The problem
Most on-board chargers use an LLC resonant converter after the PFC stage because it achieves soft switching on both sides and high efficiency near resonance. The difficulty is that an EV battery voltage swings widely as it charges, forcing the converter far from resonance where gain becomes non-linear and efficiency drops. Designing the tank to cover the range efficiently is the core problem.
Objectives
- Design the resonant tank from gain requirements using first harmonic approximation.
- Build a switching model with a full-bridge rectifier on the battery side.
- Compare FHA gain with simulated gain over frequency and load.
- Map ZVS on the primary and soft commutation on the secondary.
- Implement frequency control for a CC–CV charging profile.
What you need
Tools and toolboxes
- MATLAB — FHA gain curves, tank design sweeps and plotting.
- Simulink — Variable-frequency modulator, CC–CV controller and test sequences.
- Simscape Electrical — MOSFET bridge, resonant tank components, transformer, rectifier and battery model.
Software
- MATLAB R2023b or later
- Simulink
- Simscape Electrical
Extra parts and data
None beyond the software above.
Key concepts
- Resonant frequency
- fr = 1/(2π·√(Lr·Cr)); at fr the gain is close to unity regardless of load, which is where the converter is most efficient.
- Inductance ratio and quality factor
- Ln = Lm/Lr and Q = √(Lr/Cr)/Rac with Rac = 8·n²·RL/π²; they shape how steeply gain rises below resonance and how wide the range is.
- First harmonic approximation
- Treating the square-wave excitation as its fundamental gives an analytic gain curve that is accurate near resonance but less so far below it.
- Inductive region
- Operating above the gain peak keeps the tank input impedance inductive, which is needed for primary-side ZVS.
Step-by-step guide
- 1
Set the example specification
Choose labelled example values: 400 V input from the PFC stage, battery side 250–420 V, 3.3 kW, resonant frequency 150 kHz, charging profile constant current then constant voltage. Define the required gain range from minimum and maximum battery voltage and choose the turns ratio so that nominal battery voltage falls at resonance. These are example values for the study, not a specific product.
Checkpoint: A specification table with the required minimum and maximum gain computed.
- 2
Design the tank with FHA
Write a MATLAB function for FHA gain as a function of normalised frequency, Ln and Q. Sweep Ln and Q, and for each candidate check whether maximum gain at full load meets the requirement with margin and whether minimum gain is reachable within a sensible maximum frequency. Pick a design that balances frequency range and magnetising current. Save the sweep results so the design choice can be revisited.
Checkpoint: A chosen Ln, Q with gain curves showing the required range covered at full and light load.
- 3
Compute component values
From Ln, Q, fr and the turns ratio compute Lr, Cr and Lm. Estimate primary RMS current, resonant capacitor voltage stress and magnetising current at the worst case. Check that magnetising current at dead time is enough to discharge the MOSFET output capacitance for ZVS. Also estimate peak flux density in the transformer for a candidate core, so that the magnetising inductance and turns choice are physically achievable at the lowest switching frequency.
Checkpoint: Script prints Lr, Cr, Lm and stresses, plus a ZVS check at the lightest load.
- 4
Build the switching model
Build a MOSFET full bridge with dead time and output capacitance, the series Lr and Cr, a transformer with Lm, a diode full-bridge rectifier and an output capacitor feeding a battery model or controlled voltage source. Drive it with 50 per cent duty at variable frequency. Use a fixed-step local solver at about 10 ns. Halve the step once to confirm the results are converged.
Checkpoint: At fr, output voltage is close to input divided by the turns ratio and resonant current is near sinusoidal.
- 5
Compare simulated and FHA gain
Script sim() runs over frequency at several loads and measure gain from average input and output voltages. Plot simulated gain over FHA curves. Explain where FHA under- or over-predicts, typically below resonance at light load. Use averages over many switching cycles after the output has settled, and run each frequency long enough to reach steady state. Mark the boundary between inductive and capacitive regions on the plot, which FHA and simulation may place differently at light load.
Checkpoint: Simulated and FHA gain agree closely near resonance, with deviations elsewhere explained.
- 6
Map soft switching
For each operating point, check primary ZVS by checking current polarity at switching instants and inspecting drain voltage; check that the rectifier diodes turn off softly below resonance. Map ZVS over battery voltage and load and identify any region where it is lost. Record the minimum magnetising current at the dead-time instant for each point, since it shows how close the design is to losing ZVS, and compare it with the value calculated earlier.
Checkpoint: A ZVS map over the operating range with any lost region marked.
- 7
Implement CC–CV frequency control
Add a controller that outputs switching frequency: a current loop during constant-current charging and a voltage loop during constant-voltage, with smooth handover. Limit frequency between the chosen minimum and maximum. Run a compressed charging profile where the battery voltage ramps from 250 to 420 V. Check that frequency limits are never hit during the profile, and if they are, note the operating point and adjust the tank or limits, explaining the trade-off in the report.
Checkpoint: Charging current and voltage follow the CC–CV profile with a smooth transition.
- 8
Estimate losses and efficiency
Estimate MOSFET conduction losses, rectifier losses, and tank copper losses using example data, plus core loss from a simple Steinmetz model if you have core data. Plot efficiency over battery voltage at full power. Identify why efficiency drops at the ends of the range. Compare the efficiency curve with the frequency used at each battery voltage, which shows clearly that the drop at the ends comes from moving away from resonance and higher circulating current.
Checkpoint: Efficiency versus battery voltage plot with the main loss contributors at each end.
- 9
Research write-up
Document the design procedure, FHA versus simulation, ZVS map, control and efficiency. Discuss how design choices, such as a variable DC link from the PFC stage or a hybrid modulation at light load, could widen the efficient range. Release scripts where possible. Compare the results with published LLC designs of similar rating, and state clearly what the work adds, for example a design procedure that covers the full battery range with a stated efficiency floor.
Checkpoint: A thesis chapter draft with reproducible results and a justified tank design.
Testing & validation
- Tank design meets required gain range in FHA.
- Simulated gain compared with FHA over frequency and load.
- ZVS mapped across battery voltage and load.
- CC–CV charging profile tracked by frequency control.
- Efficiency estimated over the battery range.
Expected results
A complete LLC charger stage design with a justified tank, FHA versus simulation comparison, ZVS and efficiency maps across the battery range, and working CC–CV frequency control.
Research angle for your M.Tech thesis
Research questions: how can an LLC stage stay efficient across the full EV battery voltage range, and which strategy, such as a variable DC link, hybrid modulation or topology morphing, gives the best efficiency over a real charging profile? Metrics: efficiency over the charge profile, frequency range, ZVS coverage and component stress. Baselines: a fixed DC link with pure frequency control. Results should be checked with switching simulation beyond FHA, since FHA is least accurate where the problem is hardest. A strategy that improves efficiency at the ends of the range, with released models and, ideally, a scaled hardware test, can support a paper.
Take it further
- Make the PFC DC-link voltage variable to keep the LLC near resonance.
- Add burst mode or phase-shift control for light load.
- Replace the diode rectifier with synchronous rectification and timing control.
- Study bidirectional CLLC operation for V2G.
Viva and review questions
Why must the LLC operate in the inductive region?
Only when the tank input impedance is inductive does the current lag the voltage, so that it discharges the switch output capacitance during dead time and enables ZVS.
Why does FHA become inaccurate far below resonance?
Below resonance the rectifier current becomes discontinuous and the waveforms are far from sinusoidal, so higher harmonics carry significant power that FHA ignores.
Why put nominal battery voltage at resonance?
The converter is most efficient there, so the turns ratio is chosen so that the voltage where the battery spends most charging time corresponds to resonance.
Learn it at DIYguru
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