# I. INTRODUCTION

In consideration of the outstanding performance involving fast dynamic response, high power density and flexible voltage grade, high frequency AC (HFAC) plays an important role in a wide range of power distribution systems (PDS), such as spacecraft applications, telecommunication systems, computer and electronic commercial systems, automotive applications and Micro-grids [1]-[14]. Traditionally, there are two types of power conversion in HFAC PDS: 1) conversion from DC to HFAC [8]-[14], and 2) conversion from HFAC to DC. When compared with DC/HFAC inverters, the following objectives are significant for HFAC/DC conversion: 1) lighter weight and higher power density; 2) controlled DC output over a wide range; 3) lower electromagnetic interference (EMI); 4) higher reliability; 5) lower distortion, near-sinusoidal input current and close-to-unity power factor. Consequently, a number of studies have been conducted from the circuit topology to the control scheme.

It has been shown that using passive components is more effective than the active power factor correction (PFC) techniques for HFAC/DC converter for achieving the objectives of a high input power factor and high efficiency [15]. When compared with valley fill and charging pump circuits, the resonant converter is a better PFC choice [16], [17]. A number of approaches for the design of resonant AC/DC converters have been proposed in [18]-[23]. A resonant rectifier based on thyristor switches has been proposed with an LC-T resonant network and phase shift modulation (PSM). A close-to-unity power factor and low input harmonics have been achieved in [18], [19]. However，the implementation of PSM is complicated for thyristors. Phase density modulation (PDM) has been proposed for AC/DC converter formed by a resonant network, a bidirectional shunt switch, a transformer synchronous rectifiers and an output filter [20], [21]. However, more components and a complicated control limit its application. A resonant topology for an AC/DC converter has been reported in [24], [25], which is constituted by an LCL-T resonant network and a half-bridge switch. If the LCL-T resonant tank operates at the resonant frequency, the resonant converter behaves like a current source [26]-[29]. Moreover, it is inherently output short-circuit proof due to the existence of clamped diodes [25]. The LCL-T resonant converter satisfies the need for a constant current characteristic and close-to-unity power factor, but it is incapable of providing a controllable output. The conventional control of output voltage is to regulate the front-end converter. However, this requires more power components and has a high cost [27]. In order to simplify the interleaved circuit, this paper presents a controllable converter topology based on a LCL-T resonant tank and a bidirectional ac switch. In addition, an easier control scheme is presented for the proposed topology without the usual zero-crossing point detection of resonant current.

A wide scope of output regulation can be achieved by the proposed converter and control scheme with a low distortion input current and a close-to-unity input power factor. This paper is organized as follows. A detailed description of the proposed LCL-T resonant converter and its operating principle are given in Section II. A steady-state analysis is performed in Section III with a performance discussion, including the output voltage control, input power factor, and total harmonic distortion (THD) of the input current. Simulation results of the LCL-T resonant AC/DC converter are presented in Section IV to verify the analysis. Section V provides experimental results and Section VI summarizes the conclusion drawn from the investigation.

# II. CIRCUIT DESCRIPTION AND OPERATING PRINCIPLE

The proposed AC/DC converter is shown in Fig. 1. It is formed by an LCL-T resonant network, a bidirectional ac switch and a full-bridge rectifier. The LCL-T resonant network is comprised by a capacitor C and two inductors L1 and L2, where the inductance of L1 is close to L2. The bidirectional ac switch is comprised by two MOSFET switches Q1 and Q2 connected back to back. The backend rectifier is constructed by full-bridge diodes D1, D2, D3, and D4 and an output filter capacitor Co. The input is a HFAC voltage vs, and Ro is the load resistance.

**Fig. 1.**The proposed AC/DC converter.

Traditionally, high frequency sinusoidal voltage vs is derived from a high frequency AC bus. An LCL-T resonant circuit converts the HFAC voltage into a current source when the input frequency is equal to the resonant frequency. The impedance of the LCL-T resonant tank to the fundamental component is significantly less than the impedance to high order harmonics, which effectively reduces the THD of the input current. Therefore, the harmonics distortion of the input side is negligible under the given load conditions. Meanwhile, the fundamental component of the input current and the input voltage are nearly in the same phase if the inductance of L1 is close to L2 [25]. Therefore, a close-to-unity power factor can be achieved.

When the resonant components L1, C and L2 are tuned to the input frequency, the resonant tank is viewed as an ideal current source without an internal impedance due to a high impedance to the harmonic components [25], [26]. With the predefined resonant components and input voltage vs, the resonant current passing through the inductor L2 has a constant amplitude. The bidirectional ac switch is adopted to control the amount of bidirectional current between the resonant tank and the rectifier. The full-bridge rectifier converts the controllable bidirectional current to a unidirectional current for the load. In the existing control of resonant AC/DC converters, it is necessary to calculate the angle between the input voltage and the current pouring into the rectifier. When compared to the complicated current monitor, an easier control scheme based on an input voltage comparison is presented and analyzed in this paper. By means of regulating the conducting angle of Q1 and Q2, the amount of current feeding the rectifier is adjusted. As a result, the output voltage and output current are controllable. A filter capacitor Co is used to filter the output ripples and to provide a constant DC voltage to the load.

The operating waveforms of the proposed AC/DC topology are demonstrated in Fig. 2. iL2 is the current passing through L2, and iLL is the reference waveform with a phase angle lagging 90o behind the input voltage. The phase difference between the resonant current iL2 and iLL is Φ. GQ1,Q2 is the driving signals of the switches Q1 and Q2. vo is the voltage across the MOSFET switches. iD1,D3 is the current passing through the diodes D1, D3; while iD2,D4 is the current passing through the diodes D2,D4. β1 is the conducting angle of D1, D3; and β2 is the conducting angle of D2, D4 during an half cycle of the input voltage. α is the charging angle of the output capacitor Co. The driving signals are symmetrical with respect to the zero point of the input voltage. Therefore, it is unnecessary to calculate the angle between the input voltage and the current pouring into the full-bridge rectifier. Each operating cycle contains six intervals. The current path of the different states is shown in Fig. 3, and the operational analysis is explained as follows.

**Fig. 2.**The waveforms of the proposed AC/DC conver

**Fig. 3.**Current path in switches Q1 , Q2 and diodes D1, D2, D3, D4 in six intervals in one operating cycle.

Interval I

Interval I begins at ω1t1=(π-α)/2. Q1 and Q2 are turned off. The resonant current iL2 passes through the diodes D2 and D3 to charge the output capacitor Co. Since the ripple is filtered by the capacitor Co, the output voltage is Uo with a constant value. The voltage vo over the switches Q1 and Q2 is equal to –Uo in this interval.

Interval II

Interval II begins at ω1t2=π/2-Φ. Since the direction of iL2 has reversed, the resonant current iL2 passes through the diodes D1 and D4 to charge the capacitor Co. The voltage vo is equal to Uo in this interval.

Interval III

Interval III begins at ω1t3=(π+α)/2. Q1 and Q2 are turned on. The resonant current iL2 passes through Q1 and Q2. The charging process of the capacitor Co is suspended. Co feeds the load and the voltage vo is equal to zero in this interval.

Interval IV

Interval IV begins at ω1t4=(3π-α)/2. Q1 and Q2 are turned off. The resonant current iL2 passes through the diodes D1 and D4 to charge the output capacitor Co. The voltage vo is equal to Uo in this interval.

Interval V

Interval V begins at ω1t5=3π/2-Φ. Since the direction of iL2 has reversed, the resonant current iL2 passes through the diodes D2 and D3 to charge the capacitor Co. The voltage vo is equal to –Uo in this interval.

Interval VI

Interval VI begins at ω1t6= (3π+α)/2. Q1 and Q2 are turned on. The resonant current iL2 passes though Q1 and Q2. The charging process of the capacitor Co is suspended. Co feeds the load and vo is equal to zero in this interval.

After interval VI, a new cycle begins and the same operating principle is performed again. In order to make the output stable, the energy stored in the resonant network is regulated by Q1 and Q2 in each operating cycle.

# III. STEADY-STATE ANALYSIS

Before the steady-state analysis is conducted, some assumptions are made: 1) all of the components and devices are ideal; 2) the input voltage has a constant amplitude with a fixed frequency; 3) the output DC voltage is ripple free and the output voltage is constant.

The converter can be equivalent to a circuit with two sources as shown in Fig. 4(a). One is the input voltage source vs, and the other is the equivalent voltage source of the output rectifier vo. Based on the superposition theorem, the equivalent circuit shown in Fig. 4(a) can be decomposed into two parts. The two parts shown in Fig. 4(b) and Fig. 4(c) can be calculated and analyzed separately.

**Fig. 4.**Equivalent circuit of the controllable LCL-T resonant converter.

Since the input voltage vs is ideal and without any harmonic components, the input voltage can be expressed as below.

where, Vs is the root mean square value (RMS) of the input voltage vs.

Due to the ideal input voltage, the following relations of the current can be derived from Fig. 4(b).

where, X1 is the fundamental impedance of the inductor L1, and X1 = ω1L1 = ω1L2 = 1/ω1C. i’L1 and i’L2 are also sinusoidal waveforms without any high order harmonics.

The voltage vo can be expressed by the Fourier series as below.

where, Uo is the output voltage, and An=cos(nα/2)-cos(nΦ), Bn=sin(nΦ), and θn=arctan(Bn/An). The circuit analysis is performed by a series of harmonics.

The currents of i"L1 and i"L2 can be derived from Fig.4(c).

## A. Determination of the Phase Difference Angle Φ

Furthermore, the total input current iL1 can be derived by (2) and (5).

The fundamental component of the input current is:

The angle between the input fundamental current iL1.fundamental and the input voltage vs is π-θ1. Furthermore, the input power can be derived as below.

The output power is calculated from the output voltage and the load. The expression of the output power Po is given as below.

where, Ro is the load resistance.

Due to the assumption that all of the components and devices are ideal and without losses, the input power Pin is equal to the output power Po. The following expression can be derived from (9) and (10).

Similarly, the resonant current iL2 can be derived from (3) and (6).

It can be found from equation (12) that iL2 can be regulated by the input voltage vs and the inductance of L2. Since a larger iL2 leads to more circulating current and reactive power, a suitable selection of L2 is essential to cut down iL2.

As shown in Fig.2, iL2 reaches the zero point at the position ω1t=(π/2-Φ). Therefore, the following equation is satisfied.

By putting (11) into (13), the solution of equation (13) can be found. At a given α varying from 90o to 180o, the solution is to find the zero point of a function of Φ. As a result:

where, K=8Ro/π2X1.

The relation curves of Φ to the control angle α with different value of K are shown in Fig. 5(a). If the parameter K is predefined, the angle Φ increases as the control angle α increases. The angle Φ increases with an increase of K. The maximum Φ is close to 15o when K is 1; while the minimum Φ is close to 0o when K is 0.1.

**Fig. 5.**(a) The relation curves of angle Φ to control angle α with different K. (b) The relation curves of voltage Uo/B to control angle α at different K. (c) The relation curves of THD to control angle α with different K. (d) The relation curves of THD to Φ with different α. (e) The percentage of third, fifth, seventh harmonic of the input current as a function of control angle α (K=0.1). (f) The relation curves of power factor to control angle α with different K.

## B. Output Voltage Uo

The output voltage Uo can be derived from (11).

where,

α is the conduction angle of the switches Q1 and Q2. It is adjusted to achieve a desired output. K is determined by the resonant components and load condition. The relation curves of the output voltage Uo/B to control the angle α are shown in Fig. 5(b). It can be observed that the output voltage Uo increases as α grows from 90o to 180o. The output voltage Uo can be regulated in a wide range from 29.28% to 99.97% when K=0.1. Meanwhile, the range is from 29.16% to 99.22% when K=0.5, and it is from 28.78% to 96.98% when K=1. The variation scope decreases slowly with the increase of K.

## C. THD of the Input Current

The THD of the input current is defined as below.

where, I1 is the RMS of the fundamental current, and In is the RMS of the nth harmonic current. The THD of the input current iL1 can be derived from (7) and (8) as below.

The relation curves of the THD to control the angle α with different values of K are shown in Fig. 5(c). It can be found that the THD decreases with an increase of the angle α. When K increases, the THD decreases slightly. Fig. 5(d) shows the relation curves of the THD to the angle Φ with different values of α. When the angle α is constant, the denominator of the THD in (17) decreases as the angle Φ decreases. This is proportional to the RMS of the fundamental current. Therefore, the THD decreases as the angle Φ increases. Fig. 5(e) shows the percentage of the third, fifth, seventh and ninth order harmonics of the input current as a function of the control angle α at K=0.1. It can be found that the third harmonic is the dominant harmonic and that the percentages of the other harmonics are low relatively.

## D. Power Factor

The power factor is defined as below.

where, θ=π-θ1=π- arctan(B1/A1).

The relation curves of the power factor to the control angle α with different values of K are shown in Fig. 5(f). It can be found that as the angle α increases from 90o to 180o, the power factor remains close-to-unity and increase slightly. When K increases, the power factor decreases.

# IV. SIMULATION VERIFICATION

A prototype of the proposed LCL-T resonant converter is simulated with an operation frequency of 25kHz and a rated output power of 20W. The simulation is carried out by PSIM. The input is vs=48sin(ω1t)V with an angular frequency ω1=50000π rad/s, the MOSFET switches are IRF530N with a 100mΩ on-state resistance, the inductance of L1 and L2 is 42.5μH, C is a resonant capacitor with 0.94μF and the rated load is Ro=4.1Ω. The simulation results are shown in Fig. 6.

**Fig. 6.**Simulation waveforms of the proposed AC/DC converter, operation frequency is 25 kHz, output voltage is 9V.

The input voltage vs and input current iL1 are demonstrated in Fig. 6(a) and 6(b), respectively. The driving signal of Q1 and Q2 is shown in Fig. 6(c), the resonant current iL2 and reference waveforms iLL are demonstrated in Fig. 6(d), and the output voltage Uo is shown in Fig. 6(e).

It can be found from Fig. 6(a) and 6(b) that both the input voltage vs and current iL1 are sinusoidal and that they have the same phase angle. Fig. 6c shows that the driving signal Vg can be derived by an input voltage comparison. The charging angle of the output capacitor α is between 90o and 180o, which is used to control the output voltage. The inductor current iL2 is slightly ahead of iLL. The calculation results of the PSIM simulation are PF= 0.996 and THD=6.2%. The near-to-unity power factor and the low THD further verify the accuracy of the analysis and the excellent performance of the proposed resonant HFAC/DC converter.

# V. EXPERIMENTAL EVALUATION

A laboratory prototype is designed and tested to validate the characteristics of the proposed HFAC/DC converter. The same parameters are adopted for both the simulation and the experimental evaluations. The voltages are measured by a Probe Master Model 4231, and the current are detected by a Hantek AC/DC Current Clamp CC-65.

The operating waveforms are illustrated in Fig. 7 with a 48sin(ω1t)V input voltage and a charging angle of α=120o. It can be found that the input current iL1 is sinusoidal and that it has a low harmonics distortion. The input voltage vs and iL1 are almost in the same phase, which ensures a near-to-unity power factor. The resonant current iL2 lags behind vs by nearly 90o, and the angle Φ is small. The output voltage Uo is 9V. The experimental waveforms are in good agreement with the simulation results.

**Fig. 7.**The operating waveforms with 48sin(ω1t)V input voltage and charging angle α=120o. (a) Upper trace: input voltage vs, second trace: input current iL1. (b) Upper trace: input voltage vs, second trace: the driving signal of Q1 and Q2. (c) Upper trace: input voltage vs, second trace: the inductor current iL2. (d) Upper trace: input voltage vs, second trace: the output voltage Uo.

A varied input can be found in some applications sourced by batteries, fuel cells, etc., and the proposed converter can regulate the output voltage against input variations. When the experimental converter is fed with varied inputs, the typical waveforms are demonstrated in Fig. 8 and Fig. 9 with different values of the charging angle α.

**Fig. 8.**The operating waveforms with 55sin(ω1t)V input voltage and charging angle α=110o. (a) Upper trace: input voltage vs, second trace: input current iL1. (b) Upper trace: input voltage vs, second trace: the driving signal of Q1 and Q2. (c) Upper trace: input voltage vs, second trace: the inductor current iL2. (d) Upper trace: input voltage vs, second trace: the output voltage Uo.

**Fig. 9.**The operating waveforms with 40sin(ω1t)V input voltage and charging angle α=130o. (a) Upper trace: input voltage vs, second trace: input current iL1. (b) Upper trace: input voltage vs, second trace: the driving signal of Q1 and Q2. (c) Upper trace: input voltage vs, second trace: the inductor current iL2. (d) Upper trace: input voltage vs, second trace: the output voltage Uo.

When the input voltage increases to 55sin(ω1t)V, as shown in Fig. 8, the output voltage is kept at 9V with a charging angle of α=110o. When the input voltage decreases to 40sin(ω1t)V, as shown in Fig. 9, the output voltage is kept at 9V with a charging angle of α=130o. It can be concluded that the charging angle α can be regulated against input variations. In addition, the capability in the presence of input variations is determined by the operational scope of the charging angle α and the value of Uo/B. When the charging angle α is operated within the scope of 90o to 180o, Uo/B is shown in Fig. 5b.

Consequently, the proposed LCL-T resonant converter and control method are effective for the implementation of a high frequency power supply with precise voltage control. Meanwhile, both a low THD and a near-to-unity power factor are achieved over the operational scope.

Meanwhile, it can be found from the experimental results that the resonant current iL2 is about 10A. A larger iL2 results in design difficulty for the inductors, a larger circulation current and increased power losses. It is significant for parameter design to cut down the resonant current.

The curve of the efficiency to the load and input is illustrated in Fig. 10. The power loss mainly comes from the MOSFETs, the resonant components and the rectifier. In view of the large resonant current, the conducting losses of the MOSFETs are high. It can be found in Fig. 10 that the maximum efficiency is close to 94% at a 2Ω load; while the minimum efficiency is close to 89% at a 6Ω load. As Ro increases, the control angle α decreases to make the output stable. Therefore, the increasing conducting angle of the MOSFETs results in the increasing conducting loss and a lowering of the efficiency. It can also be found that the converter efficiency sourced by 48sin(ω1t)V is lower than that sourced by 40sin(ω1t)V. The resonant current increases along with the increasing of vs, and the conducting angle of the MOSFETs increases as well. Hence, the conducting loss becomes large and the conversion efficiency become low along with the ascending input voltage.

**Fig. 10.**The curve of efficiency to load and input.

Traditionally, the output voltage of an LCL-T resonant rectifier is regulated by its front-end converter. The resonant tank is designed for optimal parameters with a maximum efficiency [30]. However, the output is uncontrollable for a conventional resonant rectifier since it is incapable of being regulated against input variations. The proposed LCL-T resonant converter provides an effective output control using bidirectional switches. In addition, a wide scope of output regulation can be accomplished by a simple control strategy. In addition, a low distortion and a close-to-unity power factor are achieved for input side.

# VI. CONCLUSION

In order to improve the load performance of HFAC PDS, a controllable HFAC/DC converter is proposed with the modified LCL-T resonant tank. Meanwhile, an easier control method is presented for the proposed converter. The output voltage can be effectively regulated by bidirectional switches. The circuit description, operating principles, and steady-state analysis are examined in depth. A low THD and a near-to-unity power factor are both achieved. A controlled output can be achieved over a wide scope of the charging angle α. A simulation schematic and an experimental prototype are implemented with a rated output power of 20W, a rated frequency of 25 kHz, and a rated input peak voltage of 48V. The experimental results are in good agreement with the theoretical analysis and the simulation results. Consequently, the proposed resonant topology and control method are an effective solution for HFAC/DC conversion.