LLC and transformer parameter design method and system based on sine fundamental wave analysis

Abstract

The invention relates to an LLC and transformer parameter design method based on sine fundamental wave analysis, and the method comprises the steps: enabling a primary side of a transformer to be equivalent to a sine current source and a square wave voltage, enabling the sine current source and the square wave voltage to jointly serve as input signals of a full-bridge rectification circuit, obtaining a voltage difference between two rectification half-bridge midpoints, and calculating equivalent output impedance with a secondary side of the transformer as a reference; the equivalent output impedance with the secondary side as the reference is converted to the primary side of the transformer, and the equivalent load impedance of the primary side is obtained; calculating the voltage input of the primary half-bridge to the resonant cavity based on the equivalent load impedance of the primary side, solving a fundamental wave signal through Fourier series decomposition, and establishing an LLC equivalent circuit; calculating the resonant cavity gain of the LLC equivalent circuit, and designing an LLC converter based on the resonant cavity gain; and designing the E-type ferrite core transformer based on the LLC converter. On the basis of ensuring high efficiency and stability of the system, the design complexity can be remarkably reduced, and the design accuracy and adaptability are improved.

Description

Technical Field

[0001] This invention relates to the field of transformer technology, and in particular to a method and system for designing LLC and transformer parameters based on sinusoidal fundamental wave analysis. Background Technology

[0002] The LLC resonant converter is a widely used converter structure in high-efficiency, high-power-density power supply designs. Its main advantages lie in its low switching losses, good current and voltage waveform control, and high-efficiency power conversion capability, making it particularly suitable for medium-to-high power applications such as server power supplies, automotive power supplies, and new energy fields. The LLC resonant converter utilizes the resonant characteristics of the resonant cavity to achieve efficient power conversion and controls the operating state of the switching transistors by adjusting the frequency, thereby achieving stable output voltage and current.

[0003] In the design of LLC resonant converters, the most complex part is often the analysis and optimization of the resonant circuit. The resonant cavity of an LLC resonant converter typically consists of two parts: a resonant inductor (usually the main inductor) and a resonant capacitor. Due to its structural complexity and high-frequency switching characteristics, the design of an LLC converter requires in-depth analysis of the resonant cavity's response under different operating conditions.

[0004] While traditional design methods have addressed many issues in LLC converter design to some extent, several shortcomings remain. First, traditional methods often rely heavily on experimental data and simulation tools, leading to long design cycles and difficulty in adapting to rapidly changing market demands. Second, existing analysis methods often fail to provide sufficiently accurate predictions when dealing with high-order harmonics and load variations, resulting in significant discrepancies between design results and actual operation. Finally, existing design methods lack systematic and comprehensive guidance for optimizing transformer parameters and component selection.

[0005] Chinese patent application publication number CN111525807A discloses a high-order LCLCL DC-DC converter and its parameter design method based on harmonic optimization. By introducing a third harmonic optimization circuit into an LLC resonant converter, a high-order LCLCL DC-DC converter is designed, solving the problems of limited frequency modulation range, large secondary current, and lack of protection, achieving high efficiency and excellent soft-start and overcurrent protection. However, it suffers from limited prediction accuracy when dealing with high-order harmonics and load variations. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the existing technology by providing a method and system for designing LLC and transformer parameters based on sinusoidal fundamental wave analysis, so as to solve or partially solve the problem that the existing analysis and design methods have limited prediction accuracy when dealing with high-order harmonics and load changes, which may lead to a large difference between the design results and the actual operation.

[0007] The objective of this invention can be achieved through the following technical solutions: One aspect of the present invention provides a method for designing LLC and transformer parameters based on sinusoidal fundamental wave analysis, comprising the following steps: The primary side of the transformer is equivalent to a sinusoidal current source and a square wave voltage, which are used together as the input signal of the full-bridge rectifier circuit to obtain the voltage difference between the midpoints of the two rectifier half-bridges. The equivalent output impedance with the secondary side of the transformer as a reference is then calculated. The equivalent output impedance with reference to the secondary side is applied to the primary side of the transformer to obtain the equivalent load impedance of the primary side. The voltage input of the primary half-bridge to the resonant cavity is calculated based on the equivalent load impedance of the primary side. The fundamental signal is solved by Fourier series decomposition, and the LLC equivalent circuit is established. Calculate the resonant cavity gain of the LLC equivalent circuit, and design an LLC converter based on the resonant cavity gain; Design an E-type ferrite core transformer based on an LLC converter.

[0008] As a preferred technical solution, the equivalent output impedance with reference to the secondary side of the transformer is calculated using the following formula: in, The equivalent output impedance is referenced to the secondary side of the transformer. The voltage difference between the midpoints of the two rectifier half-bridges. For secondary side input current, , These are the output current and output voltage, respectively. For output load.

[0009] As a preferred technical solution, the equivalent load impedance of the primary side is calculated using the following formula: in, This is the equivalent load impedance of the primary side. Turns ratio, , These are the number of turns on the primary side and the number of turns on the secondary side of the transformer, respectively. For output load.

[0010] As a preferred technical solution, the resonant cavity gain is calculated using the following formula: in, The resonant cavity gain of the LLC equivalent circuit is given. , For switching frequency, This is the equivalent load impedance of the primary side. It is a resonant capacitor. For magnetizing inductance, It is the primary inductor. It is a resonant inductor. Turns ratio, This is a secondary side leakage sensation.

[0011] As a preferred technical solution, the LLC converter design based on resonant cavity gain includes the following steps: Based on the resonant cavity gain, and taking into account the selection of inductors, the design of magnetic components, the adjustment of switching frequency, and the changes in load conditions, the LLC resonant converter is designed.

[0012] As a preferred technical solution, the design of the E-type ferrite core transformer includes the selection of E-type ferrite core, calculation of design parameters, thermal management of LLC converter transformer, core saturation / efficiency, electromagnetic interference resistance and air gap design.

[0013] As a preferred technical solution, the selection of the ferrite core includes the selection of core material, core size and core shape; the calculation of design parameters includes operating frequency, magnetic flux density, number of winding turns, core power carrying capacity, wire diameter, number of turns, winding type and winding distribution; the thermal management of the LLC converter transformer includes heat dissipation design and temperature rise control; and the electromagnetic interference immunity includes shielding / grounding and filtering.

[0014] As a preferred technical solution, the design of the air gap takes into account the core size, the shape of the air gap, the location of the air gap, and the size of the air gap.

[0015] As a preferred technical solution, the size of the air gap is calculated using the following formula: in, For air gap size, It is the number of turns in the winding. It is the magnetic reluctance of the magnetic core. It is the magnetic reluctance of the air gap.

[0016] Another aspect of the present invention provides an LLC and transformer parameter design system based on sinusoidal fundamental wave analysis, for implementing the aforementioned LLC and transformer parameter design method, the system comprising: The secondary-side equivalent output impedance calculation module is used to convert the primary side of the transformer into a sinusoidal current source and a square wave voltage, which together serve as the input signal of the full-bridge rectifier circuit. This allows for the calculation of the voltage difference between the midpoints of the two rectifier half-bridges and the equivalent output impedance with the secondary side of the transformer as a reference. The primary-side equivalent load impedance calculation module is used to convert the equivalent output impedance with the secondary side as a reference to the primary side of the transformer to obtain the equivalent load impedance of the primary side. The LLC equivalent circuit construction module is used to calculate the voltage input of the primary half-bridge to the resonant cavity based on the equivalent load impedance of the primary side, solve the fundamental signal through Fourier series decomposition, and establish the LLC equivalent circuit. The LLC converter design module is used to calculate the resonant cavity gain of the LLC equivalent circuit and design the LLC converter based on the resonant cavity gain. The transformer design module is used to design E-type ferrite core transformers based on LLC converters.

[0017] Compared with the prior art, the present invention has at least the following beneficial effects: High accuracy and adaptability of the design: This invention decomposes the spectrum of the square wave signal input to the resonant cavity of the LLC resonant converter into harmonics of various orders, focusing on the fundamental component. Using this as the design basis, it can effectively reduce the influence of higher-order harmonics, improve the accuracy of the design and the efficiency of the system, and at the same time provide a simplified and accurate design approach for the selection of LLC converter parameters. Attached Figure Description

[0018] Figure 1 This is a flowchart of the LLC and transformer parameter design method based on sinusoidal fundamental wave analysis in the embodiment. Figure 2 This is a schematic diagram of the half-bridge LLC resonant converter structure in the embodiment; Figure 3 This is a schematic diagram of the equivalent circuit model of the transformer secondary rectifier side circuit in the embodiment; Figure 4 This is a schematic diagram of the equivalent circuit model of the LLC resonant converter resonant cavity in the embodiment; Figure 5 This is a schematic diagram illustrating the transformation of the LLC resonant converter from an actual model to an ideal model in the embodiment; Figure 6 This is a schematic diagram of the relationship between frequency and gain at different Q values ​​in the embodiment; Figure 7This is a schematic diagram showing the relationship between peak gain and Q at different k values ​​in the embodiment; Figure 8 This is a schematic diagram of the LLC resonant converter with PFC in the embodiment. Figure 9 This is a schematic diagram showing the relationship between circuit gain and frequency under different load conditions in the embodiment; Figure 10 This is a schematic diagram of the LLC and transformer parameter design system based on sinusoidal fundamental wave analysis in the embodiment. Detailed Implementation

[0019] 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, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0020] Example 1 To address the problems of the aforementioned existing technologies, this embodiment provides a method for designing LLC and transformer parameters based on sinusoidal fundamental wave analysis. The aim is to simplify the system analysis process by approximating the square wave signal input to the resonant cavity as its fundamental wave. Specifically, this embodiment performs Fourier series decomposition on the square wave input voltage to the resonant cavity at the center points of the upper and lower switching transistors, and approximates it using a sinusoidal fundamental wave. Simultaneously, it establishes the relationship between the load impedance and the output equivalent resistance seen from the secondary transformer, and then applies this relationship to the primary side of the transformer for simplified circuit analysis. This yields the parameter relationships of the circuit components, which are then combined with different core materials for transformer parameter design.

[0021] See Figure 1 The method includes the following steps: Step S1, Equivalent output impedance calculation: The primary side of the transformer is equivalent to a sinusoidal current source and a square wave voltage, which are used together as the input signal of the full-bridge rectifier circuit to obtain the voltage difference between the midpoints of the two rectifier half-bridges. The equivalent output impedance is calculated with the secondary side of the transformer as a reference.

[0022] See Figure 3 This is an equivalent circuit model of the transformer secondary rectifier side circuit, considering the rectifier circuit on the transformer secondary side, as well as the output filter capacitor and load. The secondary rectifier circuit acts as an impedance transformer in the system, distinguishing the equivalent load resistance from the actual load resistance, since their values ​​are not the same. In this case, the primary circuit can be considered as being powered by a sinusoidal current source. and a square wave voltage These two components together serve as the input signal for the full-bridge rectifier circuit. This equivalent substitution simplifies the analysis process and provides a clearer understanding for system design.

[0023] Since the forward voltage drop of the diodes on the output secondary side is negligible, there is essentially no energy loss on the secondary side except for the load; that is, most of the output energy is transferred to the load. The output current and voltage are... The output on the secondary side of the transformer, which is also the input of the full-bridge rectifier, is a very close sinusoidal signal source, denoted as a current source. The voltage difference between the midpoints of the two rectifier half-bridges is The amplitude is the output voltage. The alternating square wave. From the above analysis, the output current can be derived. Input current to the secondary side The rectified DC component (average current): Let the amplitude of the sinusoidal current input to the secondary side be... ,remember The current period is The current after full-bridge rectification is . The average value is denoted as . Therefore, we can conclude that: ,and then From the circuit structure, we can conclude that: The voltage at the midpoint of the diodes on both sides of the rectifier bridge can be seen, that is... It is a square wave, and its frequency is the same as the frequency of the input current source on the secondary side. same.

[0024] Using the Fourier series formula: get Fundamental wave: This allows us to obtain the equivalent output impedance as seen from the secondary side of the transformer: Step S2, the equivalent output impedance is referred to the primary side to establish the equivalent circuit of the primary transformer: the equivalent output impedance with the secondary side as a reference is referred to the primary side of the transformer to obtain the equivalent load impedance of the primary side.

[0025] Let the number of turns on the primary side of the transformer be... The number of turns on the secondary side is The turns ratio is The equivalent output resistance of the secondary side. Equivalent to the primary side. From the turns ratio, the equivalent load impedance of the transformer primary is: Since a transformer is not an ideal transformer, there will always be leakage inductance on both the primary and secondary sides. Let the leakage inductance on the primary side be denoted as . Secondary side leakage is Similarly, using the turns ratio of the primary side to the secondary side... The relationship will leak the secondary side. Equivalent to the original edge.

[0026] Step S3: Perform Fourier series decomposition on the voltage input of the primary half-bridge to the resonant cavity to solve for the fundamental signal and establish the complete equivalent circuit of LLC: calculate the voltage input of the primary half-bridge to the resonant cavity based on the equivalent load impedance of the primary side, solve for the fundamental signal through Fourier series decomposition, and establish the equivalent circuit of LLC.

[0027] See Figure 2 This is a schematic diagram of the structure of a half-bridge LLC resonant converter. The LLC resonant converter is divided into three parts: a square wave generator, a photocell network, and a rectifier network.

[0028] The basis for using the fundamental wave analysis method is because... or The resulting resonant network can filter out high-order harmonic currents. Therefore, even if the voltage input to the resonant network is a square wave, only the fundamental component of the current can actually pass through the network. The filtering effect of the resonant network can be described by the classical fundamental approximation principle, which assumes that only the fundamental component of the input square wave voltage actually contributes to the power transfer to the output. This simplified method allows for the efficient calculation of the resonator's voltage gain, thus enabling reasonable prediction and optimization of the resonant network's performance.

[0029] For the control switch, let the upper transistor be Q1, the lower transistor be Q2, and the midpoint of the half-bridge be point d. Since the switching transistors conduct alternately, the voltage at point d is an AC square wave. Because the resonant network has good frequency selectivity, higher harmonics will basically not enter the resonant cavity. We can approximate the decomposition by performing Fourier series decomposition to obtain the fundamental frequency of the input voltage to the resonant cavity, denoted as: Based on the above solutions, to facilitate analysis, a complete LLC equivalent circuit can be constructed as follows: Figure 4 As shown. Using the equivalent load impedance, the AC equivalent circuit is obtained. and These represent the driving voltages respectively. and reflected voltage The fundamental frequency. See also Figure 5 This is a schematic diagram illustrating the transformation from an actual model to an ideal model of an LLC resonant converter.

[0030] Step S4: Calculate the resonant cavity gain of the LLC equivalent circuit and give the relationship between the various circuit parameters: Calculate the resonant cavity gain of the LLC equivalent circuit and design the LLC converter based on the resonant cavity gain.

[0031] The equivalent circuit and parameters obtained in step S3 can be used to calculate the gain of the AC equivalent circuit of the LLC resonant converter, that is, the gain M from the input of the resonant cavity to the output of the primary side of the transformer.

[0032] The gain is then obtained from the voltage distribution relationship. The input voltage of the resonant cavity is the sinusoidal fundamental component at point d. Due to the resonant capacitor Leakage and excitation inductor Distribute the allocation. The voltage obtained is then subjected to a second voltage divider. The leakage inductance of the secondary side is equivalent to that of the primary side. Equivalent resistance of resonant cavity output Perform voltage division. The voltage on the resonant cavity is the output voltage of the resonant cavity.

[0033] The plus sign indicates that the components are connected in series, but does not represent the actual calculation.

[0034] Substitute the impedance of each component, and assume the switching frequency is... , The gain obtained is: in: Let the leakage inductance of the primary side be approximately equal to the leakage inductance of the secondary side converted to the leakage inductance of the primary side, that is: The LLC circuit has two resonant frequencies, each determined by different inductor and capacitor components. The first resonant frequency is determined by the resonant inductor. and resonant capacitor The second resonant frequency is determined by the primary-side inductance. and resonant capacitor The decision is made. In actual transformers, it is usually determined by measurements on the primary side. and The values ​​are determined by measuring the inductance on the primary side when the secondary coil is open-circuited and short-circuited, respectively.

[0035] In LLC circuits, when the operating frequency reaches the resonant frequency... At this frequency, the circuit exhibits a unique characteristic: regardless of changes in load conditions, the circuit gain remains constant. This is because at the resonant frequency, the interaction between the inductor and capacitor reaches equilibrium, and the system impedance is highly dependent on frequency changes, thus making the gain insensitive to load variations.

[0036] This characteristic enables LLC circuits to achieve relatively stable output performance in many applications, especially in converter designs in the field of power electronics, particularly under conditions of large load fluctuations. Due to the gain stability near the resonant frequency, LLC circuits can maintain stable power output while achieving high efficiency and low noise, greatly improving the reliability and performance of the power supply system.

[0037] Calculate the converter gain at the resonant frequency: Under conditions The previously calculated gain formula becomes: Setting parameters: At the resonant frequency: The gain formula is transformed again: When the switching frequency is close to the resonant frequency At this time, the LLC resonant converter exhibits a very unique and important characteristic: its gain is almost independent of load changes. This characteristic is a significant advantage of the LLC resonant converter compared to other types of converters, especially in the face of load fluctuations, where it can maintain a relatively stable operating state. This stability makes the LLC converter very attractive in a variety of applications, especially in situations with large load variations, such as power transmission, solar inverters, and LED drivers, where it can provide efficient and stable output.

[0038] To fully utilize this advantage, it is generally recommended to set the operating frequency of the LLC converter close to its resonant frequency. Within a certain range. This helps reduce switching frequency fluctuations under low load conditions, thereby maintaining the stability and efficiency of the converter. In this operating state, the LLC converter can adapt to load changes within a certain range, maintaining relatively consistent gain characteristics regardless of whether the load increases or decreases.

[0039] The gain characteristics of an LLC circuit will change to some extent with changes in load. In particular, when the system's quality factor Q decreases (i.e., the load decreases), the system's peak gain frequency will shift towards the frequency... The system will shift, and the peak gain will increase. This is because under lower load conditions, the impedance characteristics of the resonant circuit change, making the system more sensitive to frequency response, which manifests as an increase in gain.

[0040] Conversely, as the system load increases and the quality factor Q improves, the frequency of the peak gain will gradually shift towards the resonant frequency. Furthermore, the peak gain decreases accordingly. This is because under high load, the system's impedance characteristics tend to be more stable, leading to a decrease in frequency response sensitivity and consequently, a drop in gain. Therefore, when designing LLC converters, the full-load condition is usually considered the worst-case scenario, as the circuit performance is most stable under full load.

[0041] In addition, the design of magnetic components, especially the magnetizing inductor, is also an important factor in determining peak gain. and leakage The ratio between them, which is commonly referred to as value. The magnitude of this value directly affects the gain characteristics of the LLC converter. Reducing... Alternatively, reducing the Q value can increase the peak gain, because this means the magnetizing inductance... The current will be relatively small, resulting in a more efficient path for current to flow in the circuit. However, this approach also has side effects, primarily leading to an increase in circulating current. Increased circulating current can not only increase conduction losses but also introduce electromagnetic interference (EMI) problems. See also Figure 6 This is a schematic diagram showing the relationship between frequency and gain at different Q values.

[0042] Therefore, when designing LLC resonant converters, a reasonable balance must be found between increasing the gain range and balancing conduction losses and system efficiency. To optimize converter performance, designers need to comprehensively consider the selection of inductors, the design of magnetic components, the adjustment of switching frequency, and variations in load conditions to ensure that the converter can operate efficiently and stably under different operating conditions, while minimizing potential losses and adverse effects. This trade-off design process is one of the key aspects of LLC converter design, determining its final performance.

[0043] In summary, the design of LLC converters requires not only precise setting of the resonant frequency but also careful attention to the synergistic effects of factors such as the quality factor Q, magnetic component parameters, and gain adjustment. Only through reasonable design and optimization can the stability and efficiency of LLC converters be fully realized under different load conditions.

[0044] Step S5, design the transformer by combining the corresponding magnetic core material: design an E-type ferrite core transformer based on LLC converter.

[0045] Designing an E-type ferrite core transformer for an LLC resonant converter is a complex engineering task involving electromagnetics, materials science, and power electronics. LLC resonant converters are commonly used in high-efficiency DC-DC converters, especially in high-power, high-frequency applications such as server power supplies, LED drivers, and electric vehicle charging. During the design process, the selection of ferrite core materials, core geometry, winding method, and magnetic flux density all have a significant impact on the converter's efficiency, size, and cost.

[0046] 1. Selection of E-type ferrite core E-type magnetic cores are a common type of magnetic core used in high-frequency converters due to their excellent flux distribution and moderate cost. When designing a transformer, it is necessary to select a suitable magnetic core, mainly considering the following aspects: 1) Core Material: Ferrite materials typically have low losses and are suitable for high-frequency applications. Depending on the operating frequency range of the resonant converter, an appropriate material (e.g., Mn-Zn or Ni-Zn ferrite) can be selected to ensure low iron losses.

[0047] 2) Core Size: The core size should be selected based on the required power and operating frequency. The volume of the core determines its magnetic flux capacity; a core that is too small will lead to saturation, while a core that is too large will affect the system's size and cost.

[0048] 3) Core Shape: E-type ferrite cores have a better flux path design, effectively reducing flux leakage. E-type cores have low DC impedance and can adapt to high-frequency, high-current operating environments.

[0049] 2. Design parameters and calculations Operating frequency: LLC resonant converters typically operate between tens of kHz and hundreds of kHz. For high-frequency operation, the permeability and loss of the ferrite material must meet the requirements for high-frequency operation.

[0050] magnetic flux density The saturation flux density of the magnetic core must be high enough to prevent saturation at high currents. The flux density can be determined by calculating the transformer's operating conditions (e.g., input voltage, output voltage, power requirements, core size).

[0051] formula: in: It is the input voltage. It is the switching frequency. It refers to the number of turns in the winding. It is the cross-sectional area of ​​the magnetic core.

[0052] Number of turns (N): The number of turns can be calculated using the following formula based on the required turns ratio: in, For output voltage, Let be the cross-sectional area of ​​the magnetic core. Let be the cross-sectional area of ​​the conductor.

[0053] Power carrying capacity of magnetic core: The selection of magnetic core is based on the required power. Generally, the saturation power of ferrite magnetic core is proportional to the core volume, frequency, and saturation flux density.

[0054] Wire gauge and number of turns: Select an appropriate wire gauge to ensure that the current density of the winding is not too high, thus avoiding overheating. A common current density is 2A / mm². 2 If the wire diameter is too large, it increases the volume; if it is too small, it increases the loss.

[0055] Winding type: In high-frequency converters, segmented or distributed windings are often used to reduce leakage inductance and flux loss. The winding structure should be as compact as possible to improve the utilization rate of the magnetic core.

[0056] Winding distribution: For high-frequency transformers, structures such as symmetrical windings and cross windings can be used to reduce leakage inductance and improve efficiency.

[0057] 3. Thermal Management of LLC Converter Transformers Because heat is generated by the losses in the ferrite core and the resistance of the windings, effective thermal management strategies are required. Common methods include: 1) Heat dissipation design: The heat dissipation design of the transformer casing and surrounding area should be able to effectively dissipate heat to avoid overheating and performance degradation.

[0058] 2) Temperature rise control: The design must ensure that the temperature rise of the transformer is within an acceptable range, usually around 90°C.

[0059] 4. Saturation and efficiency of magnetic core In LLC converters, preventing the magnetic core from entering saturation is crucial. When saturated, the magnetic flux in the core no longer increases with increasing current, leading to a sharp drop in transformer efficiency. Therefore, a suitable magnetic core should be selected during the design phase to ensure that it does not enter the saturation region under maximum load.

[0060] 5. EMI (Electromagnetic Interference) Due to the high-frequency switching operation of LLC converters, strong EMI may be generated. The following should be considered during design: Shielding and grounding: Transformers should be shielded as much as possible to avoid interference caused by leaked magnetic fields.

[0061] Filtering: Appropriate filtering networks can be designed at the input and output terminals to reduce high-frequency noise.

[0062] 6. Air gap size design In designing the E-type ferrite core transformer for LLC resonant converters, the air gap design is a crucial step. The introduction of the air gap significantly impacts the transformer's performance, efficiency, and operational stability, especially in high-frequency, high-power power conversion systems. The air gap affects not only the magnetic flux density distribution but also the transformer's magnetic saturation characteristics, hysteresis losses, and leakage inductance. Therefore, a well-designed air gap is one of the keys to ensuring the efficient and stable operation of the LLC converter.

[0063] (1) Function of the air gap In transformer design, the main function of the air gap is: 1) Limiting magnetic flux density: The presence of an air gap effectively prevents the magnetic core from entering a saturation state under high current. Magnetic cores without an air gap are prone to magnetic flux saturation under high current, causing the core to be unable to continue transmitting more energy, thus affecting the transformer's operating efficiency and output stability.

[0064] 2) Controlling the inductance value: The introduction of an air gap can adjust the transformer's inductive reactance, thereby optimizing the transformer's inductance characteristics in the LLC resonant circuit. For LLC resonant converters, adjusting the inductance value is an important means to achieve resonance and stable output.

[0065] 3) Improve the linear range of the operating point: By designing the air gap, the nonlinear characteristics of the magnetic core can be controlled, enabling the transformer to maintain good operating efficiency under a wider range of input voltage and load conditions.

[0066] (2) Design considerations for air gaps When designing the air gap, several factors need to be considered, including the core size, the shape of the air gap, the location of the air gap, and the size of the air gap. Each factor will affect the magnetic properties of the transformer, so precise design is essential.

[0067] 1) Size of the air gap The size of the air gap directly affects the permeability and saturation characteristics of the magnetic core. A larger air gap reduces the permeability of the core, thereby reducing the magnetic flux density and increasing the inductance of the transformer. For LLC resonant converters, an appropriate air gap size helps to adjust the resonant frequency and improve efficiency. An excessively large air gap may lead to an excessively large inductance, affecting the circuit's response speed; while an excessively small air gap may not be able to effectively limit magnetic flux saturation, leading to transformer saturation and reduced efficiency.

[0068] The size of the air gap can be estimated using the following formula: in: It's the inductance value. It is the number of turns in the winding. It is the magnetic reluctance of the magnetic core. It is the magnetic reluctance of the air gap.

[0069] The inductance value can be adjusted by changing the magnetic resistance of the air gap, thereby achieving the design requirements.

[0070] 2) Location of the air gap The location of the air gap is also very important. Generally speaking, the air gap should be placed in the center of the magnetic core, or in the region where the magnetic flux distribution is most uniform. This ensures that the air gap's influence on the magnetic field is minimized, while avoiding energy loss caused by non-uniform magnetic flux. For E-type magnetic cores, the air gap is usually designed at the junction of the two arms or at the center of the core.

[0071] 3) Shape of the air gap The shape of the air gap also affects the transformer's performance. Typically, the air gap is either straight or annular. Straight air gaps are simpler to design, but may lead to uneven magnetic field distribution, affecting the core's performance; while annular air gaps, due to their more uniform air gap distribution, can better disperse the magnetic field, reducing hysteresis losses and eddy current losses.

[0072] 4) Relationship between air gap size and core material The permeability of ferrite materials gradually decreases at high frequencies, making the air gap even more crucial in high-frequency applications. The appropriate air gap size must be selected based on the material's magnetic properties during the design process. For example, ferrite materials with lower permeability typically require larger air gaps, while materials with higher permeability can use smaller air gaps.

[0073] (3) Calculation of air gap The size of the air gap is generally determined through trial and error and optimization. It can be calculated using the principle of magnetic flux balance based on the operating point of the magnetic core. The air gap design must ensure that, under maximum load, the magnetic flux density of the core does not exceed the material's saturation flux density, thus avoiding saturation.

[0074] (4) Challenges of air gap design Designing air gaps requires balancing multiple factors; here are some common challenges: 1) Uneven magnetic flux distribution: The design of the air gap may lead to an uneven distribution of the magnetic field around the air gap, resulting in magnetic loss. To reduce this problem, the magnetic field distribution can be made more uniform by optimizing the position and shape of the air gap.

[0075] 2) Excessive air gap: If the air gap is designed to be too large, it may lead to an excessively high inductance value, which in turn affects the efficiency of the converter. An excessively large air gap will also increase leakage inductance, causing the transformer's efficiency to decrease.

[0076] 3) Manufacturing process errors: In actual manufacturing, the precision of the air gap is difficult to control, so the size and position of the air gap often have certain errors. This requires allowing a certain tolerance in the design and verifying the feasibility of the air gap design through experiments.

[0077] Air gap design is crucial in the E-type ferrite core transformer of LLC resonant converters. A well-designed air gap can effectively prevent core saturation, optimize the transformer's inductance characteristics, improve efficiency, and control the magnetic field distribution. During the design process, the size, location, shape, and matching of the air gap with the core material require careful calculation and optimization to ensure the transformer operates under efficient and stable conditions.

[0078] Designing an E-type ferrite core transformer for an LLC resonant converter involves multiple steps, including core selection, operating frequency determination, flux density control, winding design, thermal management, and EMI suppression. By comprehensively considering factors such as core material, dimensions, flux density, winding design, and current density, the transformer is ensured to operate stably under high-frequency and high-efficiency conditions. Each step in the design process requires meticulous calculations to optimize transformer performance and improve the overall efficiency and reliability of the LLC converter.

[0079] The following practical example illustrates the design process of LLC and transformer: use Figure 8 This document details the circuit structure of an LLC converter with PFC, providing a complete design flow for the LLC circuit components and transformer parameters. The case study involves designing a 180W / 24V LLC resonant converter. Design requirements: Input voltage: 380V DC (PFC stage output), Output: 24V / 7.5A (180W), Hold-up time: 17ms, DC link capacitor at the PFC output: 100uF.

[0080] Step 1: Parameter Definition For system efficiency There are pre-defined baselines and approximate ranges based on requirements. Estimating power conversion efficiency is typically done to calculate the maximum input power required for a given maximum output power. Without specific reference values ​​or test data, efficiency is usually inferred based on the application. For low-voltage output applications, power conversion efficiency... Efficiency is typically estimated to be between 0.88 and 0.92; however, for high-voltage output applications, efficiency is usually higher, generally between 0.92 and 0.96. These estimated efficiency values ​​can be used to calculate the maximum input power required for a specific output power. These efficiency ranges can serve as a preliminary reference in the design process, helping to estimate power requirements and thus optimize the design and selection of the power supply.

[0081] Typically, it is assumed that the input voltage is provided by the output of a power factor correction (PFC) pre-regulator. In this configuration, when the PFC module provides the input voltage to the system, the system's voltage hold-up time requirements must be considered. Therefore, the minimum input voltage is usually set to a specific value to ensure that the system can operate stably and maintain a sufficient voltage level under load changes or input voltage fluctuations, thereby avoiding power outages or performance instability. This minimum input voltage setting typically takes into account the reliability of the power supply system and performance requirements under different operating conditions. Let the maximum and minimum input voltages provided to the LLC resonant converter by the PFC output capacitor be denoted as... , .

[0082] in This is the rated output voltage of the PFC. It is the duration of the hold. It is the capacitor that connects the DC link to the LLC resonant converter.

[0083] Example calculation: Based on design requirements, the efficiency of the LLC resonant converter is set at 95%.

[0084] (Keep one decimal place) Step 2: Determine the gain range (maximum and minimum values) of the resonant network. To minimize switching frequency fluctuations, LLC resonant converters typically operate at a resonant frequency of... Nearby operation. For systems where the input voltage is provided by a PFC module, the input voltage will reach its maximum value under normal operating conditions, which is the rated output voltage of the PFC. In design, the operating frequency of the converter at the maximum input voltage is typically set as the resonant frequency. This is to ensure that the converter gain is minimized at this frequency. The gain at the resonant frequency is the ratio between the magnetizing inductance and the primary leakage inductance. Closely related. Therefore, choosing the appropriate The value is crucial for ensuring minimum gain.

[0085] However, although smaller A value that is too small will help achieve a higher peak gain, but too small a value will result in a lower peak gain. An excessively high value may result in poor coupling of the transformer, thus affecting efficiency. To find the optimal balance between performance and efficiency, a suitable value is typically selected. The value ranges between 5 and 10. Within this range, the gain at the resonant frequency is typically 1.1 to 1.2. Once a suitable value is determined... The value can then be used to calculate the maximum input voltage. The minimum voltage gain required under different operating conditions is determined to ensure the stability and high efficiency of the converter.

[0086] Example calculation (assuming) ): Step 3: Calculate the transformer turns ratio .

[0087] in It is the forward voltage drop of the rectifier diode on the secondary side of the transformer.

[0088] Example calculation: Step 4: Calculate the equivalent impedance of the transformer secondary side referred to the primary side. Calculation example: Step 5: Design the passive component parameter values ​​for the resonant network From the previously determined ,from Figure 7 The approximate reading indicates the selection of a suitable Q value to ensure sufficient peak gain. Generally, for circuit performance considerations, a 10% to 15% margin should be left for the peak gain. The resonant parameters are calculated using the following formula: Example calculation: In the second step of the calculation, when the input voltage reaches its minimum value... At that time, maximum voltage gain The value is 1.51. To account for system margin, a 10% safety margin is typically added, therefore the peak gain should be at least 1.66. In this process, the K value is set to 8, according to... Figure 7 From the peak gain curve, the Q value is found to be 0.36. After selecting a resonant frequency of 100kHz, the system's resonant parameters can be further determined as follows: In transformer design, parameters are determined. and Then, the two inductance values ​​can be measured on the primary side by performing open-circuit and short-circuit tests on the secondary coil, respectively. Nevertheless, Precise control is often difficult in actual transformer design because it is affected by various factors such as core characteristics, winding layout, and manufacturing process. Therefore, when designing a resonant network, it is sometimes necessary to rely on the actual measurements obtained after the transformer is manufactured. The value is adjusted accordingly. Another common solution is to add an additional resonant inductor to the resonant network and connect it in series with the resonant capacitor, thereby precisely obtaining the desired value. Values ​​are set to ensure that the network performance meets expectations.

[0089] Step 6: Transformer Design The most demanding conditions in transformer design typically occur at the lowest switching frequency, which happens under the conditions of lowest input voltage and full load. To determine the lowest switching frequency, the following equation can be used: Plot the gain curve and read the corresponding minimum switching frequency value from it. Next, the minimum number of coils in the transformer's primary winding can be calculated using the following formula: in, This represents the cross-sectional area of ​​the transformer core, in meters (m²). 2 ; This represents the maximum fluctuation range of magnetic flux density, measured in Tesla (T). Without specific reference data, it can usually be... The value is set between 0.25T and 0.3T, and the magnetic flux density in this range is suitable for most common transformer designs.

[0090] Then, select the number of secondary coils to ensure that the number of primary coils is greater than... .

[0091] Example Calculation: Selecting EER3541 core transformer .from Figure 9 The gain curve shown yields a minimum switching frequency of 54kHz. Choose 0.3. Then, the minimum number of coils in the primary winding of the transformer is: Therefore, the number of turns of the primary coil (turn) Step 7: Adjusting the resonant capacitor Selection When selecting a resonant capacitor, its rated current must be fully considered, as a considerable current will flow through the capacitor during operation. To ensure the capacitor operates within a safe range, selection should be based on the root-mean-square (RMS) current it can withstand. By calculating the RMS current, the capacitor's withstand capability can be determined, preventing overheating or damage due to excessive current. Therefore, appropriately selecting the capacitor's rated current is crucial for ensuring system stability and reliability.

[0092] The root mean square current through the resonant capacitor is: The maximum voltage of the resonant capacitor is: Therefore, the withstand voltage of the PFC DC output capacitor must be greater than 325V, leaving as much margin as possible.

[0093] Example 2 Based on Example 1, see Figure 10 This embodiment provides an LLC and transformer parameter design system based on sinusoidal fundamental wave analysis, used to implement the LLC and transformer parameter design method of Embodiment 1. The system includes: (1) The equivalent output impedance calculation module on the secondary side is used to convert the primary side of the transformer into a sinusoidal current source and a square wave voltage, which together serve as the input signal of the full-bridge rectifier circuit, to obtain the voltage difference between the midpoints of the two rectifier half-bridges, and to calculate the equivalent output impedance with the secondary side of the transformer as a reference. (2) The equivalent load impedance calculation module on the primary side is used to convert the equivalent output impedance with the secondary side as a reference to the primary side of the transformer to obtain the equivalent load impedance of the primary side. (3) LLC equivalent circuit construction module, used to calculate the voltage input of the primary half-bridge to the resonant cavity based on the equivalent load impedance of the primary side, solve the fundamental signal by Fourier series decomposition, and establish LLC equivalent circuit; (4) LLC converter design module, used to calculate the resonant cavity gain of the LLC equivalent circuit and design the LLC converter based on the resonant cavity gain; (4) Transformer design module, used to design E-type ferrite core transformer based on LLC converter.

[0094] In summary, this invention approximates the input square wave signal as its fundamental component, which not only simplifies the design process but also enables more accurate calculation of the resonant cavity's response characteristics, thereby optimizing the overall system performance. This method significantly reduces design complexity and improves design accuracy and adaptability while ensuring system efficiency and stability.

[0095] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the technical scope disclosed in the present invention, and these modifications or substitutions should all be covered within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A method for designing LLC and transformer parameters based on sinusoidal fundamental wave analysis, characterized in that, Includes the following steps: The primary side of the transformer is equivalent to a sinusoidal current source and a square wave voltage, which are used together as the input signal of the full-bridge rectifier circuit to obtain the voltage difference between the midpoints of the two rectifier half-bridges. The equivalent output impedance with the secondary side of the transformer as a reference is then calculated. The equivalent output impedance with reference to the secondary side is applied to the primary side of the transformer to obtain the equivalent load impedance of the primary side. The voltage input of the primary half-bridge to the resonant cavity is calculated based on the equivalent load impedance of the primary side. The fundamental signal is solved by Fourier series decomposition, and the LLC equivalent circuit is established. Calculate the resonant cavity gain of the LLC equivalent circuit, and design an LLC converter based on the resonant cavity gain; Design an E-type ferrite core transformer based on an LLC converter.

2. The LLC and transformer parameter design method based on sinusoidal fundamental wave analysis according to claim 1, characterized in that, The equivalent output impedance, with reference to the secondary side of the transformer, is calculated using the following formula: in, The equivalent output impedance is referenced to the secondary side of the transformer. The voltage difference between the midpoints of the two rectifier half-bridges. For secondary side input current, , These are the output current and output voltage, respectively. For output load.

3. The LLC and transformer parameter design method based on sinusoidal fundamental wave analysis according to claim 1, characterized in that, The equivalent load impedance of the primary side is calculated using the following formula: in, This is the equivalent load impedance of the primary side. Turns ratio, , These represent the number of turns on the primary side and the number of turns on the secondary side of the transformer, respectively. For output load.

4. The LLC and transformer parameter design method based on sinusoidal fundamental wave analysis according to claim 1, characterized in that, The resonant cavity gain is calculated using the following formula: in, The resonant cavity gain of the LLC equivalent circuit is given. , For switching frequency, This is the equivalent load impedance of the primary side. It is a resonant capacitor. For magnetizing inductance, It is the primary inductor. It is a resonant inductor. Turns ratio, This is a secondary side leakage sensation.

5. The LLC and transformer parameter design method based on sinusoidal fundamental wave analysis according to claim 1, characterized in that, The LLC converter design based on resonant cavity gain includes the following steps: Based on the resonant cavity gain, and taking into account the selection of inductors, the design of magnetic components, the adjustment of switching frequency, and the changes in load conditions, the LLC resonant converter is designed.

6. The LLC and transformer parameter design method based on sinusoidal fundamental wave analysis according to claim 1, characterized in that, The design of the E-type ferrite core transformer includes the selection of E-type ferrite core, calculation of design parameters, thermal management of LLC converter transformer, core saturation / efficiency, electromagnetic interference immunity and air gap design.

7. The LLC and transformer parameter design method based on sinusoidal fundamental wave analysis according to claim 6, characterized in that, The selection of ferrite cores includes the selection of core material, core size, and core shape. The calculation of design parameters includes operating frequency, magnetic flux density, number of winding turns, core power carrying capacity, wire diameter, number of turns, winding type, and winding distribution. The thermal management of the LLC converter transformer includes heat dissipation design and temperature rise control. The electromagnetic interference immunity includes shielding / grounding and filtering.

8. The LLC and transformer parameter design method based on sinusoidal fundamental wave analysis according to claim 6, characterized in that, The design of the air gap takes into account the core size, the shape of the air gap, the location of the air gap, and the size of the air gap.

9. The LLC and transformer parameter design method based on sinusoidal fundamental wave analysis according to claim 8, characterized in that, The size of the air gap is calculated using the following formula: in, For air gap size, It is the number of turns in the winding. It is the magnetic reluctance of the magnetic core. It is the magnetic reluctance of the air gap.

10. A parameter design system for LLC and transformers based on sinusoidal fundamental wave analysis, characterized in that, For implementing the LLC and transformer parameter design method as described in any one of claims 1-9, the system comprises: The secondary-side equivalent output impedance calculation module is used to convert the primary side of the transformer into a sinusoidal current source and a square wave voltage, which together serve as the input signal of the full-bridge rectifier circuit. This allows for the calculation of the voltage difference between the midpoints of the two rectifier half-bridges and the equivalent output impedance with the secondary side of the transformer as a reference. The primary-side equivalent load impedance calculation module is used to convert the equivalent output impedance with reference to the secondary side to the primary side of the transformer to obtain the equivalent load impedance of the primary side. The LLC equivalent circuit construction module is used to calculate the voltage input of the primary half-bridge to the resonant cavity based on the equivalent load impedance of the primary side, solve the fundamental signal through Fourier series decomposition, and establish the LLC equivalent circuit. The LLC converter design module is used to calculate the resonant cavity gain of the LLC equivalent circuit and design the LLC converter based on the resonant cavity gain. The transformer design module is used to design E-type ferrite core transformers based on LLC converters.

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