Hybrid-controlled half-bridge LLC resonant converter soft-start method

Abstract

The application discloses a soft starting method of a half-bridge LLC resonant converter with hybrid control, and belongs to the technical field of power electronics. The half-bridge LLC resonant converter comprises an inverter circuit, an LLC resonant cavity, a transformer and a rectifier circuit. The soft starting method with hybrid control comprises a bipolar pulse width modulation strategy, a unipolar pulse width modulation strategy and frequency conversion control. The method can solve the problems of long starting time and large current impact of the traditional half-bridge LLC resonant converter during starting, can quickly and smoothly establish an output voltage, can suppress the impact current of the resonant circuit during starting, is easy to implement, is low in cost and has high engineering use value.

Description

Technical Field

[0001] This invention relates to a soft-start method for a half-bridge LLC resonant converter, belonging to the field of power electronics technology. Background Technology

[0002] Radar devices are essential foundational equipment for detection missions in aerospace and defense fields, and the power supply system is the core of this energy guarantee. To achieve longer detection ranges and more accurate detection and positioning, while the power and voltage levels of radar power supplies are constantly increasing, higher demands are also placed on their stable and safe operation. DC-DC converter technology, as the core of the radar power supply system, is undeniably crucial. Among numerous DC-DC converters, the LLC resonant converter stands out due to its soft-switching across the entire load range and ease of magnetic integration. In particular, for applications with large voltage differences between high input and low output voltages, the LLC resonant converter with a primary-side half-bridge structure is widely used due to its simple structure and small transformer turns ratio.

[0003] In addition, due to the characteristics of low-frequency pulse loads in radar, a large energy storage capacitor is usually connected in parallel at the output to support the low-frequency pulse load. When the converter starts up, the capacitor at the output needs to be charged, which will generate a large inrush current, which can easily cause breakdown of power devices and burnout of resonant capacitors due to overvoltage. For LLC resonant converters with conventional frequency modulation (PFM), soft start is generally achieved by frequency reduction. However, as in the literature "Feng W, Lee F C. Optimal Trajectory Control of LLC Resonant Converters for Soft Start-Up[J]. IEEE Transactions on Power Electronics, 2014, 29(3): 1461-1468", if the initial switching frequency fs of the frequency reduction control is not high enough (1.5fr), there will still be a large inrush current and voltage at the moment of startup; if the initial switching frequency is set higher (5fr), the current and voltage stress of the resonant cavity will be smaller at the moment of startup, but if the switching frequency decreases too quickly, a large inrush current will still be generated, triggering overcurrent protection. Summary of the Invention

[0004] Purpose of the invention:

[0005] The purpose of this invention is to address the shortcomings of existing technologies by providing a hybrid control soft-start method for half-bridge LLC resonant converters. This method solves the problems of long startup time and large current surge during startup of traditional half-bridge LLC resonant converters, enabling rapid and stable establishment of the output voltage while suppressing the surge current that occurs during startup of the resonant circuit. Furthermore, it is easy to implement, low in cost, and has high engineering application value.

[0006] Technical solution:

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] A soft-start method for a hybrid-controlled half-bridge LLC resonant converter, wherein the half-bridge LLC resonant converter includes an inverter circuit, an LLC resonant cavity, a transformer, and a rectifier circuit, wherein the inverter circuit includes at least an asymmetrical half-bridge circuit composed of two switching transistors or a symmetrical half-bridge circuit composed of two switching transistors and two capacitors, wherein the LLC resonant cavity includes at least a resonant inductor, a resonant capacitor, and a magnetizing inductor, and wherein the rectifier circuit is a full-bridge rectifier circuit; characterized in that the soft-start method includes the following steps: (1) sampling the input voltage V using a resistor voltage divider method. in (2) Based on the input voltage V in Whether the sampled value is greater than the first set voltage determines whether to enter the start state. If yes, proceed to step (3); otherwise, return to step (1). (3) Start-up begins. First, the bipolar pulse width modulation method is used. The specific process is as follows: initialize the primary side drive signal frequency f. s Set the first frequency and duty cycle D p Set the first duty cycle; according to the set function relationship D p (t) Increase the duty cycle D of the primary-side drive signal p (3) Keep the frequency of the primary driving signal unchanged; (4) Determine the duty cycle D of the primary driving signal. p Is it the second set duty cycle? If yes, proceed to step (5); otherwise, return to step (3). (5) Switch from bipolar pulse width modulation method to unipolar pulse width modulation method. The specific process is as follows: with the end state of step (3), that is, the primary side driving signal frequency f s Set the first frequency and duty cycle D p The second duty cycle is set to the initial state at this time, according to the set function relationship D. p (t) Increase the duty cycle D of the primary-side drive signal p Maintain the original side drive signal frequency f s (6) Determine the duty cycle D of the primary-side drive signal. pIs it a third set duty cycle? If yes, proceed to step (7); otherwise, return to step (5). (7) Switch from unipolar pulse width modulation method to frequency conversion control method. The specific process is as follows: with the end state of step (5), that is, the primary side drive signal frequency f s Set the first frequency and duty cycle D p The third setting is the duty cycle at this initial state, according to the set function relationship f. s (t) Decrease the primary-side drive signal frequency f s Maintain the duty cycle D of the original side drive signal p (8) Output voltage V remains unchanged; o Once the rated output voltage is reached, the soft start ends, and the half-bridge LLC resonant converter enters normal closed-loop operation.

[0009] Preferably, the bipolar pulse width modulation method is as follows: under the condition that... or or When the upper transistor of the primary-side half-bridge inverter circuit is turned on, the drive signal of the lower transistor of the primary-side half-bridge inverter circuit is complementary to that of the upper transistor, and the condition is met. At that time, the upper left and lower right corner switches of the secondary full-bridge rectifier circuit are turned on, and the lower left and upper right corner switches are complementary to the upper left and lower right corner switches; the unipolar pulse width modulation method is as follows: when the condition is met... At that time, the primary half-bridge inverter circuit's upper transistor is turned on, satisfying the condition. At that time, the lower transistor of the primary-side half-bridge inverter circuit is turned on; the frequency conversion control method is as follows: when the condition is met... At this time, the upper transistor of the primary-side half-bridge inverter circuit is turned on, and the drive signal of the lower transistor of the primary-side half-bridge inverter circuit is complementary to that of the upper transistor; wherein the switching period T s =1 / f s carrier The first modulating wave p1(t) = 0, and the second modulating wave p2(t) = 0.5-D p The third modulated wave p3(t) = 0.5 + D p The fourth modulation wave p4(t) = 1.

[0010] Preferably, the first set voltage is any value between 0 and the minimum input voltage value required for the half-bridge LLC resonant converter to operate normally; the first set frequency is greater than or equal to the resonant frequency f of the half-bridge LLC resonant converter. r The first set duty cycle is 1 / 6, and the second set duty cycle is (T) any value between the highest normal operating frequency and the lowest normal operating frequency. s -2T d ) / 2T s The third set duty cycle is 0.5, where T d This refers to the dead zone time.

[0011] Preferably, the functional relationship D p (t) represents the duty cycle D. p The curve showing the change over time t can be expressed as: or Where n is the gear ratio, k1 is the first start-up time coefficient, and the start-up speed can be controlled by changing the value of k1; the functional relationship f s (t) is the frequency f s The curve showing the change of f with time t is expressed as: f s (t)=f r -k2t, where k2 is the second startup time coefficient, and the startup speed can be controlled by changing the value of k2.

[0012] The control timing of this application will be analyzed in detail in conjunction with specific embodiments. Compared with the prior art, the present invention has the following beneficial effects:

[0013] (1) The half-bridge LLC soft-start control method proposed in this invention selects a very small initial duty cycle of the drive signal. During the startup process, the duty cycle of the drive signal is gradually increased to 0.5, which significantly reduces the startup frequency, realizes the smooth and stable rise of the gain of the half-bridge LLC resonant converter, and the output voltage is established stably. At the same time, it suppresses the inrush current that occurs in the resonant circuit and the large capacitor at the output end during startup, and the startup time is short.

[0014] (2) The half-bridge LLC soft-start control method proposed in this invention can have a starting frequency equal to the resonant frequency, and the driving circuit is easy to implement and has low cost.

[0015] (3) The half-bridge LLC soft-start control method proposed in this invention can achieve ZVS of the primary and secondary side switching transistors through reasonable parameter design, thereby reducing start-up losses and improving the reliability of the LLC resonant converter. Attached Figure Description

[0016] To more clearly illustrate the technical solutions of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained from these drawings without any creative effort.

[0017] Appendix Figure 1 This is a schematic diagram of a half-bridge LLC resonant converter according to an embodiment of the present invention;

[0018] Appendix Figure 2 A simplified circuit for a half-bridge LLC resonant converter;

[0019] Appendix Figure 3 This is a control timing diagram for the bipolar pulse width modulation method;

[0020] Appendix Figure 4 This is a control timing diagram for a unipolar pulse width modulation method;

[0021] Appendix Figure 5 This is the control timing diagram for the variable frequency control method;

[0022] Appendix Figure 6 A schematic diagram of the startup process of a hybrid control soft-start method for a half-bridge LLC resonant converter;

[0023] Appendix Figure 7 Simulation waveforms of output voltage and resonant current for traditional frequency reduction control soft-start;

[0024] Appendix Figure 8 Simulation waveforms of output voltage and resonant current for a hybrid control system with linearly increasing duty cycle during soft-start.

[0025] Appendix Figure 9 Simulation waveforms of soft-start output voltage and resonant current for a hybrid control output voltage linearly increased. Detailed Implementation

[0026] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0027] It should be noted that in the description of this invention, the terms "first," "second," and "third" are used for descriptive purposes only and should not be construed as indicating or implying relative importance; the terms "left," "right," "upper," and "lower" are used to describe relative positions.

[0028] Appendix Figure 1 This is a schematic diagram of a half-bridge LLC resonant converter according to an embodiment of the present invention. The half-bridge LLC resonant converter includes an asymmetrical half-bridge inverter circuit 101, an LLC resonant cavity 102, a transformer 103, a full-bridge rectifier circuit 104, and a processor 105 connected in series. The asymmetrical half-bridge inverter circuit 101 includes a primary-side upper transistor Q1 and a primary-side lower transistor Q2, and Q1 and Q2 form a bridge arm T. p1The bridge arm is connected to the positive and negative buses of the input power supply, which has a voltage of 710V. Point a between Q1 and Q2 and the source point b of Q2 are connected to the LLC resonant cavity at the rear end. The LLC resonant cavity 102 is connected to the resonant inductor L. r Resonant capacitor C r And excitation inductance L m Composition, its resonant frequency The resonant inductance L is the normal operating frequency of the LLC resonant converter. r = 9.76μH, resonant capacitor value C r =29.3nF, magnetizing inductance value L m =48μH, resonant frequency is 300kHz; transformer turns ratio n = 20∶3.

[0029] The full-bridge rectifier circuit 104 includes a secondary upper left transistor S1, a secondary lower left transistor S2, a secondary upper right transistor S3, and a secondary lower right transistor S4, wherein S1 and S2 are located in bridge arm T. s1 S3 and S4 are located in bridge arm T s2 The midpoints of S1 and S2 are connected to terminal c on the secondary side of the transformer, and the midpoints of S3 and S4 are connected to terminal d on the secondary side of the transformer. The drains of S1 and S3 are connected to the positive output terminal, and the sources of S2 and S4 are connected to the negative output terminal. A filter capacitor C is connected in parallel at the output terminal. o Its capacitance is 50mF.

[0030] The processor 105 includes a sampling circuit, a processor, a drive circuit, etc., and is used to acquire input voltage sample values, output voltage sample values, and output current sample values, process the sample values, and output a drive signal V. GS1 V GS2 and V GS3 V GS4 The asymmetrical half-bridge inverter circuit 101 and the full-bridge rectifier circuit 104 are controlled respectively, where V GS1 This is the Q1 drive signal, V GS2 This is the Q2 drive signal, V GS3 For S1 and S4 drive signals, V GS4 These are the drive signals for S2 and S3.

[0031] The soft-start method for a hybrid-controlled half-bridge LLC resonant converter according to embodiments of the present invention includes the following steps:

[0032] (1) The processor 105 uses a resistor voltage divider method to divide the input voltage V in Perform sampling.

[0033] (2) The processor 105 determines the input voltage V based on the input voltage V inWhether the sampled value is greater than the first set voltage determines whether the half-bridge LLC resonant converter enters the start-up state. If yes, step (3) is executed; otherwise, step (1) is returned.

[0034] (3) Upon startup, the bipolar pulse width modulation method is first used. The specific process is as follows: Initialize the primary-side drive signal frequency f. s The resonant frequency f r Duty cycle D p Set the first duty cycle; according to the set function relationship D p (t) Increase the duty cycle D of the primary-side drive signal p Maintain the original side drive signal frequency f s constant.

[0035] Appendix Figure 2 A simplified circuit for a half-bridge LLC resonant converter is attached. Figure 3 The control timing diagram for the bipolar pulse width modulation method is shown. The voltage gain expression for bipolar pulse width modulation can be calculated using the fundamental frequency component method (FHA) or time-domain analysis:

[0036]

[0037] Where f n For normalized frequency, f n =f s / f r In this embodiment, the switching frequency fs is equal to the resonant frequency fr at startup, so the voltage gain expression can be simplified to:

[0038]

[0039] To ensure that the initial voltage gain G(t0) = 0, the first set duty cycle should be 1 / 6.

[0040] Functional relation D p (t) is the curve showing the change of the duty cycle of the driving signal versus time. If the duty cycle D is made... p If it increases linearly with time t, then its expression is: If the output voltage V o If it increases linearly with time t, then its expression is: Here, k1 is the first start-up time coefficient. By changing the value of k1, the start-up speed can be controlled. A suitable value is chosen so that the resonant current is less than the threshold current and the start-up time is less than the threshold time during the start-up process. In specific implementation, k1 is first initialized, and then simulation is performed. If the simulation finds that the resonant current exceeds the threshold current during the start-up process, the value of k1 is decreased until the resonant current is lower than the threshold current. If the simulation finds that the resonant current is much less than the threshold current during the start-up process, the value of k1 is increased until the resonant current approaches the threshold current.

[0041] The threshold current is determined based on the component characteristic parameters of the half-bridge LLC resonant converter, and the threshold time is determined based on the soft-start process design parameters of the LLC resonant converter.

[0042] (4) Determine the duty cycle D of the primary drive signal p If the second duty cycle is set, proceed to step (5); otherwise, return to step (3).

[0043] Due to the parasitic capacitance of MOSFETs in actual implementation, a dead time T should be allowed between complementary drive signals. d Used to complete the charging and discharging of parasitic capacitance, therefore, when the duty cycle Dp has not increased to 0.5, the two narrow drive signals within one cycle of the bipolar pulse width modulation drive signal have disappeared, so the second set duty cycle should be (T s -2T d ) / 2T s .

[0044] (5) Switching from bipolar pulse width modulation to unipolar pulse width modulation, the specific process is as follows: with the end state of step (3), that is, the primary side driving signal frequency f s =f r Duty cycle D p =(T s -2T d ) / 2T s Given this initial state, according to the defined function relationship D... p (t) Increase the duty cycle D of the primary-side drive signal p Maintain the original side drive signal frequency f s constant.

[0045] Appendix Figure 4 This is the control timing diagram for the unipolar pulse width modulation method.

[0046] (6) Determine the duty cycle D of the primary drive signal p If the value is 0.5, proceed to step (7); otherwise, return to step (5).

[0047] (7) Switching from unipolar pulse width modulation method to frequency conversion control method, the specific process is as follows: with the end state of step (5), that is, the primary side drive signal frequency f s =f r Duty cycle D p =0.5 is the initial state at this time, according to the set function relationship f s (t) Decrease the primary-side drive signal frequency f s Maintain the duty cycle D of the original side drive signal p constant.

[0048] Appendix Figure 5The diagram shows the control timing of the frequency conversion control method. The duty cycle of the primary drive signal is maintained at 0.5, and the secondary drive signal is a synchronous rectified signal.

[0049] Functional relation f s (t) represents the frequency of the driving signal f. s The curve of the change with time t is expressed as f. s (t)=f r -k2t, where k2 is the second startup time coefficient. By changing the value of k2, the startup speed can be controlled. A suitable value is chosen so that the resonant current is less than the threshold current and the startup time is less than the threshold time during startup. In practice, k2 is first initialized, and then simulation is performed. If the simulation shows that the resonant current exceeds the threshold current during startup, the value of k2 is decreased until the resonant current is lower than the threshold current. If the simulation shows that the resonant current is much less than the threshold current during startup, the value of k2 is increased until the resonant current approaches the threshold current.

[0050] The first start-up time coefficient k1 and the second start-up time coefficient k2 are jointly adjusted to make the total start-up time less than the threshold time.

[0051] (8) Output voltage V o Once the rated output voltage is reached, the soft-start process ends, and the half-bridge LLC resonant converter enters the normal closed-loop control state.

[0052] Appendix Figure 6 This is a schematic diagram of the startup process of a soft-start method for a hybrid control half-bridge LLC resonant converter. The initial startup state is at point a on the curve, and the first startup frequency is initialized to the resonant frequency f. r The initial duty cycle is 1 / 6; subsequently, the duty cycle gradually increases according to the set function D. p (t) increases, reaching point b on the curve, at which point the duty cycle D... p =(T s -2T d ) / 2T s The first control switch is performed; the signal changes from bipolar pulse width modulation to unipolar pulse width modulation, and the duty cycle continues to increase until point c on the curve is reached. At this point, the duty cycle D... p =0.5, and a second control switch is performed; switching from unipolar pulse width modulation to frequency conversion control, the switching frequency gradually decreases from the resonant frequency until the output voltage reaches the rated value. In the figure, the vertical axis G is the normalized gain of the converter. During the soft start process of this invention, the voltage gain increases continuously and smoothly from 0, which can effectively suppress the resonant current and the output current.

[0053] Set the startup threshold time to 50ms. Figure 7The simulation waveforms of output voltage and resonant current for traditional frequency reduction control soft-start are shown. The resonant frequency of the half-bridge LLC is 300kHz, the initial start-up frequency is set to 450kHz, and the output voltage reaches the rated value of 28V after 50ms, with a peak-to-peak resonant current of 56A. (Attached) Figure 8 The simulation waveforms of the output voltage and resonant current for a hybrid control soft-start with linearly increasing duty cycle are shown. The expression for the duty cycle versus time during startup is as follows: After 50ms, the output voltage reached the rated value of 28V, and the peak-to-peak resonant current was 43A. (See attached image) Figure 9 The simulation waveforms of the soft-start output voltage and resonant current are shown for a hybrid control output voltage linearly increasing. The duty cycle versus time function expression during the startup process is as follows: After 50ms, the output voltage reaches the rated value of 28V, and the peak-to-peak resonant current is 30A. Simulation results show that during the soft-start process of this invention, the resonant current is much smaller than that of the traditional frequency-reduced start-up process, effectively suppressing the current during startup and avoiding damage to the switching transistor and triggering overcurrent protection.

[0054] Although the preferred embodiments of the present invention have been described above, those skilled in the art, once they learn the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the present invention.

[0055] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A soft-start method for a hybrid-controlled half-bridge LLC resonant converter, wherein the half-bridge LLC resonant converter includes an inverter circuit, an LLC resonant cavity, a transformer, and a rectifier circuit, wherein the inverter circuit includes at least an asymmetrical half-bridge circuit composed of two switching transistors or a symmetrical half-bridge circuit composed of two switching transistors and two capacitors, wherein the LLC resonant cavity includes at least a resonant inductor, a resonant capacitor, and a magnetizing inductor, and wherein the rectifier circuit is a full-bridge rectifier circuit. Its features are, The soft-start method includes the following steps: (1) The input voltage V is sampled by resistance voltage division method in ; (2) According to the input voltage V in Whether the sampling value is greater than the first set voltage determines whether to enter the starting state. If yes, step (3) is executed. Otherwise, return to step (1). (3) Upon startup, the bipolar pulse width modulation method is first used. The specific process is as follows: Initialize the primary-side drive signal frequency f. s Set the first frequency and duty cycle D p Set the first duty cycle; according to the set function relationship D p (t) Increase the duty cycle D of the primary-side drive signal p Maintain the original side drive signal frequency f s constant; (4) Determine the duty cycle D of the primary drive signal p Is it the second set duty cycle? If yes, proceed to step (5); otherwise, return to step (3). (5) Switching from bipolar pulse width modulation to unipolar pulse width modulation, the specific process is as follows: with the end state of step (3), that is, the primary side driving signal frequency f s Set the first frequency and duty cycle D p The second duty cycle is set to the initial state at this time, according to the set function relationship D. p (t) Increase the duty cycle D of the primary-side drive signal p Maintain the original side drive signal frequency f s constant; (6) Determine the duty cycle D of the primary drive signal p Is the duty cycle set for the third time? If yes, proceed to step (7); otherwise, return to step (5). (7) Switching from unipolar pulse width modulation method to frequency conversion control method, the specific process is as follows: with the end state of step (5), that is, the primary side drive signal frequency f s Set the first frequency and duty cycle D p The third setting is the duty cycle at this initial state, according to the set function relationship f. s (t) Decrease the primary-side drive signal frequency f s Maintain the duty cycle D of the original side drive signal p constant; (8) Output voltage V o Once the rated output voltage is reached, the soft start ends, and the half-bridge LLC resonant converter enters normal closed-loop operation.

2. The soft-start method for a hybrid-controlled half-bridge LLC resonant converter as described in claim 1, characterized in that, The bipolar pulse width modulation method is as follows: under the condition that... or or When the upper transistor of the primary-side half-bridge inverter circuit is turned on, the drive signal of the lower transistor of the primary-side half-bridge inverter circuit is complementary to that of the upper transistor, and the condition is met. At that time, the upper left and lower right corner switches of the secondary full-bridge rectifier circuit are turned on, and the lower left and upper right corner switches are complementary to the upper left and lower right corner switches; the unipolar pulse width modulation method is as follows: when the condition is met... At that time, the primary half-bridge inverter circuit's upper transistor is turned on, satisfying the condition. At that time, the lower transistor of the primary-side half-bridge inverter circuit is turned on; the frequency conversion control method is as follows: when the condition is met... At this time, the upper transistor of the primary-side half-bridge inverter circuit is turned on, and the drive signal of the lower transistor of the primary-side half-bridge inverter circuit is complementary to that of the upper transistor; wherein the switching period T s =1 / f s carrier The first modulating wave p1(t) = 0, and the second modulating wave p2(t) = 0.5-D p The third modulated wave p3(t) = 0.5 + D p The fourth modulation wave p4(t) = 1.

3. The soft-start method for a hybrid-controlled half-bridge LLC resonant converter as described in claim 1, characterized in that: The first set voltage is any value between 0 and the minimum input voltage value required for normal operation of the half-bridge LLC resonant converter; the first set frequency is greater than or equal to the resonant frequency f of the half-bridge LLC resonant converter. r Any value between less than and equal to the highest normal operating frequency; The first set duty cycle is 1 / 6, and the second set duty cycle is (T) s -2T d ) / 2T s The third set duty cycle is 0.5, where T s For the switching period, T d This refers to the dead zone time.

4. The soft-start method for a hybrid-controlled half-bridge LLC resonant converter as described in claim 1, characterized in that: The aforementioned functional relationship D p (t) represents the duty cycle D. p The curve showing the change over time t is expressed as follows: or Where n is the gear ratio, k1 is the first start-up time coefficient, and the start-up speed can be controlled by changing the value of k1; the functional relationship f s (t) is the frequency f s The curve showing the change of f with time t is expressed as: f s (t)=f r -k2t, where k2 is the second startup time coefficient, f r K2 is the resonant frequency of the half-bridge LLC resonant converter. The startup speed can be controlled by changing the value of k2.

Images