LLC resonant converter synchronous rectification non-iterative calculation method

Abstract

The invention provides an LLC resonant converter synchronous rectification non-iterative calculation method. The method comprises the steps of 1, solving corresponding modal boundary resistance; 2, listing corresponding state equations and boundary conditions: listing the corresponding state equations according to the existing sub-operation modes, and listing the corresponding boundary conditions for the existing voltage and current symmetry, energy conservation and charge conservation; step 3, substitution elimination solving: performing substitution elimination through the relationship between the gain M and the time t to obtain a new solving equation set, converting the new solving equation set into an equation only containing the time t as an unknown number, and completing the calculation of the synchronous rectification time t and the gain M by using a numerical solution method; and step 4, performing gain verification. The beneficial effects of the invention are that: 1, the resonant capacitor voltage is coupled with the output gain and the output power, so that the gain under the corresponding frequency is obtained while the simple operation of the synchronous rectification conduction time is realized;

Description

Technical Field

[0001] The present invention relates to the technical field of electronic circuits, and in particular, to a synchronous rectification non-iterative calculation method for an LLC resonant converter. Background Art

[0002] The LLC resonant converter has the characteristics of soft switching and low electromagnetic interference (EMI). When cascaded or connected in series with other topologies, it can achieve wide voltage gain and wide output range, and is widely used in the fields of rail transit, electric vehicles, and photovoltaic. In high-output power application scenarios, applying synchronous rectification technology to the LLC resonant converter can significantly improve its operating efficiency, reduce heat dissipation requirements, and increase power density.

[0003] Traditional synchronous rectification technologies can be divided into two categories: sensor-based and sensorless. Among them, sensor-based synchronous rectification requires an additional detection circuit, which increases the system volume, cannot be applied to multi-modal occasions, and is greatly affected by stray parameters in high-voltage situations; sensorless synchronous rectification does not require an additional sensor, calculates the corresponding synchronous rectification time according to the circuit model, and is less affected by stray parameters. Therefore, it is more suitable for high-voltage and high-power occasions.

[0004] Currently, LLC resonant converters are widely used in application scenarios such as electric vehicle charging and server power supplies. Synchronous rectification technology is particularly suitable for applications with a wide load range and frequent fluctuations. Whether it is in an electric vehicle charging pile or a server power supply, load changes are inevitable. When the load is heavy, synchronous rectification can significantly reduce switching losses and improve conversion efficiency; in the case of light loads, due to the low on-resistance of MOSFETs, synchronous rectification can continue to maintain low losses, thereby improving the overall performance of the system. Synchronous rectification can also effectively regulate load response, improve system stability and adaptability, and ensure that the converter can operate efficiently under various load conditions.

[0005] In traditional diode rectification, the conduction loss of the diode mainly comes from its forward voltage drop. The conduction loss of MOSFETs in synchronous rectification mainly depends on the internal resistance of the MOSFETs, and at this time, the conduction loss can be minimized, significantly improving the conversion efficiency. Traditional uncontrolled rectification also has a significant reverse recovery effect, which will generate a large current overshoot and spikes, bringing EMI problems at the same time, with low overall efficiency and a high area requirement for the radiator. It even interferes with the normal operation of the drive and the chip, reduces the stability of the converter, and causes equipment failure.

[0006] However, existing synchronous rectification technologies still have some drawbacks:

[0007] 1. Greatly affected by stray parameters

[0008] Patent CN202411120829.5 designed a synchronous rectification circuit and a high-frequency resonant converter. The body diode detection mechanism is applied in the circuit, and the on-off of the synchronous rectifier tube is realized through a pre-synchronization instruction. However, the circuit does not consider the influence of actual stray inductance on the turn-on and lag of the proposed synchronous rectification.

[0009] Based on the typical synchronous rectification voltage detection mechanism, Patent CN202411095116.8 proposed a synchronous rectification safety mechanism against misoperation. However, it is mainly integrated in the chip, with a low withstand voltage level and being greatly affected by the leakage inductance of the secondary side of the transformer, which limits its application scope.

[0010] 2. The implementation mechanism is too complex

[0011] Based on the typical synchronous rectification mechanism in the form of a comparator, Patent CN202410965809.1 realized the anti-mis-triggering mechanism of synchronous rectification by setting an inverter and a rectification signal processing unit. However, when it works, it requires a large number of logic devices, and also requires additional zero-crossing current comparison and tracking processes, and its implementation mechanism is too complex.

[0012] Based on the typical zero-crossing detection mechanism of the secondary side of the transformer, Patent CN202410911743.8 realized synchronous rectification by setting the first and second sampling circuits for voltage and current and a short-circuit protection sampling circuit. Its disadvantage is that it sets multiple groups of sampling circuits, and involves the design and manufacture of the transformer current transformer, which is relatively complex in physical implementation. Summary of the Invention

[0013] In order to solve the problems in the prior art, the present invention provides a synchronous rectification non-iterative calculation method for an LLC resonant converter, including the following steps:

[0014] Step 1, solve the corresponding modal boundary resistance: first judge the modal range in which the current load of the LLC resonant converter works at the corresponding switching frequency, and then solve the boundary resistance in this mode;

[0015] Step 2, write the corresponding state equation and boundary conditions: write the corresponding state equation according to the existing sub-operation modes, and write the corresponding boundary conditions for the existing voltage-current symmetry, energy conservation, and charge conservation;

[0016] Step 3, substitute and eliminate elements to solve: substitute and eliminate elements through the relationship between the gain M and the time t to obtain a new solution system of equations, so that it is converted into an equation with only the time t as the unknown, and then the numerical solution method can be used to complete the calculation of the synchronous rectification time t and the gain M;

[0017] Step 4, gain verification: Verify whether the gain is normal. If so, the verification passes, and the corresponding synchronous rectification time is output. If not, the verification fails, and return to Step 3, and repeat the elimination and solution process with another set of gain values. As a further improvement of the present invention, in Step 1, it includes:

[0018] Step S1: Divide the sub - operating modes of the LLC resonant converter into positive - clamped P, un - clamped O, and negative - clamped N according to the conduction state of the secondary rectification unit to obtain multiple operating states;

[0019] Step S2: Divide the operating states obtained in Step S1 into PN mode, PON mode, PO mode, and OPO mode according to the operating condition type, and select the optimal operating condition mode for synchronous rectification calculation. As a further improvement of the present invention, in Step S2, the synchronous rectification calculation method of the LLC resonant converter in the full - bridge variable - frequency mode gives priority to the PO mode. When the LLC resonant converter operates in the PO mode, two sub - modes can be obtained, and each mode is respectively:

[0020] Mode 1: [t0,t1];

[0021] At this time, the rectification unit of the LLC resonant converter is positively clamped, and the resonant inductor L r and the resonant capacitor C r undergo series resonance, and the exciting inductor L m is clamped to nV o , its current linearly increases, the resonant tank transfers energy to the secondary side, and the load current is maintained by the output capacitor C o and the resonant tank together;

[0022] Define the series - resonance angular velocity ω r as:

[0023]

[0024] According to the current operating mode, solving the current differential equation gives:

[0025]

[0026] Among them, V in represents the input power supply, t represents the time at t, i Lr (t) represents the current passing through the resonant inductor L r at time t, I Lr0 represents the initial value of the resonant - inductor current and the exciting - inductor current in Mode 1, V cr0 represents the initial value of the resonant - capacitor voltage, n represents the transformer turns ratio, V o represents the output voltage, i Lm (t) represents the current passing through the exciting inductor L mThe current, V Cr (t) represents the voltage across the capacitor C at time t r at both ends, and Z1 represents the characteristic impedance;

[0027] Mode 2: [t1, t2];

[0028] At this time, the resonant inductor L r , the exciting inductor L m and the resonant capacitor C r resonate together, the resonant tank stops transferring energy to the secondary side, the rectifying unit of the LLC resonant converter stops conducting, and the load current is all maintained by the output capacitor C o ;

[0029] Define the series-parallel resonant angular velocity ω m as:

[0030]

[0031] where k represents the ratio of the exciting inductor L m to the resonant inductor L r ;

[0032] According to the current operating mode, solving the current differential equation gives:

[0033]

[0034] where, I Lr1 represents the initial values of the resonant inductor current and the exciting inductor current in Mode 2, V cr1 represents the initial value of the resonant capacitor in Mode 2, and t1 represents the time t1

[0035] As a further improvement of the present invention, in the step 1, solve the variable boundary resistance R o , the P-mode time t, and the gain M, and according to the boundary conditions, apply the proposed method from the mode boundary, gain boundary, and current boundary to transform them into an equation containing only the single variable P-mode time t1

[0036] The beneficial effects of the present invention are: Compared with the prior art, the present invention has the following remarkable advantages: 1. The present invention links the resonant capacitor voltage with the output gain and output power, and while realizing the simple operation of the synchronous rectification conduction time, also obtains the gain at the corresponding frequency; 2. When calculating, it is not necessary to give the initial value limit conditions to realize the rapid calculation of all synchronous rectification times and gains, the calculation time is short, and it is convenient for automatic deployment and analysis; 3. Compared with the traditional time-domain synchronous rectification analysis method, the method of the present invention has a faster calculation speed, does not require iteration, is clear and simple, and is more suitable for practical engineering applications; 4. Compared with the traditional synchronous rectification analysis method, the method of the present invention is not affected by the input voltage Description of the Drawings

[0037] Figure 1 is a schematic diagram of the full - bridge LLC resonant converter topology of the present invention;

[0038] Figure 2 is a schematic diagram of Mode 1 of the present invention;

[0039] Figure 3 is a schematic diagram of Mode 2 of the present invention;

[0040] Figure 4 is a waveform diagram of the modal analysis of the present invention;

[0041] Figure 5 is a flow chart of the synchronous rectification non - iterative calculation method of the present invention;

[0042] Figure 6 is a calculation result diagram of an embodiment of the present invention;

[0043] Figure 7 is a diagram of the physical deployment structure mode of an embodiment of the present invention. Detailed Embodiment

[0044] In a synchronous rectification non - iterative calculation method of an LLC resonant converter disclosed by the present invention, the LLC resonant converter is a full - bridge LLC resonant converter, and the topological structure diagram is as shown in Figure 1 . In the full - bridge LLC resonant converter, it includes an inverter circuit, a resonant tank and a rectifier circuit. The inverter circuit is composed of switching tubes S1 - S4 and their anti - parallel diodes D1 - D4; the resonant tank is composed of a resonant capacitor C r , a resonant inductor L r and a transformer exciting inductor L m ; the rectifier circuit is composed of switching tubes S5 - S8 and their anti - parallel diodes D5 - D8; a resistive load or a battery load can be connected to the output side as required.

[0045] Due to the symmetry of the operating state of the LLC resonant converter, only the operating state of the LLC in the positive half - cycle can be analyzed, and the forward full - bridge variable - frequency mode of the LLC resonant converter is taken as an example.

[0046] During the positive - half - cycle operation, the sub - operating modes of the LLC resonant converter can be divided into three types according to the conduction state of the secondary rectification unit: P (positive clamping), O (unclamped), and N (negative clamping). Multiple operating states can be combined according to the operating conditions. Since the LLC resonant converter is often designed to operate in the under - resonant variable - frequency operating state to meet the needs of the load range and wide output gain. Therefore, it can be divided into PN, PON, PO, and OPO modes according to the type of operating conditions.

[0047] Among the above four modes, the switching tube of the rectification unit with N at the end cannot achieve ZCS turn-off and is more likely to lose the ZVS of the switching tube of the inverter unit. The OPO mode is a light-load mode with a long reactive circulating current time and low efficiency. Therefore, as a preference of the present invention, the synchronous rectification calculation method of the LLC resonant converter preferably considers the PO mode in the full-bridge variable-frequency mode. It should be noted that the calculation method is also applicable to other variable-frequency modes, as well as working modes such as reverse-clamped boost and full-bridge phase shift.

[0048] For the convenience of analysis and elaboration, the following variables are defined (the same hereinafter):

[0049] Resonant inductor current I Lrx , where x represents the x moment of t;

[0050] Resonant capacitor voltage V Crx , where x represents the x moment of t;

[0051] Magnetizing inductor current I Lmx , where x represents the x moment of t;

[0052] According to the above analysis of the LLC resonant converter, two sub-modes can be obtained when the LLC resonant converter operates in the PO mode. It should be noted that since the primary switching tube operates in the ZVS state, the influence of the stray mode generated by the junction capacitance of the primary switching tube can be ignored; while the rectification lag turn-on and early turn-off effects caused by the secondary switching tube and the stray capacitance of the transformer can be applied with a time constant for early switching. They are respectively:

[0053] Mode 1: [t0, t1];

[0054] As Figure 2 shown, Figure 2 is the circuit model of Mode 1. At this time, the rectification unit of the LLC resonant converter is forward clamped, and the resonant inductor L r and the resonant capacitor C r are in series resonance. The magnetizing inductor L m is clamped to nV o , and its current rises linearly. The resonant tank transfers energy to the secondary side, and the load current is maintained by the output capacitor C o and the resonant tank together.

[0055] Define the series resonance angular velocity ω r as:

[0056]

[0057] According to the current operating mode, solving the current differential equation gives:

[0058]

[0059] Among them, V in represents the input power supply, t represents the time at moment t, and i Lr (t) represents the current passing through the resonant inductor L r at moment t, and I Lr0 represents the initial value of the resonant inductor current and the exciting inductor current in mode 1, and V cr0 represents the initial value of the resonant capacitor voltage, n represents the transformer turns ratio, and V o represents the output voltage, and i Lm (t) represents the current passing through the exciting inductor L m at moment t, and V Cr (t) represents the voltage across the capacitor C r at both ends at moment t, and Z1 represents the characteristic impedance.

[0060] Mode 2: [t1, t2];

[0061] As Figure 3 shown, Figure 3 is the circuit model of mode 2. At this time, the resonant inductor L r , the exciting inductor L m and the resonant capacitor C r resonate together. The resonant tank is disengaged from the clamping working state and stops transferring energy to the secondary side. The rectifying unit of the LLC resonant converter stops conducting, and the load current is all maintained by the output capacitor C o .

[0062] Define the series-parallel resonant angular velocity ω m as:

[0063]

[0064] m where k represents the ratio of the exciting inductor L r to the resonant inductor L

[0065] According to the current operating mode, solving the current differential equation gives:

[0066]

[0067] Among them, I Lr1 represents the initial value of the resonant inductor current and the exciting inductor current in mode 2, and V cr1 represents the initial value of the resonant capacitor in mode 2, and t1 represents the time at moment t1.

[0068] To solve the above equations, additional auxiliary boundary conditions need to be introduced. The boundary conditions for solving the LLC resonant conversion synchronous rectification time and gain include gain boundary conditions, charge conservation boundary conditions and symmetry boundary conditions.

[0069] Applying the resonant capacitor voltage (gain) boundary condition to establish the relationship between gain and synchronous rectification time;

[0070] According to the relationship between gain and time, non-iterative processes such as elimination are completed.

[0071] Resonant capacitor voltage (gain) boundary conditions: In the full-bridge variable frequency mode, due to the resonant capacitor C r In half of the switching cycle, the input power supply V in In the energy exchange, the charge is equal to the charge obtained from the input power supply, then:

[0072] E in =V in Q=V in C r ΔU (5)

[0073] Where E in represents input energy, Q represents charging charge, and ⊿U represents the voltage difference of the resonant capacitor in the positive half cycle of the switching tube.

[0074] The output energy of the LLC resonant converter within half a switching cycle can be expressed as:

[0075]

[0076] Where T represents the switching period, R O Represents the output load resistance.

[0077] Ignoring the loss of the converter, we have:

[0078]

[0079] According to the above formula, the relationship between output power and resonant capacitor voltage is established. According to the symmetry relationship, the initial value of the resonant capacitor voltage can be obtained:

[0080]

[0081] Where V Cr2 Represents the capacitance C at time t2 r The voltage across the terminals;

[0082] Since the LLC resonant converter transfers power to the secondary side only in the P mode, the charge conservation formula can be obtained:

[0083]

[0084] According to the remaining symmetry boundary conditions:

[0085]

[0086] According to the above formula 9 and boundary conditions (formula 10), the computability is fully considered, and the detailed calculation method is as follows Figure 5 The detailed process is as follows:

[0087] Step 1, solve the corresponding modal boundary resistance:

[0088] Since the LLC resonant converter has multiple time domain modes under different loads and switching frequencies, before solving the problem, we should first determine whether the current load is operating within the corresponding mode range under the switching frequency. Taking the PO mode as an example, the calculation of its boundary resistance should be selected from the two adjacent modes of PON and OPO. The adjacent modes of the LLC resonant converter analyzed are PON and OPO. At this time, the boundary conditions of PON and PO are V Lm2 =-nV o , the boundary condition between OPO and PO is V Lm0 =nV o , the applicable range of the PO mode can be determined by solving the boundary resistance at the corresponding frequency. At this time, the boundary resistance R o , P modal time t, and gain M are converted into an equation containing only a single variable P modal time t1 by applying the proposed simplified analysis method from the modal boundary, gain boundary, and current boundary according to the above boundary conditions. The boundary conditions of PON and PO modes are determined by the input voltage V in After normalization, it can be expressed as:

[0089]

[0090] Among them, V Lm2 Represents the voltage across the inductor Lm at time t2;

[0091] The boundary resistance R can be obtained by combining the excitation inductance voltage boundary condition and the gain boundary condition. o :

[0092]

[0093] At this time, V Cr3 :

[0094]

[0095] V Cr3 Represents the capacitance C at time t3 r The voltage across the terminals;

[0096] By combining the exciting inductance current and the resonant inductance current in mode 1, we can obtain:

[0097]

[0098] By solving the equations formed by the resonant inductance currents in mode 1 and mode 2, the relationship between the gain M and the conduction time can be obtained, denoted as M(t1):

[0099]

[0100] where f r represents the switching frequency, and f s represents the resonant frequency.

[0101] By combining the resonant capacitor voltages in mode 1 and mode 2, substituting the obtained gain M(t1) for I Lr0 and substituting it into Equation 15, we can obtain:

[0102]

[0103] Using the matlab numerical tool to solve Equation 16, the corresponding time t1 can be obtained. Substituting it back into Equation 15, the boundary gain can be solved, and then the boundary resistance at each point can be obtained.

[0104] Similarly, for the boundary between OPO and PO, by using the condition V Lm0 = nV o and applying the above method, the boundary resistance at the corresponding frequency can be solved.

[0105] Step 2: Write the corresponding state equations and boundary conditions:

[0106] According to the existing sub-operation modes, write the corresponding state equations, and write the corresponding boundary conditions for the existing voltage-current symmetry, energy conservation, and charge conservation. For the convenience of analysis and processing, take the input voltage V in as the per-unit reference value 1, and the output voltage nV o is represented as the gain M. After per-unit conversion, the state equations of each sub-mode can be solved as follows:

[0107] Mode 1:

[0108]

[0109] Mode 2:

[0110]

[0111] Substitute and eliminate variables to solve:

[0112] Analyzing the written state equations and boundary condition groups, it is not difficult to find that the unknowns in the equations at this time are the duration t of the sub-mode P and the actual circuit gain M. By substituting and eliminating the variables through the relationship between the gain M and time t to obtain a new solution equation system, converting it into an equation with only time t as the unknown, the synchronous rectification time t and the gain M can be calculated using numerical solution methods. Usually, since the expression of the gain M is simple and related to power, the gain M is often selected as the elimination variable, and its substitution process is as follows:

[0113] Substitute the gain boundary into the resonant inductor current I Lrx In the equation system (Equations 14 - 18), solve for the relationship of M(t1). Then substitute M(t1) into the resonant capacitor V Crx In the equation system (Equations 17 - 18), the duration of Mode 1, that is, the synchronous rectification time, can be obtained by numerical tools.

[0114] Gain verification:

[0115] Since the order of the expression of the gain M is usually quadratic, corresponding to two values of the charging and discharging of the resonant capacitor voltage under the same voltage, there will be an extraneous root problem. The influence of the extraneous root is excluded by the gain verification set in the algorithm. If the verification fails, another set of gain values is used for calculation.

[0116] Applying the above method, in the case of the resonant inductor L r = 34 μH, the resonant capacitor C r = 120 nF, and the magnetizing inductor L m = 150 μH, the synchronous rectification calculation results are as Figure 6 shown.

[0117] For the under-resonant frequency conversion mode, a second-order surface fitting tool can be used to obtain the relationship between the synchronous rectification time, frequency, and load:

[0118]

[0119] where f represents the resonant frequency, t on represents the synchronous rectification time, and a xx are the coefficients of the fitting function.

[0120] According to the above synchronous rectification calculation model (Equation 19), it can be deployed into the LLC resonant converter. All required variables can be obtained from the closed-loop of the converter. And the corresponding control signals are given through the synchronous rectification wave generation module. It should be noted that its deployment structure diagram is as Figure 7 shown.

[0121] Based on the time-domain analysis method of the LLC resonant converter, the present invention considers the relationship between the output gain and the resonant capacitor voltage, and details the execution process of the non-iterative method. In the synchronous rectification calculation method of the LLC resonant converter, the present invention fully considers the problem of extraneous roots in the gain, simplifies the calculation complexity of synchronous rectification. Compared with the traditional synchronous rectification calculation method, the proposed method is simpler, does not depend on the initial value and the influence of working conditions, and can be extended and applied to various resonant converters.

[0122] The above content is a further detailed description of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is only limited to these descriptions. For those of ordinary skill in the technical field to which the present invention pertains, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, which should all be regarded as belonging to the protection scope of the present invention.

Claims

1. A synchronous rectification non-iterative calculation method for LLC resonant converters, characterized in that Including the following steps: Step 1, solve the corresponding modal boundary resistance: first, determine the modal range in which the LLC resonant converter operates at the current load under the corresponding switching frequency, and then solve the boundary resistance in this mode; Step 2, write the corresponding state equations and boundary conditions: write the corresponding state equations according to the existing sub - operating modes, and write the corresponding boundary conditions for the existing voltage - current symmetry, energy conservation, and charge conservation; Step 3, substitution and elimination for solution: obtain a new set of equations for solution through substitution and elimination using the relationship between the gain M and time t, so that it is converted into an equation with only time t as the unknown, and then the numerical solution method can be used to complete the calculation of the synchronous rectification time t and the gain M; Step 4, gain verification: verify whether the gain is normal. If so, the verification passes and the corresponding synchronous rectification time is output. If not, the verification fails, return to the above Step 3, and repeat the elimination and solution process using another set of gain values.

2. The synchronous rectification non-iterative calculation method of the LLC resonant converter according to claim 1, wherein In the above Step 1, it includes: Step S1: Divide the sub - operating modes of the LLC resonant converter into positive clamping P, non - clamping O, and negative clamping N according to the conduction state of the secondary rectification unit to obtain various operating states; Step S2: Divide the operating states obtained in Step S1 into PN mode, PON mode, PO mode, and OPO mode according to the operating condition types, and select the optimal operating condition mode for the calculation of synchronous rectification.

3. The LLC resonant converter synchronous rectification non-iterative calculation method according to claim 2, characterized in that, In the above Step S2, for the synchronous rectification calculation method of the LLC resonant converter in the full - bridge variable - frequency mode, the PO mode is given priority. When the LLC resonant converter operates in the PO mode, two sub - modes can be obtained, and each mode is respectively: Mode 1: [t0, t1]; At this time, the rectifier unit of the LLC resonant converter is forward clamped, and the resonant inductor L r resonates in series with the resonant capacitor C r , the exciting inductor L m is clamped to nV o , its current rises linearly, the resonant tank transfers energy to the secondary side, and the load current is maintained by the output capacitor C o and the resonant tank together; Define the series resonance angular velocity ω r as follows: According to the current operating mode, solving the current differential equation gives: Among them, V in represents the input power supply, t represents the moment of t, and i Lr (t) represents the current passing through the resonant inductor L r at the moment of t, I Lr0 represents the initial value of the resonant inductor current and the exciting inductor current in mode 1, V cr0 represents the initial value of the resonant capacitor voltage, n represents the transformer turns ratio, V o represents the output voltage, i Lm (t) represents the current passing through the exciting inductor L m at the moment of t, V Cr (t) represents the voltage across the capacitor C r at both ends at the moment of t, and Z1 represents the characteristic impedance; Mode 2: [t1, t2]; At this time, the resonant inductor L r , the exciting inductor L m and the resonant capacitor C r resonate together, the resonant tank stops transferring energy to the secondary side, the rectifying unit of the LLC resonant converter stops conducting, and the load current is all maintained by the output capacitor C o ; Define the series-parallel resonance angular velocity ω m as follows: where k represents the ratio of the exciting inductance L m to the resonant inductance L r ; According to the current operating mode, solving the current differential equation gives: where I Lr1 represents the initial value of the resonant inductor current and the exciting inductor current in Mode 2, and V cr1 represents the initial value of the resonant capacitor in Mode 2, and t1 represents the moment of t1.

4. The LLC resonant converter synchronous rectification non-iterative calculation method according to claim 3, characterized in that In the step 1, solve the variable boundary resistance R o , P-mode time t, and gain M, and according to the boundary conditions, transform them into an equation containing only a single variable P-mode time t1 by applying the proposed method from the modal boundary, gain boundary, and current boundary.

5. The LLC resonant converter synchronous rectification non-iterative calculation method according to claim 4, wherein In the step 1, the boundary conditions of the PON and PO modes can be expressed after normalization with the input voltage V in as follows: Among them, V Lm2 represents the voltage across the inductor Lm at time t2; The boundary resistance R can be obtained by combining the excitation inductance voltage boundary condition and the gain boundary condition. o : At this time, there is V Cr3 : V Cr3 represents the voltage across the capacitor C r at time t3; Combining the exciting inductance current and the resonant inductance current in Mode 1 gives: Combining the equations formed by the resonant inductance currents in Mode 1 and Mode 2 can obtain the relationship between the gain M and the conduction time, denoted as M(t1): Among them, f r represents the switching frequency, and f s represents the resonance frequency; Combine the resonant capacitor voltages in mode 1 and mode 2 and replace I with the resulting gain M(t1). Lr0 Substituting it into formula 15, we get: Using the matlab numerical tool to solve Formula 16, the corresponding time t1 can be obtained, and substituting it back into Formula 15, the boundary gain can be solved, and then the boundary resistance at each point can be obtained; The boundary condition between the PON and PO modes is V Lm2 = -nV o The boundary condition between the OPO and PO modes is V Lm0 = nV o .

6. The LLC resonant converter synchronous rectification non-iterative calculation method according to claim 1, characterized in that In step 2, for the convenience of analysis and processing, the input voltage V in is taken as the per-unit reference value 1, and the output voltage nV o is represented as the gain M. After per-unit processing, the state equations of each sub-mode can be solved as follows: Mode 1: Mode 2:

7. The LLC resonant converter synchronous rectification non-iterative calculation method according to claim 5, wherein In the above substitution and elimination for solution step, since the expression of the gain M is simple and related to power, the gain M is selected as the elimination quantity, and substitution and elimination are performed through the relationship between the gain M and time t to obtain a new set of equations for solution. The substitution process is as follows: Bring the gain boundary into the resonant inductor current I Lrx into the equations, solve to obtain the relationship of M(t1), and then substitute M(t1) into the resonant capacitor V Crx into the equations, and the duration of mode 1, i.e., the synchronous rectification time, can be obtained by solving with numerical tools.

8. The synchronous rectification non-iterative calculation method of the LLC resonant converter according to claim 1, characterized in that In the above Step 4, it is judged whether the verification is normal by verifying whether the gain is less than 1. If the verified gain is less than 1, the verification passes; otherwise, the verification fails.

9. The LLC resonant converter synchronous rectification non-iterative calculation method according to claim 1, wherein This non - iterative calculation method for synchronous rectification of the LLC resonant converter further includes: For the under - resonant variable - frequency mode, a second - order surface fitting tool can be used to obtain the relationship between the synchronous rectification time, frequency, and load: Among them, f represents the resonant frequency, and t on represents the synchronous rectification time, and a xx is the coefficient of each term of the fitting function.

10. The LLC resonant converter synchronous rectification non-iterative calculation method according to claim 1, characterized in that, The LLC resonant converter is a full-bridge LLC resonant converter, and the full-bridge LLC resonant converter includes an inverter circuit, a resonant tank and a rectifier circuit. The inverter circuit is composed of switching tubes S1 to S4 and their anti-parallel diodes D1 to D4. The resonant tank is composed of a resonant capacitor C r , a resonant inductor L r and a transformer exciting inductor L m . The rectifier circuit is composed of switching tubes S5 to S8 and their anti-parallel diodes D5 to D8. A resistive load or a battery load is connected on the output side as required.

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