LLC Transformer Design: 2 kW Integrated Inductor

LLC transformer design can integrate the series resonant inductance into transformer leakage, eliminating a separate resonant choke when the winding geometry and converter operating range support it. This article follows a 2 kW, 800 V-to-48 V magnetic-design case study, explaining the calculations, simulation trade-offs and validation requirements that design engineers and component engineers should evaluate before specifying the transformer.

The case study follows the Frenetic design walkthrough attributed in the original article to Dr. Molina. Its principal lesson is the interaction between core sizing, magnetizing inductance, controlled leakage, winding loss and cooling; the selected magnetic configuration is a starting point for converter-level development, not a complete converter construction specification.

Key Takeaways

Integrated LLC magnetics use transformer leakage as a functional resonant element. Specify its value, tolerance, reference winding and measurement conditions rather than treating leakage only as a parasitic.
The inductance ratio L_n = L_m/L_r and effective quality factor Q_e shape normalized gain. They do not independently establish regulation range, control stability or zero-voltage switching.
The stated area-product assumptions give approximately 8.46 cm⁴. This is an initial sizing estimate, not a guaranteed minimum core size or a thermal qualification.
The example selects an E65/32/27 core with 34 primary turns and reports simulated transformer loss of approximately 14.66 W, a maximum temperature near 88 °C and an inductance ratio near 7.7.
Resonant capacitance, leakage inductance, magnetizing inductance, turns ratio and switching-frequency limits must be reconciled together. Changing capacitance shifts both resonance and quality factor.
Release requires measured inductances, winding resistance, insulation verification, converter waveforms and thermal testing under the intended operating and cooling conditions.

Design target and operating context

The example concerns an isolated, high-frequency power transformer for an LLC DC/DC stage. Its calculations apply to power conversion, not to broadband signal transformers, and the electrical targets must be distinguished from demonstrated hardware performance.

Topology: LLC resonant converter.
Input: 800 V DC bus, treated as fixed for the initial study.
Output: 48 V DC.
Output power: approximately 2 kW.
Nominal series resonant frequency: approximately 100 kHz.
Converter efficiency target: above 97%.

The defining requirement is to obtain the series resonant inductance from the transformer leakage rather than from an external choke. The magnetic assembly therefore provides voltage transformation and galvanic separation while also storing resonant energy in its leakage field. This integration is supported by established LLC operating principles, but its practical benefit depends on the resulting winding loss, temperature and converter behavior. [1] The input bus voltage alone does not define the voltage across the core-linked primary winding. Before calculating turns, establish the half-bridge or full-bridge arrangement, secondary rectification, turns-ratio convention, switching range and actual winding waveform. The broader LLC resonant converter design and calculation guide provides the surrounding converter context.

LLC gain model

The fundamental harmonic approximation, or FHA, replaces the switched converter with a sinusoidal equivalent circuit. It provides a useful initial relationship between switching frequency, load and tank parameters, particularly near series resonance; switched-circuit simulation and bench testing remain necessary away from the assumptions of the approximation. [1] Define L_m as the magnetizing inductance, L_r as the effective series resonant inductance and C_r as the resonant capacitance. All inductances in the tank model must use a consistent equivalent circuit and reference winding. The dimensionless inductance ratio L_n and normalized switching frequency f_n are:

L_n = \frac{L_m}{L_r}, \qquad f_n = \frac{f_s}{f_r} \tag{1}

In Eq. (1), f_s is switching frequency and f_r is the series resonant frequency, both in hertz. The normalized tank gain magnitude M_g is approximated by:

M_g = \left|\frac{L_n f_n^2}{(L_n+1)f_n^2-1+j(f_n^2-1)f_nQ_eL_n}\right| \tag{2}

Here j is the imaginary unit and Q_e is the dimensionless effective quality factor. Equation (2) describes the fundamental-frequency voltage ratio across the tank, with the transformer ratio handled separately. It is not simply the DC output voltage divided by the DC bus voltage. At f_n = 1, the ideal expression gives M_g = 1. [1]

Let n = N_p/N_s, where N_p is primary turns and N_s is the active secondary winding turns used in the rectification model. For a center-tapped secondary, this convention uses the relevant half-winding rather than the total end-to-end turns. Ignoring losses, the familiar conversion relationships are:

V_o \approx \frac{M_gV_{in}}{2n}\quad\text{(half bridge)}, \qquad V_o \approx \frac{M_gV_{in}}{n}\quad\text{(full bridge)} \tag{3}

In Eq. (3), V_o is DC output voltage and V_in is DC input voltage. These expressions assume the corresponding conventional rectifier arrangement and gain definition. Include winding, semiconductor and interconnection voltage drops in a practical design. [1]

Why the magnetizing-to-resonant inductance ratio matters

Changing L_n reshapes the gain-versus-frequency characteristic. The engineering question is whether the resulting curves provide the required gain throughout the specified load and input range without excessive current or operation outside the intended soft-switching region.

Reducing L_n by reducing L_m, with L_r held constant, increases magnetizing current for a given winding-voltage waveform. It can provide more boost capability and a steeper gain characteristic, but increases circulating-current and loss concerns.
Increasing L_n by increasing L_m reduces magnetizing current under comparable excitation, but can reduce available boost gain and change the frequency excursion needed for regulation.
Neither direction automatically makes control easier. Compare required gain, frequency limits, the inductive operating region and switching-transition current at all relevant operating points. [1]

LLC gain-versus-frequency chart reproduced from Texas Instruments SLUP263 — Figure 1. LLC gain-versus-frequency chart retained from the original article. Source: Texas Instruments, SLUP263. [1]

The role of effective quality factor and resonant capacitance

The effective quality factor links the resonant impedance to the AC-equivalent load resistance R_e referred to the primary. The series resonance and quality factor are:

f_r = \frac{1}{2\pi\sqrt{L_rC_r}}, \qquad Q_e = \frac{\sqrt{L_r/C_r}}{R_e} = \frac{2\pi f_rL_r}{R_e} \tag{4}

In Eq. (4), L_r is in henries, C_r in farads and R_e in ohms. For the conventional FHA rectifier model used in SLUP263, the DC load resistance R_o and its primary-referred AC equivalent are:

R_o = \frac{V_o^2}{P_o}, \qquad R_e = \frac{8n^2}{\pi^2}R_o \tag{5}

Here P_o is output power in watts. Equation (5) assumes the specified turns convention and rectifier model; other secondary arrangements require their corresponding equivalent load. At fixed tank values, increasing load power reduces the equivalent resistance and increases Q_e. [1]

Capacitance is therefore not an independent late-stage adjustment. Changing C_r changes both f_r and Q_e, while the physical transformer sets L_m, leakage and winding capacitance. The magnetic and converter designs must converge together. Capacitor selection must also account for operating frequency, RMS current, peak voltage, dissipation and temperature.

Choosing initial design values

The original exploration starts with L_n approximately 5 and Q_e approximately 0.5. Retain these as initial case-study assumptions, not universal recommended values. A static gain curve does not demonstrate closed-loop stability, and the chosen values must still satisfy the required gain and switching conditions. [1]

A magnetic simulator needs absolute inductance values as well as their ratio. These values can be developed from a preliminary core and winding geometry, then checked against the load, turns ratio and resonant-frequency target before detailed optimization.

Estimating core size using area product

The area-product method combines available magnetic cross-section and winding space. It is useful for screening candidate cores, but it does not directly predict leakage, AC winding loss, hot-spot temperature or insulation compliance.

Define A_p as area product, A_w as usable winding-window area and A_c as the core cross-sectional area used in the preliminary calculation:

A_p = A_wA_c \tag{6}

When both areas are in square centimetres, A_p is in cm⁴. The original sizing relationship is retained with its unit convention made explicit:

A_p = \frac{P_t\times10^4}{K_fK_uB_mJf} \tag{7}

For Eq. (7), A_p is in cm⁴, P_t is the preliminary total winding-power allowance in watts, B_m is peak flux density in teslas, J is conductor current density in A/cm² and f is excitation frequency in hertz. K_f is the waveform factor and K_u is the fraction of window area occupied by conductor. The factor 10⁴ belongs to this mixed-unit convention and must not be carried unchanged into an all-SI calculation.

The original estimate approximates P_t as the sum of output power and input power:

P_t \approx P_o\left(1+\frac{1}{\eta}\right) \tag{8}

In Eq. (8), η is assumed efficiency expressed as a fraction. This is a preliminary sizing allowance, not a calculation of the actual RMS volt-amperes in a resonant transformer. Circulating and magnetizing currents can increase winding demand beyond a real-power-only estimate. Final winding sizing must use converter waveforms. [1]

Case study: initial LLC transformer design calculations

The following calculations preserve the original example while separating its assumptions from its simulated results. The initial area-product estimate and illustrative inductance calculation establish starting points for iteration; they do not by themselves define a complete resonant tank.

Assumed design parameters

Output power P_o: 2000 W.
Efficiency η: 0.97 for the initial loss-budget calculation.
Waveform factor K_f: 4, representing symmetrical square-wave voltage excitation in the preliminary sizing model.
Window utilization K_u: 0.25.
Peak flux density B_m: 0.12 T as an assumed starting point, subject to the selected material’s waveform-dependent loss and temperature limits.
Current density J: 4 A/mm², equivalent to 400 A/cm².
Excitation frequency f: 100 kHz for the preliminary sizing calculation.

Equation (8) gives P_t approximately 4061.86 W. Substitution into Eq. (7) gives:

A_p = \frac{4061.86\times10^4}{4\times0.25\times0.12\times400\times100000} \approx 8.46\ \mathrm{cm}^4 \tag{9}

The original approximately 8 cm⁴ statement is therefore a rounded estimate. The original exploration considered E55, E56 and E42 core families before moving to a larger final configuration. These family names are not interchangeable specifications: compare the actual core set, material, effective area, usable bobbin window and winding construction before accepting a candidate.

Original core-sizing illustration accompanying the 2 kW LLC transformer case study — Figure 2. Core-sizing illustration retained from the original Frenetic-based design example.

The assumed 97% efficiency also defines a converter-wide loss allowance. With P_loss denoting total converter dissipation:

P_{loss} = P_o\left(\frac{1}{\eta}-1\right) = 2000\left(\frac{1}{0.97}-1\right) \approx 61.86\ \mathrm{W} \tag{10}

Equation (10) replaces the loosely rounded 60 W figure. Efficiency above 97% requires total losses below this value at the specified 2 kW operating point. The transformer allocation of approximately 24 W used in the example is a separate design budget, not an efficiency result.

Estimating the minimum primary turns

Primary turns must limit core flux over the complete operating envelope. The general relationship uses the voltage v_m(t) associated with core-linked flux, excluding winding-resistance and leakage-inductance voltage drops:

\Delta B = \frac{1}{N_pA_e}\int_{t_1}^{t_2}v_m(t)\,dt \tag{11}

In Eq. (11), ΔB is flux-density change in teslas, A_e is effective core area in square metres and t₁ to t₂ is the integration interval in seconds. Use the selected core’s effective-area specification consistently rather than mixing it with a different geometric-area definition.

For symmetrical bipolar square-wave excitation with core-voltage magnitude V_m, frequency f_s and peak flux density B_max, Eq. (11) reduces to:

N_p \geq \frac{V_m}{4B_{max}A_ef_s} \tag{12}

Equation (12) assumes a peak-to-peak excursion of 2B_max and balanced volt-seconds. V_m is not automatically 800 V just because the DC bus is 800 V. In an LLC converter, the bridge, resonant network and reflected output voltage determine the core-linked waveform. Check startup, minimum operating frequency, overload and imbalance using Eq. (11), not only the nominal 100 kHz condition. [1]

The turns estimate constrains flux and influences winding length, resistance, leakage and magnetizing inductance. Copper cross-section is determined separately from winding RMS current and the chosen current density; turn count alone does not establish conductor requirements.

Estimating leakage inductance as the resonant inductance

For suitable non-interleaved, concentric windings, a one-dimensional leakage-field model provides a useful initial estimate. Let L_σ,p denote the equivalent leakage inductance referred to the primary. A dimensionally consistent SI form is:

L_{\sigma,p} \approx \frac{\mu_0\,\mathrm{MLT}\,N_p^2}{a}\left(c+\frac{b_1+b_2}{3}\right) \tag{13}

In Eq. (13), µ₀ is the permeability of free space, approximately 4π × 10⁻⁷ H/m; MLT is representative mean length per turn; a is the overlapping winding height; b₁ and b₂ are the primary and secondary radial winding builds; and c is their separation. All lengths are in metres and the result is in henries. The model assumes compatible winding heights and an approximately one-dimensional field distribution. [2][3]

Original leakage-flux illustration accompanying the transformer winding-geometry discussion — Figure 3. Leakage-flux illustration retained from the original article. Leakage-field geometry must be matched to the assumptions of the analytical model.

Equation (13) must not be applied unchanged to sectional bobbins, strongly interleaved structures, unequal winding heights or arrangements with significant three-dimensional end fields. Interleaving changes the magnetomotive-force distribution, so its effect cannot be represented merely by inserting a smaller spacing into the same expression. McLyman discusses construction-specific alternatives and the associated capacitance trade-offs. [2]

For integrated resonant magnetics, insulation thickness, winding placement and production tolerances affect a functional tank parameter. Analytical estimates are useful for choosing an initial stack-up and assessing feasibility, but field simulation and prototype measurements should establish the final equivalent inductance.

Recent geometry-aware research continues to refine leakage estimates for particular winding arrangements. A 2025 study models and experimentally evaluates controlled winding displacement in a three-phase high-frequency transformer. Its practical relevance here is the need to match the model to the actual geometry; its three-phase converter results should not be transferred directly to this LLC transformer. [3]

Illustrative inductance calculation and tank consistency

The original numerical example assumes approximately 10 µH of primary-referred resonant inductance and an inductance ratio of 5. The corresponding magnetizing inductance is:

L_m = L_nL_r = 5\times10\ \mu\mathrm{H} = 50\ \mu\mathrm{H} \tag{14}

Equation (14) is arithmetically correct, but it establishes only the inductance ratio. To combine L_r = 10 µH with f_r = 100 kHz, Eq. (4) requires:

C_r = \frac{1}{(2\pi f_r)^2L_r} \approx 253.3\ \mathrm{nF} \tag{15}

At the same resonance, Q_e = 0.5 would require R_e approximately 12.57 Ω. Meanwhile, the stated 48 V, 2 kW output gives R_o = 1.152 Ω. The turns ratio and rectifier model must reconcile these resistances through Eq. (5). The 10 µH and 50 µH values are therefore retained as an illustration, not as verified final inductances for the 800 V-to-48 V design.

Simulation-driven design with Frenetic

The original exploration uses the Frenetic Magnetic Simulator to compare 33 configurations across multiple core sizes. The useful output is a set of coupled electrical and thermal trade-offs, rather than a single inductance value considered in isolation.

Calculate magnetizing inductance and the equivalent leakage inductance using a consistent reference circuit.
Evaluate core loss and winding loss for the applied voltage and current waveforms.
Predict winding and core temperatures using stated cooling and ambient conditions.
Compare achieved inductance ratio, winding-window use and construction feasibility.

Observation 1: the initial area-product estimate did not establish thermal feasibility

In the reported exploration, smaller core candidates did not satisfy the combined loss and temperature objectives. The approximately 8.46 cm⁴ calculation screens magnetic and winding-space demand under simplified assumptions; it does not capture every circulating-current, AC-loss or heat-transfer effect.

This does not make area product a guaranteed lower bound. The result can be optimistic or conservative depending on its assumptions. Improve the estimate with actual RMS currents, usable winding space and material data, then evaluate the resulting construction thermally.

Observation 2: analytical leakage estimates require geometry-specific validation

The original example reports differences between analytical leakage estimates and simulation. Treat that as a finding for the examined geometries, not proof that analytical formulas always overestimate leakage. Their accuracy depends on field assumptions, winding overlap, layer arrangement, separation and treatment of end effects. [2][3]

Manufacturing constraints also limit tuning freedom. A simulated adjustment to insulation or winding spacing is useful only if the finished component can reproduce it while maintaining the required electrical insulation and dimensional tolerances.

Observation 3: reducing magnetizing inductance can increase thermal stress

When L_n is reduced by lowering L_m while L_r and the winding-voltage waveform remain comparable, magnetizing current increases. This adds primary winding current without directly increasing useful output power, raising the importance of AC winding loss. [1]

Changing gap geometry can introduce additional local fringing-field loss. A larger discrete gap can be problematic near conductors, but distributed or multiple smaller gaps do not inherently produce greater loss; their effect depends on field distribution and placement. The ratio L_n alone is insufficient to predict temperature because it can also change through L_r.

Observation 4: larger cores changed the attainable inductance ratio

The reported exploration moved toward larger cores to improve the loss and temperature balance, while the achieved ratio rose above its initial target. A larger effective core area can permit fewer turns for the same applied volt-seconds and flux limit, and fewer turns can reduce leakage through the turn-squared dependence in suitable models.

However, a larger core does not automatically have shorter mean turn length, lower current density or lower leakage. Those quantities depend on the complete winding and core geometry. Compare each candidate’s actual turn count, conductor area, winding build, overlap and gap rather than inferring the result from core size alone.

Observation 5: the explored winding concept limited leakage adjustment

Within a core family and a similar winding arrangement, the original exercise found limited practical freedom to change leakage. Flux constraints limit turn-count reductions, while available window space, insulation and conductor dimensions constrain winding movement.

This is a constraint of the explored design space, not a universal property of every core family. Sectional windings, different overlap, partial interleaving or other magnetic structures can produce different leakage ranges, but require renewed loss, insulation and manufacturability assessment. [2][3]

Final design choice and key numbers

The original case study selects an E65/32/27 configuration after comparing the candidate magnetic designs. The following values describe the reported magnetic simulation outcome, rather than measured performance of a complete converter.

Parameter	Case-study value	Engineering interpretation
Core geometry	E65/32/27	Core geometry alone does not define material, gap, bobbin or insulation.
Primary turns	34	Must be checked against the actual winding volt-seconds and operating range.
Transformer loss	Approximately 14.66 W	Reported simulation result at the case-study operating point.
Maximum temperature	Approximately 88 °C	Absolute temperature, not temperature rise.
Inductance ratio	L_m/L_r approximately 7.7	Ratio does not specify the absolute inductances.
Transformer loss allocation	Approximately 24 W	Case-study design budget, separate from converter efficiency.

Table 1. Selected magnetic configuration and interpretation of the reported results.

Original final transformer-design illustration from the Frenetic-based 2 kW LLC case study — Figure 4. Final transformer-design illustration retained from the original case study.

The reported 14.66 W is 9.34 W below the example’s 24 W transformer allocation. Against the 61.86 W converter-wide allowance at exactly 97% efficiency, it would leave approximately 47.20 W for all other losses if the transformer prediction were realized at the same operating point. This arithmetic is a budget comparison, not verification of converter efficiency.

Likewise, a maximum temperature of 88 °C cannot establish temperature rise without ambient temperature. Thermal acceptance must account for cooling, mounting, nearby heat sources, insulation-system limits and the locations of winding and core hot spots.

Accepting L_n approximately 7.7 instead of 5 means returning to the converter model with the achieved absolute L_m and L_r. Recheck gain, capacitor stress, frequency limits, circulating current and switching transitions. Adjusting C_r can shift resonance and quality factor, but cannot change the transformer’s physical inductance ratio or guarantee recovery of every desired operating condition. [1]

Typical applications for this LLC transformer approach

The integration principle is relevant to isolated resonant power stages where a controlled series inductance is required and magnetic volume or component count matters. The particular 800 V-to-48 V example represents one conversion requirement, not a universal architecture for telecom, industrial or automotive equipment.

High-voltage DC distribution stages supplying an isolated low-voltage rail, where the actual input range and insulation requirements match the transformer design.
Industrial isolated DC/DC stages in which the source bus, output rail and cooling arrangement are defined explicitly.
Server, storage or telecom power stages using an appropriate resonant architecture; the relevant bus voltage must be established for the actual system.
Auxiliary low-voltage conversion in vehicle-related systems, subject to their electrical, environmental and qualification requirements. A 48 V output should not be confused with a traction-battery charging output.

Removing a separate resonant choke may reduce component count and interconnections, but it does not automatically improve EMI or total efficiency. The resulting leakage field, interwinding capacitance, winding loss and common-mode coupling must be evaluated in the complete converter. [1][2]

Design-in notes for magnetics engineers

A useful transformer specification converts converter requirements into measurable component limits. Keep the electrical model, mechanical drawing, insulation construction and inspection method aligned throughout simulation, prototyping and sourcing.

Electrical and thermal design checklist

Define topology, bridge configuration, rectification, turns ratio, input range, output range, power and switching-frequency limits.
Specify absolute L_m and L_r ranges, their reference winding and the equivalent circuit. Choose an acceptable ratio from verified gain and current requirements rather than imposing a generic 5–8 rule.
Use the area-product estimate for initial screening. Replace real-power-only assumptions with the winding RMS and peak currents from the converter model.
Check flux excursion at the worst applied volt-seconds, including startup, minimum frequency, overload and drive imbalance.
Use loss data for the actual core material, waveform, frequency and temperature. Evaluate winding AC loss, gap fringing and termination loss separately from core loss.
Compare conductor options using frequency-dependent loss and manufacturability. Round wire, litz wire, foil and PCB windings require different modeling assumptions.
Iterate resonant capacitance and switching limits with the achieved transformer values. Check capacitor RMS current, peak voltage and dissipation at the resulting operating points.
Set ambient temperature, airflow, mounting orientation, enclosure and any potting or cooling interfaces before accepting a predicted hot-spot temperature.
Verify regulation, zero-voltage-switching margin, startup, light-load behavior and protection with switched-circuit simulation and hardware. [1]

Inductance measurement and model extraction

Measure open-circuit winding inductance with the other winding open, and measure primary-referred short-circuit inductance with the specified secondary terminals connected by a short, low-impedance link. Record frequency, excitation amplitude, temperature, fixture compensation and instrument equivalent-circuit mode.

Do not automatically equate open-circuit primary inductance with L_m, or short-circuit inductance with the required tank L_r, when coupling is intentionally reduced. Fit the measured terminal behavior to the chosen transformer model, including the treatment of primary and secondary leakage. Different equivalent-circuit conventions can assign different element values while describing the same terminal measurements.

Avoid double-counting leakage by including it both through imperfect coupling and as a duplicate external series inductor in the simulation. Check model impedance over the intended frequency range and retain winding capacitance when it affects resonance or switching behavior. The measurement and model conventions should be included in the supplier specification.

Insulation, qualification and safety

Galvanic separation does not, by itself, establish safety isolation. Specify the required insulation function and applicable end-equipment requirements before fixing bobbin geometry, winding margins, barriers or interleaving. The high-voltage bus, transients, environment and construction determine the necessary insulation assessment.

Document working voltage, repetitive peak voltage, relevant transients and the intended insulation function.
Define required creepage, clearance, solid-insulation construction and dielectric verification through the applicable product safety assessment.
Specify wire insulation, barriers, bobbin material, winding margins, core accessibility and termination separation.
Confirm maximum winding and core temperatures against the qualified insulation system and component materials.
Keep safety spacing intact while tuning leakage. An insulation change is also a magnetic, capacitive and mechanical design change.
Use suitably rated laboratory equipment and qualified procedures for high-voltage testing. Small-signal LCR measurements do not verify insulation integrity or full-power operation.

Catalog versus custom components and purchasing specification

A catalog transformer is suitable only when its guaranteed parameters and test conditions match the application. The integrated leakage target and high-voltage insulation requirements in this case make a custom magnetic component a practical option, but custom construction is not a substitute for a complete specification.

Identify the exact core material, core set, gap, bobbin and mechanical envelope rather than specifying only E65/32/27.
Specify primary and secondary turns, polarity, pinout, winding order, conductor construction and terminations.
Separate typical values from guaranteed limits for inductance, leakage, DCR, dimensions and insulation tests.
Define acceptable inductance variation with temperature and excitation, and the production test conditions used to assess it.
Agree on thermal validation conditions, acceptable material substitutions and change-control requirements.
Qualify representative production samples for electrical, thermal and mechanical performance before release.

Conclusion

Integrating resonant inductance into an LLC transformer is a coupled converter-and-magnetics design task. The original 2 kW example remains useful because it shows how an initial area-product estimate and target inductance ratio evolve when winding loss, geometry and thermal constraints are included.

The selected E65/32/27 configuration and its reported simulation results should guide further development, not be treated as a complete reproducible converter design. A release-ready solution requires absolute inductances, a consistent resonant tank, a defined insulation system and measured performance across the intended operating envelope.

FAQ

These answers distinguish initial magnetic sizing from complete converter verification and component qualification.

Can transformer leakage replace the resonant inductor in an LLC converter?

Yes, when the transformer provides the required effective series inductance across the intended operating conditions. The design must control winding geometry, inductance tolerance, insulation and loss. Removing an external choke changes the magnetic assembly and its parasitic parameters, so regulation, switching transitions and temperature must be checked in the complete converter.

How should the magnetizing-to-resonant inductance ratio be selected?

Select the ratio from the gain required over input and load variation, the available switching-frequency range and acceptable circulating current. Reducing magnetizing inductance can increase boost capability but also increases magnetizing current under comparable excitation. Neither a ratio of 5 nor the reported final ratio near 7.7 is a universal recommendation or proof of stable control.

Does the area-product calculation determine the final core size?

No. The stated assumptions give approximately 8.46 cm⁴, but area product is only an initial screening method. The final construction must also accommodate insulation, actual winding currents, AC resistance, leakage requirements and cooling. The original exploration selected a larger E65/32/27 configuration after comparing magnetic and thermal results.

Can the resonant capacitor be chosen after the transformer is fixed?

Only through a renewed converter-level check. Capacitance changes both series resonant frequency and effective quality factor, so it cannot be adjusted independently of leakage inductance, reflected load and switching limits. The illustrative 10 µH resonant inductance requires approximately 253.3 nF for 100 kHz resonance, but those values alone do not establish the complete converter design.

Do the reported transformer results prove 97% converter efficiency?

No. The case study reports approximately 14.66 W transformer loss and a maximum temperature near 88 °C from magnetic simulation. Converter efficiency also includes semiconductor, capacitor, interconnection and other losses. Temperature rise requires the ambient temperature, while thermal acceptance requires the actual cooling and mounting conditions. Full-converter measurements are needed to establish achieved efficiency.

What should a buyer specify for a custom integrated LLC transformer?

Specify the complete core and winding construction, turns ratio, polarity, absolute inductance limits, leakage reference winding, DCR and measurement conditions. Include insulation requirements, dimensional limits, thermal validation conditions and production tests. Separate typical values from guaranteed limits, and agree on material substitutions and change control before approving production samples.

How to develop an LLC transformer with integrated resonant inductance

This procedure connects preliminary sizing to component qualification. Repeat the converter and magnetic checks whenever a geometry or tank parameter changes.

Develop an integrated LLC transformer through coordinated converter modeling, magnetic design, measurement and qualification.

Define the converter and insulation requirements
Specify bridge configuration, rectification, input and output ranges, power, switching limits, cooling and insulation function. Define the turns-ratio convention and determine the winding voltage and current waveforms.
Establish a consistent initial resonant tank
Choose provisional magnetizing and resonant inductances, capacitance and turns ratio. Check normalized gain, reflected load, resonance and effective quality factor together rather than selecting the inductance ratio in isolation.
Screen cores and calculate primary turns
Use the area-product estimate to shortlist actual core and bobbin combinations. Calculate flux from winding volt-seconds and check nominal operation, minimum frequency, startup and imbalance before selecting turns and conductor area.
Develop a manufacturable leakage geometry
Choose winding order, overlap, separation, conductor construction and gap placement. Apply an analytical leakage model only within its geometry assumptions, then refine the equivalent inductances with field simulation where necessary.
Iterate losses and temperatures
Evaluate core, winding and termination losses using actual waveforms and appropriate material data. Recalculate temperatures under the intended ambient, airflow, mounting and enclosure conditions, and revise the construction if margins are inadequate.
Recheck the converter with achieved magnetic values
Update the converter model with absolute inductances, winding resistance and relevant capacitances. Reconcile resonant capacitance and frequency limits, then check gain, circulating current, capacitor stress, switching transitions and protection.
Measure and validate prototypes
Measure winding inductances, short-circuit inductance, resistance and relevant capacitance under documented conditions. Validate insulation, full-power waveforms, efficiency and hot-spot temperatures across the intended operating envelope.
Freeze the production specification
Document guaranteed electrical limits, core material, gap, winding construction, insulation, dimensions and test methods. Qualify production samples and agree on substitutions, acceptance criteria and change control with the supplier.