Series-Resonant Converter with Reduced-Frequency-Range Control

Yungtaek Jang, Milan M. Jovanović, Juan M. Ruiz, and Gang Liu1, 2 Power Electronics Laboratory, Delta Products Corporation, 5101 Davis Drive, Research Triangle Park, NC, USA

1 Electrical Engineering, Fudan University, Shanghai 200433, People’s Republic of China 2 Delta Power Electronics (Shanghai) Co. Ltd, 201209, People’s Republic of China

Abstract— In this paper, a control method that improves performance of series-resonant converters that operate with a wide input-voltage and/or output-voltage range by substantially reducing their switching-frequency range. The switching-frequency-range reduction is achieved by controlling the output voltage with a combination of variable-frequency and delay-time control. Variable-frequency control is employed to control the primary switches, while delay-time control is used to control secondary-side rectifier switches provided in place of diode rectifiers. The performance evaluation of the proposed control was done on a 690-W prototype operating in a 200-450-V input-voltage range and delivering a 13.8-V output voltage. The prototype circuit exhibits the maximum full-load efficiency of 95.8% with a switching frequency variation from 48 kHz to 72 kHz over the entire input-voltage range.

I. INTRODUCTION Resonant converters use a resonant-tank circuit to shape

switch voltage and/or current waveform to minimize switching losses and allow high-frequency operation while maintaining high conversion efficiencies. As a result, resonant converters are extensively used in state-of-the-art power supplies that offer the highest power densities and efficiencies [1]-[5]. Generally, resonant converters operate with variable switching-frequency control. When operating above the resonant frequency, resonant converter operates with zero voltage-switching (ZVS) of the primary switches. Generally, variable switching-frequency control is seen as a drawback of a resonant converter especially in applications with a wide input-voltage and/or output-voltage range. Specifically, as the input or output voltage range increases, the control frequency range also increases so that driving and magnetic component losses also increase, thereby reducing conversion efficiency. Furthermore, in many applications, converters are restricted to operate within a relatively limited frequency range to avoid interfering with other parts of the system. While resonant converters can operate at a constant frequency (“clamp-mode” operation) [6], such an operation is not desirable because the increased circulating energy in the resonant tank circuit significantly degrades conversion efficiency. As a result, there have been several attempts to improve performance of resonant converters operating in a wide input-voltage range and/or a wide output-voltage range by reducing the switching frequency range by adding “range” windings and/or switches to effectively change the turns ratio of the transformer [7]-[10]. While these approaches have

been proven to improve performance, their major downsides are additional cost and complexity.

In this paper a new control method that improves the performance of resonant converters that operate with a wide input-voltage range and/or a wide output-voltage range by substantially reducing their switching-frequency range is introduced. Reduction in the switching frequency range is achieved by controlling the output voltage with a combination of variable-frequency feedback control and open-loop delay-time control. Variable-frequency control is used to control the primary switches of an isolated resonant converter, while delay-time control is used to control secondary-side rectifier switches provided in place of diode rectifiers. The secondary-side control is implemented by sensing the secondary current and/or the primary current and by delaying the turning-off of the corresponding secondary switch(es) with respect to the zero crossings of the secondary or the primary current. Generally, the delay time is determined by the input voltage and/or the output voltage and is set to properly adjust the voltage gain. Since delay-time control increases the energy in the resonant tank circuit and makes the series resonant converter exhibit a boost characteristic, the delay-time control is typically designed to supplement the variable-frequency feedback control at low input and/or high output voltages. The evaluation of the proposed delay-time control was performed on a 690-W prototype operating in the input-voltage range from 200 V to 450 V.

II. SERIES-RESONANT CONVERTER WITH REDUCED-

FREQUENCY-RANGE CONTROL Figure 1 illustrates the proposed control method in a

series-resonant converter with a full-bridge secondary synchronous rectifier. However, it should be noted that the described control method is also applicable to the center-tap secondary implementation. As illustrated in Fig. 1, output voltage regulation is achieved using a combination of variable-frequency feedback control and open-loop delay- time control. Specifically, variable-frequency control is applied to primary switches SP1-SP4, and delay-time control is applied to secondary-side switches SS1-SS4. Figures 2(a) and (b) show waveforms of primary switches SP1-SP4, secondary switches SS1-SS4, and resonant inductor current iLR for two secondary side control methods; one with asymmetric gating and the other with symmetric gating. As shown in Figs. 2(a) and (b), in both implementations, all same-leg pairs of

978-1-4799-6735-3/15/$31.00 ©2015 IEEE 1453

switches operate in a complementary fashion with a small dead time between their commutations to achieve ZVS.

In Fig. 2(a), the delay-time control is implemented by delaying the turn-off of switches SS2 and SS3 with respect to corresponding zero crossings of resonant current iLR so that both switches SS2 and SS3 are turned on during delay-time intervals [T0-T1] and [T3-T4] shorting the secondary of transformer TR. This control method is easy to implement since it requires modulation of only two secondary-side switches. As illustrated in Fig. 2(a), switches SS2 and SS3 are modulated to provide necessary time delay, while switches SS1 and SS4 are operated with complimentary gate signals to that of switches SS2 and SS3, respectively. Because switches SS1 and SS4 are not actively modulated, they can be replaced by diode rectifiers, which further simplifies the circuit and may be beneficial in some applications. However, since in this asymmetrical-gating control implementation, switches SS2 and SS3 operate with a greater duty cycle compared to switches SS1 and SS4, they also carry greater average currents and, consequently, exhibit increased thermal stress compared to switches SS1 and SS4 and require better thermal design. The uneven thermal stress of the secondary-side switches can be eliminated by implementing a symmetric-gating control shown in Fig. 2(a). In this implementation, all secondary-side switches operate with the same duty cycle of 50%. The delay-time control is implemented by delaying the turn-off of switches SS1 and SS2 with respect to corresponding zero crossings of resonant current iLR so that switches SS2 and SS3 are turned on during the delay-time interval [T0-T1] and switches SS1 and SS4 are turned on during the delay-time interval [T3-T4] shorting the secondary of transformer TR. In this implementation, if advantageous, switches SS3 and SS4 can be replaced by diode rectifiers.

To facilitate explanation of operation, Fig. 3 shows the topological stages of the converter with the proposed delay-time control during a half of the switching period. The converter exhibits three topological stages. In the first

topological stage, shown in Fig. 3(a), that occurs during the delay-time period [T0-T1], the secondary of the transformer is shorted. As a result, no energy is transferred from the LR-CR resonant tank to the output and the resonant tank is driven by input voltage VIN only. The second topological stage, shown in Fig. 3(b), occurs during the [T1-T2] period. Since during this stage the resonant current flows to the output, resonant-tank energy is transferred to the load. During this stage the voltage driving the resonant tank is given by the difference between input voltage VIN and primary-reflected output voltage nVO, i.e., by VIN-nVO. In the third topological stage that occurs during the [T2-T3], shown in Fig. 3(c), the resonant-tank energy continues to be delivered to the output. However, since during this stage the input-voltage polarity is negative because of the commutation of primary switches at t=T2, a part of the resonant-tank energy is returned to the

Fig. 1. Series-resonant converter with proposed secondary-side-switch

delay-time control.

ZCD

DELAY-TIMECONTROL

sensing & scaling

N1

N2n=

i LR

SP1

SP2

VIN

L RTR

N1 VO

+

-

LOAD

CO

SS4

SS3

N2

SS1

SS2

SP4

SP3

CR

CONTROL

VOsensing & scaling

VCO

DRIVERDRIVER

ERORR AMPLIFIERw/ COMPENSATION

SS1 SS2SP2SP1

VO(scld)

VIN(scld)

VO(REF)

VO(scld)

+ -VEA

f S

VE

VIN(scld)

i LR

VIN

SS3 SS4SP4SP3

(a)

(b) Fig. 2. Switch-gating and resonant-inductor current waveforms of series-

resonant converter with proposed delay-time control: (a) asymmetric gating and (b) symmetric gating.

SP3

SP4

SP1

SP2OFF ON

t

t

ONOFF

OFFON

t

Ts

t

t

SS1

SS2

iLR

Delay Time

T0 T1 T2 T3 T4

Delay Time

t

ONOFF

ON OFF

t

SS3

SS4

ON OFF

TD TD

SP3

SP4

SP1

SP2OFF ON

t

t

ONOFF

OFFON

t

Ts

t

t

SS1

SS2

iLR

Delay Time

T0 T1 T2 T3 T4

Delay Time

t

ONOFF

ON OFF

t

SS3

SS4

ON OFF

TD TD

1454

input. In fact, this circulating energy is used to achieve ZVS of the primary switches. During this stage the voltage driving the resonant tank is given by the difference between the negative input voltage VIN and primary-reflected output voltage nVO, i.e., by -VIN-nVO.

As seen from Fig. 3(a), because in this topological stage the secondary of the transformer is shorted, the voltage across resonant tank CR-LR during delay-time interval [T0-T1] is VIN instead of VIN –nVO which is the case with no delay- time control. Therefore, with the delay-time control, a higher voltage is applied across resonant inductor tank and, consequently, a higher amount of energy is stored in resonant inductor LR. Therefore, at the same input voltage and switching frequency, secondary-side delay-time control provides a higher output voltage compared to the conventional frequency control. This boost characteristic makes optimizing circuit performance possible by enabling selection of a higher turns ratio in the transformer to reduce the primary conduction losses and a larger magnetizing inductance to reduce the circulating (i.e., magnetizing) current loss. Because of its boost characteristic, the proposed delay-time control is most effective when applied in a low input-voltage range or in a high output-voltage range. Specifically, the maximum delay time, which is

approximately TS/4, where TS is the switching period, is set at the minimum input voltage or the maximum output voltage. This delay time is progressively reduced for higher input voltage or lower output voltage. In typical applications, the delay-time control is not used at the middle and high input voltages, or nominal and low output voltages.

The proposed control method can be implemented by either analog or digital technique, or their combination. A microcontroller- or DSP-based implementation is preferred since the delay time that depends on input or output voltage can be easily programmed.

III. DERIVATION OF DC VOLTAGE CONVERSION RATIO To provide tools for design optimization of the series-

resonant converter with the proposed delay-time control, its dc-conversion ratio M=nVO/VIN is derived using the normalized state-plane analysis. The normalization was done with the following base parameters: Base voltage VBASE = VIN

Base impedance ZBASE = ZO =

Base current IBASE = =

Base time

Base frequency π

Base angular frequency ω

The normalized variables are defined as: Normalized input voltage _ 1

Normalized output voltage _

Normalized resonant-capacitor voltage

vCR_N =

Normalized peak resonant-capacitor voltage

vCR_PK_N = _ _

Normalized output current IO_N = =

Normalized resonant inductor current

_

Normalized delay time _

Normalized switching frequency

(a) [T0-T1]

(b) [T1-T2]

(c) [T2-T3]

Fig. 3. Topological stages of series-resonant converter with proposed

delay-time control during half of switching period when resonantinductor current is positive [T0-T3].

+

L R CR

V IN

i LR + v -CR

V IN +

L R CR

+nV O

i LR + v -CR

+

L R CR

+ V IN nV O

i LR + v -CR

1455

Other variables and parameters used are defined as:

Transformer turns ratio n =

Quality factor

Delay-time stage (Fig. 3(a)) angle α = ωO[T0-T1]

Energy-delivery stage (Fig. 3(b)) angle β = ωO[T1-T2]

Energy-circulating stage (Fig. 3(c)) angle γ = ωO[T2-T3]

Half switching period angle λ = α +β + γ = ω = π

Figure 4, shows the normalized state trajectory of the

converter during one half of a switching half cycle. Since the proposed converter exhibits three topological stages during a half switching cycle, trajectory consists of three corresponding arcs, as shown in Fig. 4. It should be noted that the centers of these arcs are on the vCR_N axis with the distances from the origin that are equal to the respective normalized voltage across resonant tank LR-CR. Since according to Figs. 3(a)-(c), the resonant tank voltages during the three topological stages are VIN, VIN-nVO, and –VIN-nVO, respectively, the centers of the corresponding arcs in the normalized vCR_N – iLR_N state plane are at (0, 1), (0, 1-M), and (0,-1-M).

To be able to complete the construction of the state-plane trajectory in Fig. 4, it is necessary to determine radius R1 of the arc that corresponds to the stage in Fig. 3(a) which is the first stage in the half cycle. To facilitate this derivation, Fig. 5 shows resonant voltage vCR and current iLR waveforms

during a half switching cycle when resonant-inductor current iLR is positive. As can be seen from Fig. 5, during the shown half switching period, the positive resonant-inductor current continuously charges the resonant capacitor so that the voltage across resonant capacitor increases from its negative to its positive peak, i.e., changes for 2VCR_PK. The relationship between the resonant-capacitor voltage change and stored charge during the half switching cycle is given by · 2 _ (1)

or 1 2 · 2 _ , (2)

where Area1 and Area2 are defined in Fig. 5.

Since during the delay-time topological stage shown in Fig. 3(a), i.e., during the [T0-T1] interval, the resonant-inductor current is given by

· sin _ · sin , (3)

where, as shown in Fig. 5, initial capacitor voltage VCR(0)=VCR_PK, Area1 can be calculated as

1 _ · sin · . (4)

Area2 can be calculated by recognizing that the output (load) current reflected to the primary is the average of the resonant inductor current iLR over a half switching period. Since iLR flows through the output only during the interval [T1-T3], the reflected output current at the primary side is given by 2 (5)

From equations (2)-(5), it follows that

Fig. 5. Steady-state waveforms of resonant-capacitor voltage VCR and

resonant-inductor current iLR during half switching period where resonant-inductor current is positive (iLR>0).

i LR

Delay Time

T0 T1 T2 T3

Area 2Area 1

t

VCR VCR_PK

-VCR_PK

TD

T /2S

t

I On

Area 2=T /2S

Fig. 4. State plan representation for one half of switching cycle [T0-T3]

where vCR_N and iLR_N are normalized resonant capacitor CR voltageand resonant inductor LR current, respectively.

1R 1 - M

0

LR_Ni

CR_NV

α

β

γ

3R

x

M

2

h

2R

βp

CR_PK_NV

CR_PK_N-V

-1

-1 - M

= 1IN_NV

2R

1456

_ · sin · · · 2 _ , (6)

which after normalization with replacing 1⁄ and assuming that t=T0=0 can be written as 1 _ _ · sin θ · θ λ · _ 2 _ _ . (7)

Finally, from (7), normalized peak resonant-capacitor voltage can be solved as

_ _ λ· _ . (8)

From the normalized state-plane diagram in Fig. 4, it follows that radii R1, R2, and R3 are related to VCR_PK_N as

R1 = VCR_PK_N + 1, (9)

R2 = = , (10)

R3 = VCR_PK_N + M + 1. (11)

By using the law of cosine for the triangle that is formed by radii R2 and R3, as well as angles β+βP and γ, dc-conversion ratio M of the series-resonant converter with the proposed delay-time control can be derived as 2 2 cos π , (12)

where . (13)

Since λ = α + β + γ, Eq. (12) can be rewritten as 4 2 cos π λ , (14)

Using Eqs. (9), (10), and (11), Eq. (14) can be expressed as VCR_PK_N 1 M M VCR_PK_N 1 1 cosα) V _ _ 1 M VCR_PK_N 1 M 2M VCR_PK_N 1 cosα cos λ α βP 2 0 . (15)

Because an explicit solution for dc-conversion ratio M = nVO/VIN given by Eq. (15) is not available, it is numerically calculated for a given quality factor Q and normalized delay time TD_N=α/(2λ)=TD/TS. As examples, Figs 6(a) and (b) show the plots of dc conversion ratio M as function of normalized switching frequency and normalized delay time TD_N as a parameter for Q=1 and Q=0.2, respectively. When delay time is zero (α=0°, TD=0), the converter characteristic is the same as that of a conventional series resonant converter. As delay time TD increases, dc gain M increases and exhibits a boost characteristic.

To illustrate the effectiveness of the delay-time control to reduce control-frequency range, Figs. 7 (a) and (b) show, respectively, the control-frequency range of the LLC converter and the proposed series-resonant converter with delay-time control designed for 200-450-V input-voltage range and 13.8-V output. For comparison, magnetizing

inductance LM was chosen to be four times larger than the resonant inductance LR in the case of LLC resonant converter, whereas magnetizing inductance LM of the proposed series-resonant converter is assumed infinite. For both converters turns ratio of the transformer is n=N1/N2=21. Operating points marked A, B, and C in Figs. 7(a) and (b) represent operating points when the converters deliver full power from input voltage 200 V, 300 V, and 450 V, respectively. As can be seen from Figs. 7(a) and (b), the series-resonant converter with the proposed delay-time control exhibits a significantly narrower frequency range compared to that of the LLC converter. Specifically, the frequency range of the converter with delay-time control is from 1.5 (operating A) to 1.62 (operating point C), whereas the corresponding range for the conventional LLC is from 0.67 to 1.71, i.e., the proposed delay-time control reduces the range for more than eight times (1.04/0.12≈8.7).

(a)

(b)

Fig. 6. Calculated dc-voltage conversion ratio characteristics of series-

resonant converter with proposed delay-time control for Q-factor:(a) Q=0.2; (b) Q=1.

0

2

4

=0

=0.35

=0.3

=0.25=0.15

Q = = 0.2

2

3

0

1

4

5

1.6 1.91.31 2.2 2.5

M =

0

2

4

=0

=0.35

=0.3

=0.25=0.15

M =

Q = = 1

2

3

0

1

4

5

1.1 1.151.051 1.2 1.25

1457

IV. BI-DIRECTIONAL IMPLEMENTATION Because the series-resonant converter with proposed

delay-time control exhibits buck-boost characteristics, it is very suitable for bidirectional power applications. However, to enable a proper bidirectional implementation, the power stage needs to be slightly modified. As shown in Fig. 8, the modification consists of making the power stage symmetrical by placing resonant inductor LR1 and capacitor CR1 on the primary side and resonant inductor LR2 and capacitor CR2 on the secondary side. By having the resonant capacitors in series with both primary and secondary windings of transformer TR, any dc-bias current at the primary side as well as the secondary side of the transformer is blocked, i.e., saturation of transformer TR is prevented. A microcontroller-

or DSP-based implementation is preferred since the roles (functions) of the primary switches and the secondary switches can be easily configured based on the power-flow direction.

V. EXPERIMENTAL RESULTS

The performance of the proposed converter with the delay-time control was evaluated on a 690-W prototype designed to operate from the 200-450-V input-voltage range and deliver a nominal output voltage of 13.8-V. Because the specified full load power is relatively low (<1 kW), the half-bridge topology is selected, as shown in Figure 9. The resonant frequency of the prototype was set at fO=40 kHz. To make dc voltage conversion ratio M equal to 1 when the input voltage is approximately 260 V, 9:1 turns ratio of transformer TR is chosen. As a result, the delay time of the secondary-side switches is set to zero when the converter operates from 275-V to 450-V input, i.e., when M<1, so that in this range the proposed converter operates as a conventional series-resonant converter. However, when the input voltage drops below 275 V, the controller starts monotonically increasing the delay time to provide the boost characteristics necessary to maintain the output voltage

(a)

(b) Fig. 7. Comparison of control-frequency ranges of: (a) conventional LLC

resonant converter; (b) proposed series-resonant converter withdelay-time control. Points A, B, and C represent operating pointswhen converters deliver full power from input voltage 200 V, 300V, and 450 V, respectively. Output voltage of both converters isVO=13.8 V and their transformer’s turns ratio is n=N1/N2=21.

0

5

5

2

Q=0.2

Q=0.45

Q=1.01

= 4 Q =

1

1.5

0

0.5

2

1.50.50 2 2.50.67

1.449

0.644

A

B

C

11.71

1.04

M =

Q=0.2, =0.165

Q=0.45, =0.075

Q=1.01, =0.035

Q =

1.5

1

1.5

0

0.5

2

1.91.31 2.2 2.5

1.449

0.644

0

2

A

B

C

1.61.62

0.12

M =

Fig. 9. Experimental prototype circuit.

TRETD59/28-3C94

Primary: Litz 0.1mmx300, 9 turnsSecondary: 42 mils 9mm width

Copper foil, 1 turnLm=800 uH

TR

VO

+

-

CO

SS4

SS3

N2

SS1

SS2

CR1

CR2

SP1

SP2

L R

N1

LPQ35/35-DMR

Litz 0.1mmx300 28T, 79 uH

RS , S

IPW65R041CFDP1 P2 S - S

BSB008NE2LXS1 S4

VIN

+

-

CO45 x 22uFMLCC-25V

R1 R2C , C100nF/

942C12P1K

i Pi S

Fig. 8. Implementation of bidirectional series-resonant converter with proposed delay-time control.

SP1

SP2

CF1

SS4SS1

CONTROLLERV2

SP3 SP4SP1 SP2 SS3 SS4SS1 SS2

TR

SS3SS2

SP4

SP3

BI-DIRECTIONAL POWER FLOW

L R1

CR1V2V1

LR2

CR2CF2

V1

1458

regulation with the selected turns ratio of transformer TR. As shown in Fig. 9, the prototype is built using

IPW65R041CFD MOSFET (VDS = 650 V, RDS = 0.041 Ω, COSS=400 pF, Qrr=1.9 μC) from Infineon for each switch. To obtain the desired inductance of resonant inductors LR of approximately 79 μH and also to achieve high efficiency at light-load, each inductor was built using a pair of ferrite cores (PQ-35/35, DMR90) with 28 turns of Litz wire (Φ 0.1mm, 300 strands) and approximately 5 mm gap. Litz wire was used to reduce the fringing-effect-induced winding loss near the gap of the inductor core. Transformer TR was built using a pair of ferrite cores (ETD-59/28, 3C94) with 9 turns of Litz wire (Φ 0.1mm, 300 strands) for the primary winding

and 1 turns of copper foil (42 mils thickness, 9 mm width) for the secondary winding. The measured magnetizing and leakage inductances at the primary winding are 800 μH and 2.5 μH, respectively. A film capacitor (100 nF, 1200 VDC) was used for each resonant capacitor, CR1 and CR2. Forty-five parallel connected ceramic capacitors (22 μF, 25 VDC) were used for output capacitor CO. The output-voltage regulation that employs variable-frequency control together with open-loop (preprogrammed) delay-time control was implemented by a TMS320F28027 microcontroller with 32-bit CPU from TI.

Figures 10(a)-(e) show the measured waveform of primary current iP and the gate waveforms of secondary switches SS3 and SS4 of the experimental circuit when it delivers full power from 200-V, 240-V, 275-V, 350-V, and 450-V input, respectively. As shown in Fig. 10(a), at the 200-V input, normalized delay time TD_N is approximately 0.18. As it can be seen from the gate waveforms, secondary-side switches SS3 and SS4 operate in complimentary fashion with a small dead time between their commutations. The turn-off moment of switch SS3 is delayed after the zero crossing of primary current iP which coincides with that of secondary current iS because the magnetizing current of the transformer is small due to a relatively high magnetizing inductance.

(a)

(b)

(c)

VIN=200 V, VO=13.8 V, PO=690 W, fS=51 kHz

iP[10 A/div]

VGATE_SS3

[10 V/div]

VGATE_SS4

[10 V/div]

5 μsec/div

VIN=240 V, VO=13.8 V, PO=690 W, fS=50 kHz

iP[5 A/div]

VGATE_SS3

[10 V/div]

VGATE_SS4

[10 V/div]

5 μsec/div

0.1

VIN=275 V, VO=13.8 V, PO=690 W, fS=48 kHz

iP[5 A/div]

VGATE_SS3

[10 V/div]

VGATE_SS4

[10 V/div]

5 μsec/div

0

(d)

(e)

Fig. 10. Measured full-load primary-current and gate-voltage waveforms of secondary switches SS3 and SS4 for input voltage: (a) VIN= 200 V; (b) VIN = 240 V; (c) VIN = 275 V (d) VIN = 350 V; and (e) VIN = 450 V. Time scale is 5 μS/div.

VIN=350 V, VO=13.8 V, PO=690 W, fS=59 kHz

iP[5 A/div]

VGATE_SS3

[10 V/div]

VGATE_SS4

[10 V/div]

5 μsec/div

0

VIN=450 V, VO=13.8 V, PO=690 W, fS=72 kHz

iP[5 A/div]

VGATE_SS3

[10 V/div]

VGATE_SS4

[10 V/div]

5 μsec/div

0

1459

When the converter operates from input voltage of 240 V, TD_N is decreased to 0.1, as shown in Fig. 10(b). At input voltages greater than 275 V, TD_N is set to zero, as shown in Figs. 10(c)-(e).

Figure 11 shows measured efficiency of the prototype as a function of load current for different input voltages. As can be seen from Fig. 11, the converter exhibits the maximum full-load efficiency of 95.8% at 275-V input. Figure 12 shows the measured full-load switching frequency of the experimental prototype as function of input voltage. The measured full-load switching frequencies are in the 48-72 kHz range over the entire input-voltage range. As seen from

Fig. 12, the delay-time control reduces the switching frequency range by limiting the minimum switching frequency.

V. SUMMARY

In this paper, a control method that offers improved performance of series-resonant converters that operate with a wide input- and/or output-voltage range by substantially reducing their switching-frequency range has been introduced. Reduction in the switching frequency range is achieved by regulating the output voltage with a combination of closed-loop variable-frequency control of primary-side switches and open-loop delay-time control of secondary-side switches.

The performance of the proposed control was evaluated on a 690-W prototype operating from the 200-450-V input-voltage range and providing a nominal 13.8-V output. The measured efficiency of the proposed rectifier in the 50-100% load range is approximately between 91% and 96%. Over the entire input-voltage range, the full-load switching frequency varies from 48 kHz to 72 kHz.

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[8] B.C. Kim, K.B. Park, and G.W. Moon, “Asymmetric PWM control scheme during hold-up time for LLC resonant converter,” IEEE Transactions on Industrial Electronics, vol. 59, no. 7, pp. 2992-2997, July 2012.

[9] I.H. Cho, Y.D. Kim, and G.W. Moon, “A half-bridge LLC resonant converter adopting boost PWM control scheme for hold-up state operation,” IEEE Transactions on Power Electronics, vol. 29, No. 2, pp. 841-850, February 2014.

[10] T. LaBella, W. Yu, J. Lai, M. Senesky, D. Anderson, “A bidirectional-switch-based wide-input range high-efficiency isolated resonant converter for photovoltaic applications,” IEEE Transactions on Power Electronics, vol. 29, No. 7, pp. 3473-3484, July 2014.

Fig. 11. Measured efficiency of experimental prototype as function of

output current for different input voltages.

VO = 13.8 V

VIN = 200 V

VIN = 350 V

VIN = 450 V

VIN = 275 VVIN = 240 V

OUTPUT CURRENT [A]

EFFI

CIE

NC

Y [%

] 96

94

92

90

88

86

84

82

80

785 10 20 30 40 50

Fig. 12. Measured full-load switching frequency of experimental prototype as function of input voltage.

PO = 690 WVO = 13.8 V

= 0

= 0.18

= 0.1

24 kHz

OUTPUT VOLTAGE [V]

SWIT

CH

ING

FR

EQU

ENC

Y [k

Hz]

75

70

65

60

55

50

45200 410 450350 380275 310240

1460