Rectifier Modeling as Equivalent Resistance

• Full bridge rectifier with capacitive load (C big) and load resistor RDC
• Sinusoidal input current I sin(ωt) creates rectified current IX
• Average value of IX = (2/π) × I
• Output power = (2/π) × VD × I
• AC side sees square wave voltage VRE with fundamental component
• Fundamental of square wave = (4/π) × VD × sin(ωt)
• Equivalent AC resistance RA = (4/π) × VD/I
  • Alternative expressions: RA = (8/π²) × VD²/Power = (8/π²) × RDC
• Enables modeling rectifier as resistor for power transfer analysis under fundamental harmonic approximation

Series Resonant DC-DC Converter Structure

• Half bridge inverter (VDC input) → LC tank → transformer (N1:N2) → rectifier → VD output
• Inverter output VIN: square wave between VDC and 0, period 2π/ωs
• Fundamental harmonic approximation assumes sinusoidal tank current IL
• High Q tank loaded by rectifier system ignores harmonic currents
• Only fundamental components matter for power transfer

Converter Gain Analysis Model

• Inverter gain (GI): V_inverter1/VDC = 2/π (for half bridge)
• Tank gain (GT): |VR1|/|V_inverter1| - frequency dependent, controls power
• Transformer gain (GX): |VRE1|/|VR1| = N2/N1
• Rectifier gain (GR): |VD|/|VRE1| = π/4 (for full bridge)
• Total voltage gain: VD/VDC = GI × GT × GX × GR
• Tank gain is primary control variable via switching frequency

Tank Gain Characteristics

• Tank quality factor: Q = √(L/C)/Rr
• At resonance: tank gain = 1 (LC acts as short circuit)
• Above resonance: net inductive reactance causes voltage division, gain drops
• High Q: steep gain vs frequency characteristic
• Low Q: gradual gain vs frequency characteristic
• Operating point determined by required conversion ratio and load power

Control Strategy and Operating Modes

• Primary control: vary switching frequency to adjust tank gain
• Load variations affect equivalent AC resistance Rr
• Different power levels create different tank gain curves
• Light load challenges: tank Q approaches zero, wide frequency ranges
• Alternative control methods:
  • Burst control (on/off operation using output capacitor)
  • Phase shift control
  • Outphasing control
  • PWM control variants

Design Trade-offs and Applications

• Advantages:
  • Zero voltage switching capability at high frequencies
  • High efficiency possible (>96%)
  • Compact size for high power density
• Disadvantages:
  • Higher peak voltage/current stresses vs PWM converters
  • Complex analysis and control modeling
  • Poor power factor due to reactive components
• Tank topology choices:
  • Series resonant: gain ≤ 1, poor light load performance
  • Parallel resonant: high voltage gain possible, better light load
  • LCC/LLC tanks: combined properties

Induction Cooker Case Study

• Single switch quasi-resonant converter
• LC tank with inductor doubling as heating coil
• Ferrite pieces direct magnetic field to pan (load)
• Switch on: constant voltage ramps inductor current
• Switch off: parallel resonance rings voltage up/down
• Zero voltage switching with single active switch
• Power control via switch on-time duration
• High power factor operation:
  • Current ramp proportional to rectified line voltage
  • Power proportional to line voltage squared
  • Switching frequency >> line frequency
• Demonstration specifications:
  • Peak voltage: 700-800V
  • Peak current: 70A at 1800W
  • Burst mode at low power (500W)
• Cost effective: $50 retail price due to simple topology