LLC Resonant Converter Example¶

High-efficiency resonant DC-DC converter with Zero Voltage Switching (ZVS) and Zero Current Switching (ZCS) operation.

Overview¶

The LLC resonant converter offers: - Zero Voltage Switching (ZVS) for all switches across wide range - Zero Current Switching (ZCS) for secondary-side diodes - High efficiency (>96%) with minimal active losses - Wide input voltage range with frequency modulation - Soft-switching reduces EMI and switching losses - Ideal for high-power density applications

Specifications¶

Parameter	Value
Input Voltage	360-400V DC
Output Voltage	48V DC
Output Power	1 kW
Resonant Frequency (fr)	250 kHz
Switching Frequency Range	200-300 kHz
Transformer Turns Ratio	9:1 (step-down)
Efficiency Target	>95%
Output Ripple Voltage	<1%

Circuit Files¶

llc_basic_operation.ipes - Basic LLC resonant tank operation
llc_frequency_sweep.ipes - Gain vs frequency analysis
llc_load_variation.ipes - Efficiency across load range
llc_zvs_verification.ipes - Switch voltage and current waveforms

LLC Tank Topology¶

Primary Side:              Resonant Tank:        Secondary Side:

   Vin ──┐                 Lr       Cr              ┌─ Vout
        │                ───⊏⊐───┤├───┬────        │
      ┌─┴─┐              │        │    │       ┌────┴────┐
      │S1 │──────────────┤    T    │    ├──Cr──┤ D1  D2  ├─┐
      │S4 │──────┐       │   ::   │    │       │      │  │ C_out
      └───┘      │       │        │    │       │  D3  D4 │ ───
      ┌───┐      │       └────────┴────┴───────┤         │
      │S2 │──────┼─────────────────────────────┤ │ Tr   ├─┘
      │S3 │      │                             │  ::    │
      └─┬─┘      │       Lm (Magnetizing)      │         │
        │        │            │                └─────────┘
        └────────┤            │
               GND           GND

Tank Components: - Lr: Series resonant inductance (μH range) - Cr: Series resonant capacitance (nF range) - Lm: Magnetizing inductance (parallel with primary winding) - T: High-frequency transformer (250 kHz rated)

Theory¶

Resonant Frequencies¶

The LLC tank exhibits two natural resonant frequencies:

Series Resonance: $$f_r = \frac{1}{2\pi\sqrt{L_r C_r}}$$

All current flows through Lr and Cr; Lm is "invisible" at series resonance.

Parallel Resonance: $$f_p = \frac{1}{2\pi\sqrt{(L_r || L_m) C_r}} = \frac{1}{2\pi\sqrt{\frac{L_r L_m}{L_r + L_m} C_r}}$$

At parallel resonance, current divides between Lr and Lm.

Quality Factor and Impedance Ratio¶

Quality Factor: $$Q = \frac{Z_0}{R_{ac}} = \frac{\sqrt{L_r/C_r}}{R_{ac}}$$

Where the AC load resistance (referred to primary): $$R_{ac} = \left(\frac{8}{\pi^2}\right) n^2 R_{load}$$

And n is the transformer turns ratio (primary to secondary).

Inductance Ratio: $$L_n = \frac{L_m}{L_r}$$

Typical design range: Ln = 3 to 7

Voltage Gain via Fundamental Harmonic Analysis (FHA)¶

The voltage gain is frequency-dependent:

\[M(f_n) = \frac{L_n f_n^2}{\sqrt{(1 + L_n - L_n f_n^2)^2 + \frac{Q^2}{f_n^2}(f_n - 1/f_n)^2 L_n^2}}\]

Where fn = fsw/fr is the normalized frequency.

Key characteristics: - At fr: M = 1/(1+Ln) (minimum gain, highest Q) - At fp: Maximum gain plateau - Above fp: M increases toward M∞ = 1 (ideal transformer)

Operating Regions¶

Operating Region	fsw vs fr	Characteristics	ZVS	ZCS
Light Load	fsw < fr	High impedance, current lags voltage	Yes	Yes
At Resonance	fsw = fr	Minimum impedance, lowest losses	Yes	Yes
Heavy Load	fsw > fr	Lower impedance, current leads voltage	Yes	Yes

Energy Storage Analysis¶

Peak current in resonant tank: $$I_{peak} = \frac{V_{in}}{Z_0}$$

ZVS Condition:

For soft switching, the energy stored in Lr must be sufficient to charge/discharge the switch capacitances:

\[E_r = \frac{1}{2}L_r I_{peak}^2 \geq E_{sw} = \frac{1}{2}C_{sw}(2V_{sw})^2\]

This ensures voltage reaches zero before current reverses.

Design Procedure¶

Step 1: Select Resonant Frequency¶

Choose fr based on: - Core loss (smaller cores require higher frequency) - Component availability - EMI considerations - Typical range: 100-500 kHz

For 1 kW converter, fr = 250 kHz is common.

Step 2: Design Resonant Tank¶

Design Equations:

For desired output voltage Vo: $$n = \frac{V_{in}}{V_o \cdot M_{max}}$$

Where Mmax is the desired maximum gain (typically 1.2-1.5).

\[L_r = \frac{Z_0}{2\pi f_r}\]

\[C_r = \frac{1}{2\pi f_r Z_0}\]

Characteristic impedance Z0 is chosen based on: $$Z_0 = \sqrt{\frac{L_r}{C_r}} = 10 - 20 \, \Omega$$

Lower Z0 → higher current ripple but higher gain range.

Step 3: Select Magnetizing Inductance¶

Lm is determined by: $$L_m = L_n \cdot L_r$$

Higher Ln → steeper gain curve but narrower soft-switching range.

Step 4: Component Selection¶

Resonant Inductor: - Gapped ferrite core or distributed air gap - Rated for peak current: Ipeak = Vin/(2πfrZ0) - Tolerance: ±10% (affects gain curve)

Resonant Capacitor: - Film or ceramic with low ESR - Voltage rating ≥ 1.5× peak voltage across Cr - Example: 48 nF at 450V (2 × 24 nF in series)

Transformer: - Ferrite core (EE, EI, or RM series) - Primary inductance ≈ 3–5 × Lr (becomes Lm) - Leakage inductance < 5% of primary inductance - Frequency rating: fr+safety margin

Power Switches: - MOSFETs or IGBTs rated for Vin - CIss, Qoss important for ZVS margin - Example: 600V SiC MOSFET for 400V input

Output Rectifier: - Schottky or SiC diodes (low forward voltage) - Current rating ≥ Iout_max × 1.5 - SiC better for high-frequency, lower loss

Step 5: Output Filter¶

LC Filter: $$L_{out} = \frac{V_o(1-D)}{f_{sw} \Delta I_L}$$

\[C_{out} = \frac{I_{out} D}{f_{sw} V_r}\]

Where ripple current ≔ 20% of output current, voltage ripple ≔ 1%.

Control Strategy¶

Frequency Modulation¶

The simplest control method varies switching frequency to regulate output voltage:

Vout sensing
     │
     ▼
  ┌────────┐
  │ PI Reg │ ──► fsw command
  └────────┘
     ▲
     │
  Vout (measured)

PI Controller: $$f_{sw} = f_r + K_p(V_{out}^* - V_{out}) + K_i \int (V_{out}^* - V_{out}) dt$$

Range: fsw ∈ [fr, 2×fr] typically

Advantages: - Simple to implement - Natural soft-switching over wide range - Single control variable

Duty Cycle Modulation (Alternative)¶

Primary switches can also use modulated duty cycle while fsw = fr: - More complex (requires multiple control loops) - Maintains resonant frequency advantage - Useful for bidirectional converters

Efficiency Considerations¶

Loss Components:

Core Loss (Pcore): Proportional to Bpeak × f1.6
Copper Loss (Pcu): I²R in windings and tank
Switching Loss: Minimized by ZVS
Diode Loss: Forward drop × Iavg in secondary
Capacitor ESR Loss: ESR × I²

Typical Loss Budget (1 kW converter): - Core: 30-40 W - Windings: 20-30 W - Switches: 10-15 W (ZVS advantage) - Diodes: 15-25 W - Total: 50-70 W (95-98% efficiency)

Exercises¶

Frequency Sweep: Plot gain vs frequency; identify series and parallel resonance
ZVS Verification: Capture switch voltage and current; verify zero crossing at turn-on
Load Variation: Measure efficiency at 25%, 50%, 75%, 100% load; plot curves
Component Sensitivity: Vary Lr, Cr, Lm ±10%; observe gain curve shift
Soft-Switching Range: Determine minimum and maximum fsw for ZVS at light and full load
Thermal Management: Estimate junction temperature of switches and diodes at rated power
Output Ripple Analysis: Measure and reduce ripple via Cout and Lout tuning