This study presents a single-phase power factor correction AC–DC converter that operates in discontinuous conduction mode. This converter uses the pulse-width modulation technique to achieve almost unity power factor and low total harmonic distortion of input current for universal input voltage (90 V _rms to 264 V _rms ) applications. The converter has a simple structure and electrical isolation. The magnetizing-inductor energy of the transformer can be recycled to the output without an additional third winding. The steady-state analysis of voltage gain and boundary operating conditions are discussed in detail. Finally, experimental results are shown to verify the performance of the proposed converter. DC power sources are widely used in industrial products and consumer electronics, such as battery chargers, DC power supplies, uninterruptible power supplies, inverters, and instruments. Thus, AC–DC power conversion is an important consideration. Diode-bridge or thyristor rectifiers can realize AC–DC power conversion, but such rectifiers will result in power pollution, including pulsating input current, low power factor, and high total harmonic distortion of input current(THD _i ). Several power factor correction (PFC) AC–DC converters have been investigated to address these issues. These converters possess non-isolated and isolated topologies. Non-isolated topologies include the boost [1] - [4] , buck [5] - [7] , buck-boost [8] - [10] , Cuk [11] , SEPIC [12] , [13] , and ZETA types [14] . These converters are operated in continuous conduction mode and discontinuous conduction mode (DCM) for different output-power applications. Isolated topologies include forward [15] - [17] and flyback types [18] - [20] . The forward types achieve low output voltage ripple and high THD _i . Nevertheless, this converter requires the third winding to recycle the magnetizing-inductor energy of the transformer. The flyback types are shown in Fig. 1 (a). This converter achieves high power factor and low THD _i . Moreover, flyback types have a simple structure and low cost but have low efficiency because of the transformer leakage inductor. The clamping method is presented in [21] , [22] to recycle leakage inductor energy. However, this method makes the power circuit complicated. We propose a single-phase PFC AC–DC converter, as shown in Fig. 1 (b). The proposed converter circuit configuration is very simple. The configuration includes only a set of input filter L_f – C_f , a diode-bridge rectifier, a transformer T_r , an inductor L ₁ , an output diode D_o , and an output capacitor C_o . The proposed converter does not have the transformer leakage inductor issue associated with the flyback converter. Moreover, transformer magnetizinginductor energy can be recycled to the output without an additional third winding. This converter is operated in DCM by using the pulse–width modulation technique to achieve high power factor and low THD _i for universal input-voltage applications. The equivalent circuit of the proposed converter is shown in Fig. 2 . The transformer is modeled as a magnetizing inductor L_m and an ideal transformer. Some key waveforms in a half line-source period are shown in Fig. 3 . The operating principle is analyzed as 0 < ωt < π, where ω is the line angular frequency, because of the symmetrical characteristics of the single-phase system. Mode 1, [kT_s, t_k1]: S ₁ is switched on. The current- flow path is shown in Fig. 4 (a). The line source energy is transferred to the magnetizing inductor L_m of the transformer and the inductor L ₁ . Thus, the currents i_Lm and i _{L 1} are increased linearly. Given that magnetizing inductor L_m is significantly larger than inductor L ₁ , the magnetizing-inductor current i_Lm becomes lower than inductor current i _{L 1} . The energy stored in magnetizing inductor L_m is the residual magnetism of the transformer. The energy stored in output capacitor C_o is discharged to load R . This mode ends when S ₁ is switched off. Mode 2, [t_k1, t_k2]: S ₁ is switched off. The current-flow path is shown in Fig. 4 (b). The energies stored in magnetizing inductor L_m and inductor L ₁ are released to output capacitor C_o and load R . The currents i_Lm and i _{L 1} are decreased linearly. This mode ends when the currents i_Lm and i _{L 1} are equal to zero. Therefore, the transformer residual magnetism can be released to empty during each switching period. Mode 3, [t_k2, (k+1)T_s]: S ₁ remains switched off. The current-flow path is shown in Fig. 4 (c). The energies stored in magnetizing inductor L_m and inductor L ₁ are empty at t = t_k2 . The energy stored in output capacitor C_o is discharged to load R . This mode ends when S ₁ is switched on at the beginning of the next switching period. Given that the single-phase system is symmetrical, the following analysis is discussed for 0 < ωt < π. For simplicity, the effect of the input filter is neglected. The line voltage is given by where V_rms and V_m are the root-mean-square value and line voltage amplitude, respectively. The line voltage is considered a piecewise constant during each switching period because switching frequency f_s is larger than line frequency f ₁ . If m is the switching number within [0, π/ ω ], then m is equal to f_s /2 f ₁ . The following analysis is considered during switching period [ kT_s , ( k +1) T_s ], where k = 0, 1, ….., m -1. The magnetizing inductor L_m is ignored in the following analysis because it is significantly larger than inductor L ₁ . When S ₁ switched turned on, the voltage across inductor L ₁ is obtained as where es(tk) is the input-voltage level during switching the period [ kT_s , ( k +1) T_s ], and the turns ratio of transformer n = N ₂ / N ₁ . Then, The inductor current i _{L 1} is given by When t is equal to t _{k 1} , the peak value of inductor current i _{L 1} is where t_on = t _{k 1} – k_Ts = d_Ts . When S ₁ is switched off, the voltage across inductor L ₁ is given by Then, By solving (7), we derive the inductor current i _{L 1} as follows: Given that i _{L 1} ( t _{k 2} ) = 0, the peak value of inductor current i _{L 1} is where t_r,k = t _{k 2} – t _{k 1} . Using (5) and (9), time duration t_r,k can be given by As shown in Fig. 3 , the average value of unfiltered input current i _{N 1} in one switching period T_s can be computed as where i _{L 1 p} is the inductor current peak value for each switching period. Substituting (1) and (5) into (11), we derive the following equation: The average value of unfiltered input current i _{N 1} is sinusoidal and in phase with the input voltage. Moreover, the harmonic components of current i _{N 1} are distributed over the switching frequency multiples. The harmonic components are easily filtered out by using input filter L_f – C_f . The input filter cutoff frequency is significantly lower than the switching frequency. From Fig. 3 , the average value of the output-capacitor current i_co during [ kT_s , ( k +1) T_s ] can be obtained as Substituting (1), (5), and (10) into (13) yields The average value of output–capacitor current i_co during a half line-source period [0, π/ ω ] is written as follows: Given that m is larger than 1, equation (15) is approximated as: The output voltage differential equation is given by The DC model equation is written as where V_o and D are the DC quantities of v_o and d , respectively. The normalized inductor time constant is then defined as Substituting (19) into (18), the voltage gain is derived as The current i _{L 1} must be zero in each switching period to ensure that the proposed converter is operated in DCM. From Fig. 3 , time duration t_s,k is obtained as When the maximum value of t_s,k is equal to T_s and | e_s | is equal to V_m , the proposed converter is operated in boundary conduction mode. Therefore, substituting t_s,k = T_s and | e_s | = V_m into (21) can determine the boundary voltage gain as Using (20) and (22), the curves of voltage gain and boundary voltage gain are shown in Fig. 5 . When the voltage gain M is equal to its boundary voltage gain M_bc , the boundary normalized inductor time constant τ _{L 1 B} is given by τ _{L 1 B} is plotted in Fig. 6 . We can observe that the proposed converter is operated in DCM when τ _{L 1} < τ _{L 1 B} . The appropriate τ _{L 1 B} is selected under the required voltage gain to ensure that the proposed converter is operated in DCM. The inductor L ₁ needs to satisfy the following inequality: Using (14), the average value of output–capacitor current i_co during one switching period is simplified as follows: Substituting (18) into (25), output–capacitor current i_co is expressed as Therefore, the output voltage ripple in one switching period is given by Then, the output voltage ripple function during time interval [0, π/ ω ] is obtained as Using (28), the output voltage ripple during time interval [0, π/ ω ] is derived as Thus, Output capacitor C_o must satisfy the following inequality to meet the following output voltage ripple percentage specification: The prototype circuit is applied in the laboratory to demonstrate the performance of the proposed converter. Electrical specifications and circuit components are set as follows: The voltage gain M is varied from 0.27 to 0.79 according to the electrical specifications. Substituting M = 0.79 and n = 0.5 into (22), the maximum duty ratio D_max is derived as 0.61. Substituting D_max = 0.61 into (23), τ _{L 1 B} is obtained as 0.038. Using (24), the inductor L ₁ is given by The inductor L ₁ is 60 μ H, and the core is EI-40. Thus, τ _{L 1} is equal to 0.03 at full load R = 100 Ω and is equal to 0.006 at light load R = 500 Ω. Substituting the two values of τ _{L 1} and n = 0.5 into (20), the operating area of the experimental prototype is shown in Fig. 7 . The proposed converter is operating in DCM. Under the operating conditions V_rms = 90 V and R = 100 Ω, M and τ _{L 1} are derived as 0.79 and 0.03, respectively. Substituting M = 0.79, n = 0.5, and τ _{L 1} = 0.03 into (20), duty ratio D is obtained as 0.55. The ripple percentage of V_o is selected as 5%. From (31), the output capacitor inequality is given by Thus, output capacitor C_o is selected as 600 μ F. The control circuit is shown in Fig. 8 . Figs. 9 and 10 show the experimental waveforms under V_rms = 115 V, V_o = 100 V, P_o = 100 W and V_rms = 230 V, V_o = 100 V, P_o = 100 W, respectively. In Figs. 9 (a) and 10 (a), we observe that input current is sinusoidal and is in phase with input voltage. The current waveforms of the transformer primary and secondary sides i _{N 1} and i _{N 2} are shown in Figs. 9 (b) and 10 (b), respectively. The waveforms are taken at the peak value of input voltage. The current i _{N 2} drops to zero during each switching period, which indicates that the transformer residual magnetism is released to empty during each switching period. The currents i _{L 1} and i_Do are shown in Fig. 9 (c) and 10 (c), respectively. We observe that the proposed converter is operated in DCM. The waveform v _{S 1} across the switch drain source is shown in Figs. 9 (d) and 10 (d). The measured efficiencies of the proposed converter and flyback converter are compared in Fig. 11 . We observe that efficiency is improved in the proposed converter. The measured power factor and THD _i are shown in Fig. 12 . The measured power factor is higher than 0.96, whereas the measured THD _i is lower than 5.8%. The forward and flyback PFC AC–DC converters are efficient choices for electrical isolation because of their simple structure. However, the forward AC–DC converter cannot achieve high power factor and low THD _i . Additionally, this converter requires a third winding to recycle transformer magnetizing inductor energy. The flyback AC–DC converter can achieve high power factor and low THD _i . Nevertheless, the transformer leakage inductor results in low efficiency. Therefore, we present a single-phase AC–DC converter that has a simple structure and is operated in DCM to achieve high power factor and low THD _i . A steady-state analysis is conducted. We implement a hardware circuit with simple control logic in the laboratory. The experimental results reveal the performance of the converters. The measured efficiencies reveal that the proposed converter exhibited higher efficiency than the conventional flyback converter. Chia-Ching Lin was born in Taiwan, R.O.C., in 1959. He graduated from the Department of Electrical Engineering , Far East University, in 1980. He received his M.S. degree in Electrical Engineering from National Cheng-Kung University in 2006. He is currently with the Department of Electrical Engineering, Far East University, Tainan, where he is an Assistant Professor. His research interests are power factor correction and dc-dc converters.. Lung-Sheng Yang was born in Taiwan, R.O.C., in 1967. He received his B.S. degree in Electrical Engineering from National Taiwan Institute of Technology, Taiwan, his M.S. degree in Electrical Engineering from National Tsing-Hua University, Taiwan, and his Ph.D degree in Electrical Engineering from National Cheng-Kung University in 1990, 1992, and 2007, respectively. He is currently with the Department of Electrical Engineering, Far East University, Tainan, where he is an Assistant Professor. His research interests are power factor correction, dc-dc converters, renewable energy conversion, and electronic ballasts. Ren-Jun Zheng was born in Taiwan, R.O.C., in 1987. He received his B.S. and M.S. degrees from the , and 2007, respectively. He is currently with the Department of Electrical Engineering, Far East University, in 2011 and 2013, respectively. His research interests include power factor correction converter and electronic ballasts.