Chapter 1 establishes the central idea for the entire Ultimate Guide to Resonant Converter Transformer Design: a resonant transformer is not merely a conventional transformer connected to a resonant converter. Its turns ratio, magnetizing inductance, leakage inductance, winding arrangement, parasitic capacitance, loss, and physical construction can directly influence the converter’s gain, operating-frequency range, soft-switching behavior, efficiency, EMI, and manufacturability.
In This Chapter — Click to Expand
Table of Contents
1. Why Resonant Converter Transformer Design Is Different
A conventional transformer is often introduced as a component that transfers AC power between windings according to a turns ratio. That description remains useful in a resonant converter, but it is incomplete. In an LLC converter, the transformer is embedded inside a frequency-dependent network whose behavior is intentionally shaped by inductance and capacitance.
The magnetic component therefore participates in two jobs at the same time. It must provide voltage transformation and galvanic isolation where required, and it must realize magnetic parameters that interact with the resonant tank. A change to winding spacing can change leakage inductance. A change to interleaving can change both leakage and capacitance. A change to primary turns can change flux density and magnetizing inductance. Those changes can move the converter away from the operating behavior assumed by the original electrical design.
SOLIDMAG ENGINEERING INSIGHT
The Transformer Is an Electrical Network Element, Not Just a Voltage-Ratio Device
In resonant conversion, transformer geometry can change the resonant network itself. That is why circuit design, magnetic design, winding design, and manufacturing tolerances must converge together.
The correct objective is not to optimize the transformer independently. It is to create a repeatable transformer whose realized electrical parameters support the intended converter behavior.
Figure 1-1. Comparison of a conventional isolated transformer role with an LLC resonant-transformer role. The LLC side should show the bridge, Lr, Cr, magnetizing branch Lm, transformer ratio, secondary rectification, and the interaction between physical transformer parameters and the resonant tank.
2. Conventional Transformer vs. Resonant Converter Transformer
The table below summarizes the design distinction that drives the rest of this guide.
| Design Characteristic | Conventional Transformer Emphasis | Resonant Converter Transformer Emphasis |
|---|---|---|
| Turns ratio | Primary voltage-scaling relationship | Still required, but overall converter gain also depends on tank impedance and switching frequency |
| Magnetizing inductance | Often made high enough to limit magnetizing current | An intentional design variable that affects gain, circulating current, and soft-switching margin |
| Leakage inductance | Normally minimized within practical limits | May be minimized, controlled, or intentionally used as part of resonant inductance |
| Interwinding capacitance | Parasitic to manage | Parasitic that can materially affect common-mode current, EMI, high-frequency behavior, and sometimes resonant response |
| Winding arrangement | Balances loss, isolation, regulation, and manufacturability | Also becomes a direct method of setting leakage and capacitance |
| Operating frequency | Often fixed or narrowly varying | Commonly swept over a designed frequency range for regulation |
| Validation | Ratio, loss, temperature, isolation, leakage, regulation | All of those plus realized Lm, Lr/leakage, capacitance, gain range, and soft-switching behavior |
ENGINEERING CAUTION
Do Not Start an LLC Transformer by Solving Only the Turns Ratio
The ideal turns ratio can establish the basic voltage-scaling relationship, but it does not determine the complete input-to-output gain of an LLC converter.
The operating point also depends on resonant frequency, switching frequency, load, Lr, Lm, Cr, rectifier configuration, losses, and the chosen gain range. Treating turns ratio as the whole design can force the converter to operate at undesirable frequencies or outside the intended soft-switching region.
3. The Transformer Is Part of the Resonant Tank
A simplified LLC power stage contains a square-wave source, a series resonant inductance Lr, resonant capacitance Cr, the transformer magnetizing inductance Lm, an ideal transformer ratio, and the reflected load. In a real transformer, leakage inductance and distributed capacitance are added to that model.
The exact equivalent circuit depends on the analysis method and how transformer leakage is referred between windings. For first-pass LLC design, the circuit is often reduced to a primary-referred resonant model so that the designer can work with a defined Lr, Lm, Cr, turns ratio, and equivalent AC load.
Figure 1-2. Simplified primary-referred LLC resonant tank and transformer model showing the bridge excitation, Cr, Lr, magnetizing branch Lm, ideal transformer, reflected load, and annotations identifying where real transformer leakage and parasitic capacitance enter the model.
4. Ideal Turns Ratio Still Matters—but It Is Not the Whole Gain Equation
For the ideal transformer portion of the model, the fundamental voltage ratio remains:
| Variable | Meaning |
|---|---|
| VP | Primary winding voltage for the ideal transformer relationship |
| VS | Secondary winding voltage for the ideal transformer relationship |
| NP | Primary turns |
| NS | Secondary turns |
The corresponding ideal current relationship is inversely proportional to turns ratio:
These relationships are still essential because integer turns ultimately set the physical transformer ratio. However, a regulated LLC converter changes switching frequency to move along its resonant gain characteristic. The transformer ratio should therefore be selected together with the required minimum and maximum converter gain rather than by applying the ideal ratio in isolation.
5. Series Resonance Begins with Lr and Cr
The higher characteristic resonant frequency normally used as the LLC series resonant frequency is established by Lr and Cr:
| Variable | Meaning |
|---|---|
| fr | Series resonant frequency of Lr and Cr |
| Lr | Total resonant inductance represented in the selected primary-referred model |
| Cr | Resonant capacitance |
At this frequency, the reactances of the ideal series Lr and Cr cancel. In a practical converter, losses, transformer parameters, rectifier behavior, dead time, device capacitance, and load still matter, but fr remains one of the primary reference frequencies for design.
6. Magnetizing Inductance Creates the Second L in LLC
Magnetizing inductance is the second inductive element that gives the LLC topology its name. It represents the current required to establish magnetic flux in the transformer core when referred to the primary.
The idealized magnetizing-current slope follows the familiar inductor relationship:
The instantaneous magnetic energy associated with the magnetizing branch is:
A smaller Lm produces more magnetizing current for the same applied voltage and time interval. That current can help maintain the inductive current needed for primary-side ZVS, but it also adds circulating current and conduction loss. A larger Lm reduces magnetizing current but can reduce available soft-switching margin and change the achievable gain curve.
SOLIDMAG ENGINEERING INSIGHT
High Magnetizing Inductance Is Not Automatically Better
In a conventional transformer, designers often want magnetizing inductance to be as large as practical so no-load current is small. LLC design is different because magnetizing current participates in converter behavior.
The appropriate Lm is a system tradeoff among gain, circulating current, ZVS margin, transformer construction, core loss, copper loss, and operating range.
7. LLC Has Two Important Characteristic Resonant Frequencies
In addition to the Lr–Cr resonance, a second lower characteristic frequency appears when Lr and Lm participate together with Cr. A common simplified expression is:
Different references may call this lower frequency fm, fp, fo, or another symbol. The naming convention is less important than defining the equation and model clearly. Throughout this guide, fr will refer to the series resonance of Lr and Cr, while fm will refer to the lower characteristic resonance using Lr + Lm.
DESIGN ASSUMPTION
Educational LLC Frequency Example
Assume Lr = 20 µH, Lm = 100 µH, and Cr = 100 nF. These values are illustrative and are not a recommended design for a particular power level.
The example shows why the transformer magnetizing inductance cannot be separated from converter analysis. Changing Lm moves the lower characteristic frequency and changes the shape of the gain characteristic even if Lr and Cr stay unchanged.
Figure 1-3. Conceptual LLC frequency-response map identifying the lower characteristic frequency fm, the Lr–Cr series resonant frequency fr, the inductive operating region used for primary ZVS, and the capacitive region that should generally be avoided in normal regulated operation.
8. The Inductance Ratio Ln Shapes the Design Space
A useful normalized design parameter is the ratio of magnetizing inductance to resonant inductance:
For the educational values above:
The inductance ratio influences available gain, circulating current, resonant-frequency separation, and the operating range over which the converter can maintain the desired switching behavior. Chapter 4 will develop these relationships quantitatively using gain curves and quality factor.
ENGINEERING CAUTION
Do Not Copy Ln from Another Power Supply
An inductance ratio that works well for one converter may be poor for another because input range, output range, rectifier arrangement, load range, switching devices, controller limits, efficiency target, and thermal constraints can all be different.
Use normalized design ratios to organize the search space, not as universal constants.
9. Leakage Inductance Can Be an Intentional Resonant Component
In a conventional transformer, leakage inductance is created by magnetic flux that links one winding imperfectly with another. Designers often reduce it because it causes voltage spikes, regulation error, and energy that must be managed elsewhere.
An LLC converter can use a different strategy. The resonant inductance may be implemented as a separate inductor, as controlled transformer leakage, or as a combination of both. In a simplified primary-referred model:
The word “effective” matters. A real transformer has distributed primary and secondary leakage, and the value that belongs in the resonant model depends on how the circuit is referred and measured. Chapter 8 will treat this rigorously and define the measurement method.
SOLIDMAG ENGINEERING INSIGHT
Leakage Is Not Automatically a Defect in an LLC Transformer
If leakage is intentionally used as resonant inductance, the design goal is not minimum leakage. The goal is the correct, repeatable leakage value with acceptable tolerance.
That requirement turns winding spacing, interleaving, sectioning, bobbin geometry, and insulation thickness into resonant-tank design variables.
10. Coupling Coefficient Is Not Simply a Higher-Is-Better Number
Coupling coefficient provides a useful way to describe how strongly two windings share magnetic flux. For primary inductance LP, secondary inductance LS, and mutual inductance M:
For an idealized two-winding coupled-inductor model, the primary inductance measured with the secondary perfectly shorted is:
This simplified relation helps explain why reduced coupling increases measured short-circuit or leakage inductance. Real production measurements require defined winding connections, frequency, amplitude, fixture, and shorting method.
SOLIDMAG ENGINEERING INSIGHT
Maximum Coupling Is Not Always the LLC Objective
Aggressive interleaving can increase coupling and reduce leakage, but it often increases interwinding capacitance and can complicate isolation or manufacturing.
If the design intentionally needs transformer-derived resonant inductance, excessively high coupling can force the designer to add a separate resonant choke or redesign the winding structure.
11. Soft Switching Depends on the Magnetic Design
One of the main reasons to use an LLC converter is the ability to achieve soft switching over a useful operating range. Primary MOSFETs can be turned on under zero-voltage-switching conditions when the resonant tank remains sufficiently inductive and current is available during dead time to charge and discharge the switch-node capacitances.
Magnetizing current is one contributor to that commutation current. Therefore Lm, switching frequency, dead time, device output capacitance, load, and resonant-tank current all interact. A transformer with the wrong magnetizing inductance can reduce ZVS margin even if the turns ratio and power rating appear correct.
Secondary rectifiers can also approach zero-current switching under appropriate LLC operating conditions. The exact boundary depends on switching frequency and load, so Chapter 3 will develop the operating regions rather than assuming that every operating point is automatically soft switched.
ENGINEERING CAUTION
“LLC” Does Not Guarantee ZVS Everywhere
Soft switching is an operating condition, not a permanent property of the topology label. A converter can lose ZVS if the operating point, dead time, Lm, resonant current, device capacitance, or load moves outside the intended design region.
The transformer design must therefore be verified at the worst relevant line, load, frequency, temperature, and tolerance corners.
12. Parasitic Capacitance Is Part of the High-Frequency Circuit
Every practical winding structure contains capacitance: turn-to-turn, layer-to-layer, primary-to-secondary, winding-to-core, and sometimes winding-to-shield. These capacitances are not visible in the ideal transformer symbol, but their impedance decreases as frequency rises.
As an example, 100 pF has a reactance magnitude of about 15.9 kΩ at 100 kHz but only about 1.59 kΩ at 1 MHz. The high-frequency switching edges therefore see a much stronger capacitive path than the fundamental switching frequency alone might suggest.
Interwinding capacitance can create common-mode current, affect EMI, alter switching-node ringing, and interact with the effective resonant network. Winding structures that reduce leakage by increasing overlap often increase capacitance. That tradeoff becomes one of the central physical-design problems in Chapters 11 and 13.
13. External Resonant Inductor vs. Integrated Leakage
There are two common implementation philosophies for the series resonant inductance.
| Approach | Advantages | Challenges |
|---|---|---|
| Separate resonant inductor | Lr can be designed, measured, tuned, and changed independently; transformer can emphasize coupling | Adds another magnetic component, volume, cost, copper/core loss, and assembly |
| Transformer-integrated leakage | Can reduce component count and improve power density; uses an unavoidable transformer parameter productively | Leakage becomes sensitive to winding geometry, insulation, assembly, and tolerance; changing Lr may require transformer redesign |
| Hybrid | Allows part of Lr to come from controlled transformer leakage and the remainder from an external inductor | Still requires careful measurement and tolerance allocation between two magnetic elements |
Figure 1-4. Comparison of three resonant-inductance implementations: external Lr with tightly coupled transformer, transformer-integrated leakage supplying Lr, and hybrid Lr split between external inductance and controlled transformer leakage.
DESIGN ASSUMPTION
Choose the Lr Architecture Before Finalizing the Winding Stack
A winding designed for minimum leakage is structurally different from a winding designed to produce a controlled resonant inductance. Decide whether Lr is external, integrated, or hybrid before locking interleaving, sectioning, insulation spacing, and bobbin geometry.
14. The Transformer Must Work Across an Operating Window
An LLC transformer is not designed for one voltage, one load, and one switching frequency. It must remain acceptable across an operating window. At minimum, the design process should identify the important combinations of:
- Minimum, nominal, and maximum input voltage.
- No-load, light-load, nominal-load, full-load, and overload conditions where applicable.
- Minimum, nominal, and maximum switching frequency.
- Maximum required converter gain and minimum required converter gain.
- Minimum and maximum magnetizing inductance after tolerance.
- Minimum and maximum resonant inductance after external-inductor and leakage tolerance.
- Resonant-capacitor tolerance.
- Semiconductor output-capacitance and dead-time variation relevant to ZVS.
- Core-material and permeability variation.
- Winding resistance and temperature variation.
- Ambient-temperature range and maximum winding/core temperature.
- Isolation, creepage, clearance, and manufacturing tolerances.
Later chapters will convert these dimensions into an operating-corner matrix so that no single nominal design point is mistaken for the complete design.
ENGINEERING CAUTION
The First Harmonic Approximation Is a Design Model, Not Final Proof
First-harmonic analysis is extremely useful for organizing LLC gain and resonant-tank design, especially near the intended operating region. It does not reproduce every switching transition, nonlinear device capacitance, rectifier behavior, parasitic resonance, saturation effect, or control transient.
Use analytical models for design and screening, then verify the important operating corners with time-domain simulation and hardware measurements.
15. What the Physical Transformer Must Accomplish
A practical resonant transformer must satisfy several requirements simultaneously. Passing one of them does not make the design complete.
| Requirement Group | What the Transformer Must Deliver |
|---|---|
| Voltage transformation | The required integer turns ratio and winding polarity |
| Magnetizing behavior | Lm within a defined tolerance and measurement condition |
| Resonant behavior | Controlled leakage contribution when leakage is part of Lr |
| Flux capability | Acceptable flux-density excursion and saturation margin at worst-case volt-seconds |
| Core loss | Material and geometry compatible with frequency, waveform, temperature, and flux swing |
| Winding loss | Acceptable DC and AC resistance for the actual current spectrum |
| Parasitics | Leakage and capacitance consistent with gain, ZVS, EMI, and ringing objectives |
| Isolation | Required dielectric strength, creepage, clearance, insulation system, and margins |
| Thermal performance | Acceptable hot-spot temperatures across the operating window |
| Manufacturability | A winding and assembly process that repeatedly produces the specified Lm, leakage, ratio, DCR, insulation, and geometry |
| Validation | Measurable production parameters linked back to converter requirements |
16. Recommended Resonant Transformer Design Workflow
The complete Ultimate Guide will develop the design in the following sequence:
- Identify the resonant topology and define the converter operating requirements.
- Establish the LLC operating regions, gain range, and required switching-frequency window.
- Select resonant-tank parameters Lr, Lm, and Cr together with the appropriate quality factor and inductance ratio.
- Choose turns ratio from the required converter gain rather than from ideal voltage ratio alone.
- Choose integer turns, core geometry, magnetic material, and flux-density target.
- Determine whether resonant inductance is external, transformer-integrated, or hybrid.
- Select conductors from actual winding RMS current and high-frequency loss requirements.
- Create the winding stack and intentionally control leakage, capacitance, insulation, and manufacturing fit.
- Calculate core loss, copper loss, thermal performance, and tolerance margins.
- Verify creepage, clearance, insulation system, dielectric requirements, and EMI implications.
- Define manufacturing drawings, winding instructions, Lm/leakage/DCR limits, and production test methods.
- Validate the complete converter across line, load, frequency, temperature, and component tolerance.
- Automate candidate generation, operating-corner checks, winding geometry, CAD variables, and design-package output while preserving traceability.
Figure 1-5. End-to-end resonant transformer design traceability chain from converter requirements through topology and tank design, transformer electrical targets, core and winding geometry, parasitic control, loss and thermal analysis, manufacturing tolerances, production tests, and converter validation.
SOLIDMAG ENGINEERING INSIGHT
Resonant Transformer Design Is an Iterative Loop
The electrical targets create the winding geometry, but the winding geometry changes leakage, capacitance, resistance, and sometimes the effective resonant values. Those realized values must then be fed back into the converter analysis.
A strong automated design system should make that iteration faster and more traceable, not hide it.
17. Chapter 1 Engineering Checklist
Before moving to Chapter 2, verify that the following distinctions are clear:
- The ideal transformer turns ratio is necessary but does not equal the complete regulated LLC gain.
- Lr and Cr establish the primary series resonant frequency fr.
- Lm is an intentional converter design variable, not merely a parasitic no-load property.
- Lr + Lm with Cr creates a lower characteristic resonant frequency.
- The ratio Ln = Lm/Lr is an important normalized design parameter.
- Transformer leakage can be an unwanted parasitic, an intentionally controlled resonant element, or both depending on architecture.
- Maximum coupling is not automatically the best LLC transformer objective.
- Interwinding capacitance can materially affect common-mode current, EMI, ringing, and high-frequency behavior.
- Primary ZVS depends on the actual operating point and available commutation current; the topology name alone does not guarantee it.
- The transformer must be designed across the full operating window, not at one nominal condition.
- Physical winding geometry and manufacturing tolerance must be fed back into the resonant electrical model.
CHAPTER TAKEAWAY
The Transformer and Resonant Tank Must Converge Together
A successful resonant transformer is one whose measured turns ratio, Lm, leakage, capacitance, losses, temperature, and insulation construction match the needs of the converter across its real operating range.
Chapter 2 now expands the topology side of that problem by comparing SRC, PRC, LCC, LLC, and CLLLC resonant structures.
18. Conclusion — The Transformer and Converter Must Be Designed Together
Resonant converter transformer design begins with a different mental model than conventional transformer design. The magnetic component cannot be reduced to turns ratio, core area, and copper loss because its nonideal characteristics may be deliberate elements of the power-transfer network.
Turns ratio establishes basic voltage scaling. Magnetizing inductance affects gain, circulating current, and soft-switching margin. Leakage inductance can become resonant inductance. Winding capacitance creates high-frequency current paths. Core and conductor choices determine loss and temperature. Insulation and spacing change the same geometry that sets leakage and capacitance. Manufacturing variation determines whether the design remains repeatable.
The rest of this Ultimate Guide develops those relationships one layer at a time until the result is not merely a resonant-tank calculation, but a transformer that can be built, measured, validated, documented, and ultimately automated.
Technical References for This Chapter
The equations and engineering relationships in this chapter are consistent with standard LLC resonant-converter models used in manufacturer application guidance. Use the latest controller datasheet, semiconductor data, ferrite data, and safety requirements for a production design.
- STMicroelectronics AN2450 — LLC Resonant Half-Bridge Converter Design Guideline.
- Texas Instruments SLUA923 — Improving ZVS and Efficiency in LLC Converters.
- Texas Instruments Power Tips — Designing an LLC Resonant Half-Bridge Power Converter.
- Infineon — Design of a 600 W Half-Bridge LLC Converter.
Related SolidMagnetics Resources
Ultimate Guide to Resonant Converter Transformer Design
Return to the complete 15-chapter guide roadmap.
Chapter 2 — Resonant Converter Topologies: SRC, PRC, LCC, LLC, and CLLLC
Compare the resonant families and see how topology changes the magnetic-component requirements.
Chapter 4 — Resonant Tank Design: Lr, Lm, Cr, Q, Ln, and Gain
Develop the resonant-tank equations and operating-window design in detail.
Chapter 8 — Resonant Inductance and Controlled Transformer Leakage
Translate a resonant-inductance target into a controlled transformer leakage design and measurement plan.
Ultimate Guide to Flyback Transformer Design
Compare resonant transformer behavior with the energy-storage behavior of a flyback transformer.
Resonant Converter Transformer Designer
Reserved SolidMagnetics design-request URL for the future automated resonant-transformer workflow.
RESONANT CONVERTER TRANSFORMER DESIGN
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