC resonant circuit. In [27], the passive components including isolated transformer are idealized and the ideal model of converter can be established. The overall conduction loss model is qualitatively analyzed on the bases of simulation and experiment. In [28], the influence of conduction resistance related to the switches is taken into account in the equivalent model of full-bridge converter. The DC resistance of inductive components and the equivalent series resistance (ESR) of filter capacitor are also in the proposed model. In [29], the converter is equivalent to the RL circuit which represents the overall losses. The power loss model includes the switching loss, the conduction loss of IGBTs, and the loss resulted from forward voltage drop of rectifier diodes. In [30], both sides of isolated transformer are converted. The AC resistance of winding at both sides of transformer and the equivalent AC resistance of filter circuit represent the overall conduction losses of full-bridge converter in the power loss model.
Reference [31] has certain representativeness. Every junction capacitance between drain and source of MOSFET at both sides of transformer is replaced by the linear capacitance in the switching loss model. The values of junction capacitance and the switching time are both taken from the datasheet of relevant MOSFET. In [31], the conduction loss contains the loss come from resistance of switches, and the core loss and copper loss of inductive components. The core loss is calculated according to the typical Steinmetz equation and the copper loss is calculated according to the DC resistances in the conduction loss model. Though the power loss model is reasonable and it has been applied in the aforementioned literatures, there are still some problems in analyzing the power efficiency of actual converter.
1) The parameters of switches at the arms of full-bridge and the parameters of diodes in the rectifier circuit all come from the corresponding datasheets. These parameters are measured under certain conditions, rather than be suitable for any experimental conditions.
2) The fast recovery diodes treated as reverse freewheeling are antiparallel with the related switches at the actual arms of full-bridge circuit. However, existing literatures do not consider the effect of the diodes.
3) The core loss of the inductive components is derived from traditional Steinmetz equation which is suitable for sinusoidal excitation. The core loss is also obtained according to the modified Steinmetz equation, which involves change rate of magnetic induction intensity in real time. The later way is relatively complicated.
4) The DC resistance of the winding is directly selected according to the equivalent resistance of inductor and isolated transformer. Skin effect of winding under high frequency is not taken into account.
In order to simplify the calculation of manual operation, the power loss model of full-bridge converter under light load is fully analyzed by using the Saber software. Two power loss models are established in this paper. The first model corresponds to the typical model, and the second model corresponds to the proposed model. The typical model is derived from the [31], and the proposed model is obtained by improving the typical model. The reference has proved that it is feasible and effective to adopt the pulse width modulation (PWM) for full-bridge converter under light load condition. So the PWM strategy is applied in the two models and the actual converter. Investigation is developed according to the fact that the input voltage, the output voltage, the output current, and the switching frequency in the two models are all the same that in the actual converter. The proposed model is established by considering the antiparallel freewheeling diodes at the arms of full-bridge and ignoring the barrier junction capacitances of rectifier diodes. Meanwhile, it needs to be compensated and corrected the turningoff loss of MOSFETs, the equivalent core loss resistance of inductive components, and the equivalent conduction loss resistance of converter. The whole aforementioned modified parts come from the typical model. Furthermore, the local indexes and global indexes are formulated. The theoretical results of the two models are compared with the experimental results according to the indexes, so that the approximation degree between the two power loss models and the actual converter can be measured. There are four sections in this text. The principle of the two models is formulated in the first section. Aided analyses and design based on the Saber software are shown in the second section. The actual full-bridge converter is used to verify the theoretical results in the third section. Furthermore, the comprehensive analyses on the results and the comparisons of indexes are presented in the fourth section. Whether the proposed model is closer to the actual converter than the typical model is judged by a series of analyses and verifications.

Formulation of power loss model
The full-bridge converter studied in this paper is shown in Fig 1. The constant voltage source U in represents the input voltage. Q1 to Q4 stand for the certain type of MOSFET. L P and L M represent the leakage inductance and excitation inductance of isolated transformer respectively. The turns ratio between primary side and two secondary sides is N:1:1 in the transformer. D1 and D2 mean the specific type of Schottky rectifier diodes. L f , C, and R indicate the filter inductor, filter capacitor, and load respectively. The output voltage of converter is always regulated to U o .
The reference [31] has confirmed that the PWM strategy is feasible and effective for the full-bridge converter under light load condition. So the PWM strategy is adopted in this paper.
In addition, continuous current mode (CCM) of the filter inductor L f is regarded as the research background which is corresponding to the 1% load to 10% load.

Typical model
In order to establish the power loss model of Fig 1 under light load, the typical model shown in Fig 2 can be obtained on the bases of [31]. Same parts of Fig 1 will be removed in the next description. U Gi represents the driving signal of corresponding MOSFET and the subscript "i" is counted from one to four. R i1 and R i2 are the driven resistors of related MOSFET and the subscript "i" is counted from one to four. V Zi means the certain type of zener diode of relevant MOSFET and the subscript "i" is counted from one to four. R core indicates the equivalent core loss resistance of isolated transformer and filter inductor. R P , R S1 , and R S2 are the equivalent copper loss resistances of winding at two sides of isolated transformer. R Lf is the equivalent copper loss resistance of the filter inductor L f .
(A) Estimation of R P , R S1 , R S2 , and R core . The approximate estimates of equivalent copper loss resistances R P , R S1 , R S2 , and the estimates of equivalent core loss resistance R core are presented as follows.
R P : Assume that the resistance coefficient with winding in the transformer is ρ. The length of corresponding winding is L. The corresponding winding is wrapped by enameled wire whose strands are x. The radius of enameled wire is r. Assume that the resistance referred to every share of enameled wire is R P1 . R P is equivalent to the parallel resistors whose the number  is x. Each parallel resistor is the R P1 and it is listed as follows: The solving process of R S1 and R S2 is similar to that of R P . R core : One of the inductive components is taken an example. Assume that the initial time of each switching period T is t 0 , and the switching frequency is treated as f. Instantaneous voltage is u(t). The initial value of magnetic induction intensity is B 0 and the peak value is ΔB, which the instantaneous value is expressed as B(t). The effective cross sectional areas and effective volumes of skeleton are S and V respectively. The number of turns is n. The empirical constants corresponding to the magnetic core are κ, α, and β. The α is usually taken from one to two and the β is usually taken from two to three. The average value of core loss per unit volume is expressed as p core . Therefore, the average expression of integral core loss P core(i) is calculated as follows: Based on the voltage characteristics of inductive components, voltage U AB can be approximately represented by In summary, R core can be approximated according to the following expression: (B) Characteristics of typical model. The typical model mainly has the following characteristics.
1) The parameters of MOSFETs and Schottky diodes are directly applied the default values according to the corresponding actual datasheets.
2) The core loss of inductive components is estimated by the traditional Steinmetz equations, and the corresponding equivalent core loss resistance can be obtained.
3) The copper loss of inductive components is directly calculated according to the DC resistance of relevant winding.

Proposed model (A) Proposed modeling method.
For the sake of making the proposed model more accurate to reflect the actual power efficiency than the typical model, it is necessary to correct the core loss of inductive components and the switching loss of full-bridge circuit on the bases of typical model. It is known that switches at the arms of full-bridge can realize zero voltage turning-on when the inductor at primary side of transformer is large. The switching loss is almost dominated by the turning-off loss because of the large leakage inductance. Furthermore, turning-off loss of these switches is studied in this paper.
Assume that the range of output current for the converter is from I o(min) to I o(max) . The theoretical input power is P in1 and the theoretical output power is P o1 in the typical model. The experimental input power is P ine and the experimental output power is P oe . Q1 is taken as an example. The average turning-off voltage, the average turning-off current, and the turning-off duty cycle are shown as U off , I off , and D off respectively under the theoretical analyses on the typical model and proposed model. The turning-off loss of Q2, Q3, and Q4 are all the same that of Q1.
When the output current is I o(min) , the following expressions are presented: 4U off ð1Þ I off ð1Þ D off ð1Þ k 1 ¼ ðP ineð1Þ À P oeð1Þ Þ À ðP in1ð1Þ À P o1ð1Þ Þ 2 where the U off(1) , I off(1) , and D off(1) are the theoretical U off , I off , and D off in the typical model when the output current is I o(min) . P ine(1) , P oe(1) , P in1(1) , and P o1(1) are the P ine , P oe , P in1 , and P o1 under the I o(min) . When the output current is I o(max) , the following expression is shown: 4U off ð2Þ I off ð2Þ D off ð2Þ k 2 ¼ ½ðP ineð2Þ À P oeð2Þ Þ À ðP in1ð2Þ À P o1ð2Þ Þ� À DP core where the U off (2) , I off (2) , and D off (2) are the theoretical U off , I off , and D off in the typical model when the output current is I o(max) . P ine (2) , P oe (2) , P in1(2) , and P o1(2) are the P ine , P oe , P in1 , and P o1 under the I o(max) . The coefficients k 1 and k 2 satisfy the following equations: Eq (3) represents compensation of core loss in the improved method. The a and b in (4) and (5) are the compensating factors of turning-off loss in the proposed model of full-bridge converter.
In the proposed model, the modified equivalent core loss resistance R core and the modified equivalent turning-off loss resistance R switch are expressed respectively as follows: P core in (6) is namely the core loss shown in (2). I o in (7) is the output current of converter. R switch(Io) in (8) is namely the R switch under the I o . U off(Io) , I off(Io) , and D off(Io) are the theoretical U off , I off , and D off in the proposed model when the output current is I o .
The proposed model is divided into two steps due to the need to estimate equivalent resistance R switch . The first step is shown in Fig 5  1) The certain type of freewheeling diodes V D1 to V D4 are antiparallel with their corresponding MOSFETs Q1 to Q4.
2) The barrier junction capacitances of the rectifier diodes D1 to D2 are neglected.
3) The equivalent core loss resistance R core is obtained by the (6). 4) The equivalent copper loss resistances R P , R S1 , and R S2 are calculated according to the skin effect of winding. The equation can be seen in (9).
5) The influence resulted from the ESR of filter capacitor C is considered.
Turning-off loss of switches at the arms of full-bridge is compensated on the bases of Fig 5. The corresponding equivalent resistance R switch is obtained according to the (7) and (8) (B) Estimation of R P , R S1 , and R S2 . The approximate estimates of equivalent copper loss resistances R P , R S1 , and R S2 are listed as follows.
R P : Assume that the resistance coefficient with winding in the transformer is ρ and the unit is O.m/mm 2 . The length of corresponding winding is L and the unit is m. The corresponding winding is wrapped by enameled wire whose strands are x. The radius of enameled wire is r and the unit is mm. The frequency of current in the corresponding winding is f and the unit is Hz. Assume that resistance referred to each strand of enameled wire is R P1 . R P is equivalent to the parallel resistors whose the number is x. Each parallel resistor is the R P1 and it is listed as follows: The solving process of R S1 and R S2 is similar to that of R P .
(C) Characteristics of proposed model. Similarly, the proposed model has the following characteristics which are different from the typical model.
1) The corresponding antiparallel freewheeling diode of MOSFET is considered. Switching loss is characterized by the related equivalent resistance in the main circuit.
2) The influence resulted from the barrier junction capacitance of Schottky rectifier diode is neglected.
3) Eq (3) is directly applied to estimate and compensate the core loss of inductive components on the foundation of typical model and experiment. Furthermore, the (6) is applied to obtain the equivalent core loss resistance. 4) According to the skin effect, equivalent copper loss resistance of inductive components is represented by the AC resistance of winding.
5) The ESR of the filter capacitor is applied in the proposed model.

Applicability of proposed model
In this paper, other devices such as IGBT can be applied in the proposed model. It can be explained according to the compositions of equivalent circuit and the proposed modeling method.
The aforementioned subsection "Proposed model" is mainly the proposed modeling method. It is essentially a comprehensive method by combining boundary measurement with linear compensation. The following formulation is the description of the compositions of equivalent circuit.
In Fig 5 and  obtained according to the comprehensive modeling method by combining boundary measurement with linear compensation. Considered the definition of switching loss, the proposed method does not need much prior knowledge and it is not limited to specific main switches.
(2) Transformer The equivalent circuit of transformer can be seen in Fig 9. It mainly includes the leakage inductance, the magnetizing inductance, the equivalent core loss resistance and the equivalent copper loss resistances.
In this paper, the leakage inductance and magnetizing inductance are obtained by the shortcircuit test and open-circuit test. The equivalent copper loss resistances are calculated according to the AC resistances of winding. The equivalent core loss resistance comes from the inductive components and the main source of core loss is transformer. Under the light load condition, the R core in Fig 5 and Fig 6 also plays an important role in this equivalent circuit and it is modified by the boundary measurement which does not need much prior knowledge.
In summary, R switch and R core are the important compositions of equivalent circuit. The solving process of them is the combination of boundary measurement and linear compensation. Furthermore, the proposed model which is based on the comprehensive method does not need much prior knowledge. Therefore, the model is not limited to the application of specific components.

Aided analyses by the Saber software (A) Main parameters
The following formulations are all derived from the practical converter. As shown in Fig 1, the type of switches Q1 to Q4 is IRFP460. The type of Schottky rectifier diodes is V50100PW. The  leakage inductance L P is 600μH and the excitation inductance L M is 11.5mH. The turns ratio between the primary side and the two secondary sides is 8.42:1:1. The filter inductor L f is 250μH and the filter capacitor C is 470μF. U Gi in Fig 2 and Fig 6 is a square wave excitation that the amplitude is 15V and the frequency is 24kHz. R i1 and R i2 are 6.2O and 10kO respectively in the two models. The type of V Zi in the two models is IN4744A. The type of V Di in the proposed model is MUR3060WT. All the aforementioned subscript "i" is counted from one to four. When the average output voltage U o is equal to 12V, the approximation degree between the two models and the actual converter is verified by investigating the following cases respectively.
The current under full load is 10A.
In order to reduce the amount of manual calculation, the Saber software is fully used to analyze the two models. The Q1 to Q4 and V Z1 to V Z4 in the two models, and V D1 to V D4 in the proposed model are directly called from the corresponding types in the principle library of Saber. Furthermore, the whole parameters are default according to the actual datasheets. The D1 and D2 are applied with their respective SPICE models as follows.

(B) SPICE model of rectifier diode
Assume that the forward instantaneous voltage and current of each rectifier diode are v and i respectively. The reverse voltage of each rectifier diode is v r . The barrier junction capacitance of each rectifier diode is C j . The following parameters are involved in the SPICE model constructed by (10) and (11). These parameters include the reverse saturation current I S , the emission coefficient N, the voltage equivalent of temperature V T , the zero bias capacitance C j0 , the junction voltage V j , and the capacitance gradient factor M: According to the datasheet of V50100PW, the (10), and the (11), aforementioned parameters in the SPICE model can be solved.

(C) Formulation of the local indexes and global indexes
PWM strategy is adopted in the full-bridge converter and the switching frequency is 24kHz. Conduction time of each MOSFET in each switching period is defined as t on whose unit is μs. The t on is namely the duration time that high level of U Gi in one period under both aided analyses and experiment. The subscript "i" is also counted from one to four. For convenience of analysis, t on is chosen as an integer. The determination process of t on is shown in Fig 10. When the input voltage, output voltage, and output current of full-bridge converter are given, the power efficiency is obtained according to the input current. In this paper, the input current of converter can be illustrated as Fig 11 under both aided analyses and experiment. As can be seen from Fig 11, the I in represents the average input current. For each period of input current, the rise time of instantaneous current is approximately close to the half of switching period T/2. Assume that the output voltage is U o and the load resistor is R. The power efficiency η can be formulated by (12): The local indexes and the global indexes are given as follows so that the approximation degree between the two models (typical model and proposed model) and the actual converter can be measured respectively. In terms of the proposed model, the local indexes are designated according to the judgment standard for the rationality of adding the antiparallel freewheeling diodes at the arms of full-bridge and neglecting the barrier junction capacitance of each Schottky diode in the rectifier circuit. In terms of the two models, the global indexes are designated according to the rationality that the equivalent turning-off loss resistances, the influence of equivalent core loss resistance of inductive components, and the influence of equivalent conduction loss resistances are all considered.  1) Eq (1) is solved according to the actual parameters of winding. These parameters can be seen in the appendix. We can know that R P , R S1 , R S2 , and R Lf are 0.2496O, 0.0127O, 0.0127O, and 0.0333O respectively.
2) The fitting coefficients of ferrite for inductive elements given by manufacturer are as follows. Other relevant parameters can be seen in the appendix. Eq (2) is combined with Fig 3  and Fig 4. We can know that R core is 17.42kO when U in is 115V and R core is 17.044kO when U in is 120V. The aforementioned fitting coefficients are presented: k ¼ 2:2429; a ¼ 1:55; and b ¼ 2:5214: 3) The undetermined parameters of SPICE model related to the D1 and D2 are listed as follows:  Based on Figs 12-16, the following results can be obtained. 1) The drain-source voltage of Q1 and Q4 can be estimated as zero when they are turningon.
2) The approximate amplitude of the midpoint voltage of two arms is 115.0V. And the approximate amplitude of the voltage of filter inductor is 1.0V.
3) The input current can be treated as triangular waveform and the rise time is close to the half of switching period T/2.  1) The sensitivity of time axis is always 25μs/div, and the sensitivity of longitudinal axis is gradually adjusted from 50mV/div to the large range until the following requirement is reached. The largest sensitivity of longitudinal axis is 5V/div.
2) At each sensitivity of longitudinal axis, 30 sets of waveforms are measured. Then the average values and mean square deviations are calculated. When the mean square deviation is 3) At the final sensitivity of longitudinal axis, the waveform whose average value is most approximate to the calculated average value is chosen as the typical input current of converter.
Based on Fig 17, the following results can be obtained.
1) The input current can be treated as triangular waveform and the rise time is close to the half of switching period T/2.
2) The average input current is 0.0210A.   1) The drain-source voltage of Q1 and Q4 can be estimated as zero when they are turningon.
2) The approximate amplitude of the midpoint voltage of two arms is 120.0V. And the approximate amplitude of the voltage of filter inductor is 1.5V.
3) The input current can be treated as triangular waveform and the rise time is close to the half of switching period T/2.  1) The drain-source voltage of Q1 and Q4 can be estimated as zero when they are turningon.
2) The approximate amplitude of the midpoint voltage of two arms is 120.0V. And the approximate amplitude of the voltage of filter inductor is 1.5V.
3) The input current can be almost treated as triangular waveform and the rise time is close to the half of switching period T/2.
4) The average input current and the output voltage are 0.10996A and 12.030V. 5) The rise time and fall time of U AB are 2.7418μs and 2.5332μs. 6) The fluctuation degree of the reverse bias voltage related to the D1 and D2 is large. 7) The conduction time of each MOSFET in each switching period t on is 17μs. In order to solve (6) and (8) in the proposed model, it is also necessary to obtain the actual average input current when the level of output current I o is 1A. The experimental waveform of input current can be seen in Fig 28. It is the voltage waveform of 1O sampling resistor, so it can reflect the input current.
Based on Fig 28, the following results can be obtained.
1) The input current can be almost treated as triangular waveform and the rise time is close to the half of switching period T/2.

Proposed model (A) Calculated parameters. Based on
Based on Fig 16, Fig 17, Fig 27, and Fig 28, it can be known that the P ine(2) , P one (2) , P in1(2) , and P o1(2) are 15W, 12W, 13.1952W, and 12W respectively. When the k 1 and k 2 are calculated, U off(1) and U off(2) are estimated as 60V uniformly. I off(1) , I off(2) , D off(1) , and D off (2) are calculated from the marks in Fig 16 and   1) Eq (9) is solved according to the actual parameters of winding. These parameters can be seen in the appendix. We can know that R P , R S1 , R S2 , and R Lf are 0.4982O, 0.0254O, 0.0254O, and 0.0348O respectively.
2) Eq (6) is applied. Then it can be known that R core is 13.415kO when U in is 115V and R core is 13.126 kO when U in is 120V.
3) The undetermined parameters of SPICE model related to the D1 and D2 are listed as follows:  1) The drain-source voltage of Q1 and Q4 can be estimated as zero when they are turningon.
2) The approximate amplitude of the midpoint voltage of two arms is 115.0V. And the approximate amplitude of the voltage of filter inductor is 1.0V.
3) The input current can be treated as triangular waveform and the rise time is close to the half of switching period T/2.  1) The drain-source voltage of Q1 and Q4 can be estimated as zero when they are turningon.
2) The approximate amplitude of the midpoint voltage of two arms is 120.0V. And the approximate amplitude of the voltage of filter inductor is 1.5V.
3) The input current can be treated as triangular waveform and the rise time is close to the half of switching period T/2.  1) The drain-source voltage of Q1 and Q4 can be estimated as zero when they are turningon.
2) The approximate amplitude of the midpoint voltage of two arms is 120.0V. And the approximate amplitude of the voltage of filter inductor is 1.5V.
3) The input current can be almost treated as triangular waveform and the rise time is close to the half of switching period T/2.
4) The average input current and the output voltage are 0.12162A and 12.058V. 5) The rise time and fall time of U AB are 3.0271μs and 2.9455μs.

Experimental verification
Experimental platform for the isolated full-bridge DC-DC converter has been built so that the approximation degree between the two models and the actual converter can be verified. This platform is regulated by the real-time data acquisition and the control card Qs1501 which supports the real-time window target (RTWT) and the XPC target environment. The parameters of driving circuit and the main circuit have been described in the second section. They are listed in Table 1 as follows.
When the levels of output current I o are 0.1A, 0.5A, and 1A respectively, the following waveforms can be seen.
The measured waveforms can be seen from Figs 44-49. In Fig 44, the CH1 means the drain-source voltage of Q1 and the CH2 means the gatesource voltage of Q1.
In Fig 45, the CH1 means the drain-source voltage of Q4 and the CH2 means the gatesource voltage of Q4.
In Fig 46, the waveform means the midpoint voltage of two arms. In Fig 47, the CH1 means the reverse voltage of D2 and the CH2 means the reverse voltage of D1. 1) The drain-source voltage of Q1 and Q4 can be estimated as zero when they are turningon.
2) The approximate amplitude of the midpoint voltage of two arms is 115.0V. And the approximate amplitude of the voltage of filter inductor is 0.8V.
3) The output voltage is 12.0V. 4) The rise time and fall time of U AB are both 3μs. 5) The fluctuation degree of the reverse bias voltage related to the D1 and D2 is small. 6) The conduction time of each MOSFET in each switching period t on is 8μs.
The measured waveforms can be seen from Figs 50-56. In Fig 50, the CH1 means the drain-source voltage of Q1 and the CH2 means the gatesource voltage of Q1.
In Fig 51, the CH1 means the drain-source voltage of Q4 and the CH2 means the gatesource voltage of Q4.
In Fig 52, the waveform means the midpoint voltage of two arms. In Fig 53, the waveform means the input current obtained by the 1O sampling resistor. In Fig 54, the CH1 means the reverse voltage of D2 and the CH2 means the reverse voltage of D1.
In Fig 55, the CH1 means the output voltage and the CH2 means the total voltage corresponding to the secondary side of transformer and the Schottky rectifier diode.
In Fig 56, the waveform means the voltage of filter inductor. Based on Figs 50-56, the following results can be obtained.
1) The drain-source voltage of Q1 and Q4 can be estimated as zero when they are turningon.
2) The approximate amplitude of the midpoint voltage of two arms is 120.0V. And the approximate amplitude of the voltage of filter inductor is 1.2V.
3) The input current can be treated as triangular waveform and the rise time is close to the half of switching period T/2.  In Fig 58, the CH1 means the drain-source voltage of Q4 and the CH2 means the gatesource voltage of Q4.
In Fig 59, the waveform means midpoint voltage of two arms. In Fig 60, the CH1 means the reverse voltage of D2 and the CH2 means the reverse voltage of D1.
In Fig 61, the CH1 means the output voltage and the CH2 means the total voltage corresponding to the secondary side of transformer and the Schottky rectifier diode.
In Fig 62, the waveform means the voltage of filter inductor. Based on Figs 57-62, the following results can be obtained.
1) The drain-source voltage of Q1 and Q4 can be almost estimated as zero when they are turning-on.
2) The approximate amplitude of the midpoint voltage of two arms is 120.0V. And the approximate amplitude of the voltage of filter inductor is 1.2V.
3) The output voltage is 12.0V. 4) The rise time and fall time of U AB are both 3μs. 5) The fluctuation degree of the reverse bias voltage related to the D1 and D2 is small. 6) The conduction time of each MOSFET in each switching period t on is 19μs.

1.
Observing the gate-source voltage of Q1 and Q4, and the drain-source voltage of Q1 and Q4 in the following indicated figures, we can summarize and list the obtained results.
Furthermore, the related conclusion is drawn as follows. The waveforms of Q3 and Q2 are not shown because they are the same as that of Q1 and Q4 respectively. Experiment: Fig 44, Fig 45, Fig 50, Fig 51, Fig 57, and Fig 58. (B) Results. Whether the drain-source voltage of Q1 and Q4 can be estimated as zero when they are turning-on is regarded as the observed results. The respective situations are summarized and presented in Table 2 and Table 3.
(C) Conclusion. Whether it is the model or the actual converter, it all can prove that MOSFETs can realize zero voltage turning-on when PWM strategy is used. Under the light load condition, switching loss of converter is mainly the turning-off loss of MOSFETs.

2.
Observing the midpoint voltage of two arms and the voltage of filter inductor in the following indicated figures, we can summarize and list the obtained results. Furthermore, the related conclusion is drawn as follows.
(A) Indicated figures. Typical model: Fig 13, Fig 15, Fig 19, Fig 21, Fig 24, and Fig 26. Proposed model: Fig 31, Fig 33, Fig 36, Fig 38, Fig 41, and Fig 43. Experiment: Fig 46, Fig 49, Fig 52, Fig 56, Fig 59, and Fig 62. (B) Results. The approximate amplitude of the midpoint voltage of two arms and the approximate amplitude of the voltage of filter inductor can be treated as the key characteristic of respective voltage. They are summarized and presented in Table 4 and Table 5. 3. Observing the input current of the converter in the following indicated figures, we can summarize and list the obtained results. Furthermore, the related conclusion is drawn as follows.
(A) Indicated figures. Typical model: Fig 13, Fig 19, and Fig 24. Proposed model: Fig 31, Fig 36, and Fig 41. Experiment: Fig 17, Fig 28, and Fig 53. (B) Results. Whether the respective input current can be treated as triangular waveform and the rise time is close to the half of switching period T/2 is regarded as the observed results. The respective situations are summarized and presented in Table 6.

4.
Observing the input current and the output voltage in the following indicated figures originated from the typical model, we can summarize and list the obtained results. Furthermore, the related conclusion is drawn as follows.
(A) Indicated figures. Input current: Fig 13, Fig 19, and Fig 24. Output voltage: Fig 15, Fig 21, and Fig 26. (B) Results. The average input current and the output voltage can be considered as their respective key characteristic. They are summarized and presented in Table 7.
(C) Conclusion. When the levels of output current I o are 0.1A, 0.5A, and 1A, the related power efficiency can be deduced from this table. According to the (12), the corresponding values of power efficiency are 61.33%, 80.70%, and 91.40% respectively.

5.
Observing the input current and the output voltage in the following indicated figures originated from the proposed model, we can summarize and list the obtained results. Furthermore, the related conclusion is drawn as follows. Output voltage: Fig 33, Fig 38, and Fig 43. (B) Results. The average input current and the output voltage can be considered as their respective key characteristic. They are summarized and presented in Table 8.
(C) Conclusion. When the levels of output current I o are 0.1A, 0.5A, and 1A, the related power efficiency can be deduced from this table. According to the (12), the corresponding values of power efficiency are 51.67%, 74.41%, and 83.02% respectively.
6. Observing the measured input current and the output voltage in the following indicated figures originated from the experiment, we can summarize and list the obtained results. Furthermore, the related conclusion is drawn as follows.
(A) Indicated figures. Input current: Fig 17, Fig 53,   (B) Results. The average input current and the output voltage can be considered as their respective key characteristic. They are summarized and presented in Table 9.
(C) Conclusion. When the levels of output current I o are 0.1A, 0.5A, and 1A, the related power efficiency can be deduced from this table. According to the (12), the corresponding values of power efficiency are 49.69%, 71.02%, and 80.00% respectively.

Comparisons of indexes
Approximation degree between the two theoretical power loss models and the actual converter is investigated according to the indexes designed in the second section.  Table 10 and Table 11. Furthermore, the related conclusion is drawn as follows.  Experiment: Fig 46, Fig 52, and Fig 59. (B) Results: According to the corresponding measured data, the rise time and fall time of U AB are summarized and presented in the following tables respectively.
The aforementioned experimental data are also estimated according to the corresponding storage data in the Tektronix oscilloscope TDS2012B.
(C) Conclusion: The differences of the data between the proposed model and the actual converter are all smaller than that between the typical model and the actual converter when the converter works under the light load condition.

2.
Observing the reverse bias voltage related to the D1 and D2, the total voltage corresponding to the secondary side of transformer and the Scotty rectifier diode in the following indicated figures, we can summarize and list the obtained results. Furthermore, the related conclusion is drawn as follows.
(A) Indicated figures: Typical model: Fig 14, Fig 15, Fig 20, Fig 21, Fig 25, and Fig 26. Proposed model: Fig 32, Fig 33, Fig 37, Fig 38, Fig 42, and Fig 43. Experiment: Fig 47, Fig 48, Fig 54, Fig 55, Fig 60, and Fig 61. (B) Results: The fluctuation degree of the reverse bias voltage can be treated as the key characteristic of respective voltage. For convenience, the "Large" and "Small" are used to judge the fluctuation degree under the same output current. The respective situations are summarized and presented in Table 12.

(C) Conclusion:
It can be qualitatively concluded that the differences of fluctuation degree between the proposed model and the actual converter are all smaller than that between the typical model and the actual converter when the converter works under the light load.
Through the analyses of aforementioned two local indexes, the following inference can be known. For the proposed model, it is reasonable and effective that the influence of the antiparallel freewheeling diodes at the arms of full-bridge circuit is considered and the barrier junction capacitance of Schottky diode in the rectifier circuit is neglected. Therefore, to some extent, it can be qualitatively judged that the proposed model is closer to the actual converter than the typical model.

Global indexes.
On the bases of aforementioned inferences about the two models, the conduction time of each MOSFET in each switching period t on and the power efficiency of converter η are deeply compared. The range for the levels of output current I o are expanded to  Table 13 and  Table 14.
For the time t on in Table 13 and the power efficiency η in Table 14, it is the fact that the differences between the proposed model and the actual converter are almost smaller than that between the typical model and the actual converter. Therefore, for the proposed model shown in Fig 6, the equivalent turning-off loss resistance R switch , the equivalent core loss resistance of inductive components R core , and the other equivalent conduction loss resistances of converter are reasonable and effective. Even it can be quantitatively judged that the proposed model can better formulate the actual converter than the typical model.
In terms of the local indexes and the global indexes, we can obtain the following summary according to the comprehensive comparisons between the two models and the actual converter. The conclusion is that the proposed model shown in Fig 6 is more approximate to the actual converter than the typical model under the light load condition.

Conclusion
In this paper, the full-bridge converter works under the light load condition that the filter inductor current operates in the CCM. It is taken as the research background. Power loss models of converter are established on the bases of investigated condition. Firstly, the typical model has been developed according to the existing achievements. The PWM strategy is applied in the actual converter. Secondly, the antiparallel freewheeling diodes are added at the arms of full-bridge and each barrier junction capacitance of Schottky diode in the rectifier circuit is neglected. Meanwhile, the theoretical results of typical model and actual input current under the minimum and maximum output current are fully utilized. Then, the proposed model is founded by compensating and correcting the equivalent turning-off loss resistance, the equivalent core loss resistance of inductive components, and the equivalent conduction loss resistance of converter. The lastly but important, the two power loss model are compared with the actual converter respectively in accordance with the local indexes and the global indexes.