Resonant Converters

Conventional PWM converters control output voltage by varying duty cycle while switching abruptly between on and off states. This hard switching causes significant power loss at high frequencies because the switch must simultaneously carry current and support voltage during transitions. Resonant converters resolve this by incorporating an LC resonant tank circuit that shapes the switch current or voltage waveform so that the switching transition occurs at zero current or zero voltage, eliminating the crossover loss entirely.

Core Concept Explanation

The fundamental problem with hard switching is that during a switch turn-on event, the device must conduct load current while simultaneously dropping from full bus voltage to near zero. The product of instantaneous current and voltage creates a power loss spike every switching cycle. At 100 kHz this happens 100,000 times per second, so even a small energy loss per transition accumulates to significant dissipation.

Resonant converters introduce an inductor Lr and capacitor Cr as a resonant tank whose natural oscillation is exploited to create zero crossings. In zero-current switching (ZCS), the resonant tank is in series with the switch. The inductor limits the current rise rate and the capacitor enables the current to swing naturally through zero. The switch is turned off at this zero crossing so there is no current to interrupt, eliminating turn-off losses completely.

In zero-voltage switching (ZVS), the resonant capacitor is placed in parallel with the switch or load. The capacitor voltage swings through zero before the switch is turned on, so the device begins conducting with zero voltage across it. This eliminates turn-on losses and the reverse recovery charge problem of the anti-parallel body diode. ZVS is especially effective in MOSFETs operating at megahertz frequencies.

Mathematical Expression

The natural oscillation of the tank circuit is described by the resonant frequency and the characteristic impedance. For a series or parallel LC tank:

fr = 1 / (2 x pi x sqrt(Lr x Cr))

The characteristic impedance Zr = sqrt(Lr / Cr) determines the peak resonant current for ZCS or the peak resonant voltage for ZVS. For ZCS operation, the peak switch current is:

Ipeak = Vin / Zr + Iload

For a ZCS converter to achieve zero crossing, the condition Vin / Zr must be greater than Iload must be satisfied. This means the resonant current amplitude must exceed the DC load current so the sum can swing through zero. This sets a minimum load condition below which ZCS is not achievable.

Output voltage control in resonant converters is typically achieved by varying the switching frequency relative to fr. Operating above fr results in inductive behavior (ZVS region) while operating below fr gives capacitive behavior (ZCS region). The voltage gain versus frequency characteristic is a resonant peak near fr.

Practical Understanding

The LLC resonant converter is the dominant topology used in modern high-efficiency power supplies. It uses a series inductor Ls, a magnetizing inductor Lm, and a series capacitor Cr. At resonant frequency the voltage gain equals the turns ratio and both ZVS of primary switches and ZCS of secondary diodes are achieved simultaneously, which is why LLC converters routinely achieve efficiencies above 97 percent in server and telecom applications.

One significant disadvantage of resonant converters is that the switching frequency must vary to regulate output against load changes, unlike PWM where frequency is fixed and duty cycle varies. This variable frequency operation complicates EMI filter design because the noise spectrum is not at a fixed frequency. Spread-spectrum techniques and careful filter design address this in production equipment.

ZCS is preferred at lower frequencies where diode reverse recovery is a problem, such as with slow bipolar transistors or when using SiC diodes. ZVS is preferred at higher frequencies with MOSFETs because MOSFET turn-on loss (due to charging of Coss) is eliminated and the body diode reverse recovery issue is avoided by ensuring the body diode conducts before the channel is enabled.

Given:
Series resonant converter, Lr = 50 uH, Cr = 20 nF

Why this formula applies:
The tank resonant frequency determines the switching frequency for ZCS operation

Formula:
fr = 1 / (2 x pi x sqrt(Lr x Cr))

Substitution:
fr = 1 / (2 x 3.1416 x sqrt(50e-6 x 20e-9))

Calculation:
Lr x Cr = 1e-12
sqrt(1e-12) = 1e-6
2 x pi x 1e-6 = 6.2832e-6

Final Answer:
fr = 1 / 6.2832e-6 = 159.15 kHz

Exam Tip: GATE frequently asks to identify whether a converter achieves ZVS or ZCS from circuit configuration. Series Lr-Cr with switch gives ZCS (current zero crossing). Capacitor in parallel with switch gives ZVS (voltage zero crossing). Also remember: ZVS requires operation above resonant frequency in LLC topology.

Mechanism: Resonant Waveform and Switching Condition

• ZCS forces the switch current to a sinusoidal resonant waveform so it naturally passes through zero. The switch is turned off at this instant so there is no current flowing through the device and therefore no turn-off energy loss.
• ZVS uses the resonant capacitor to discharge the switch voltage to zero before the gate signal is applied. The switch turns on with zero drain-source voltage so no capacitor charge energy is dissipated in the channel resistance.
• LLC resonant converters combine both mechanisms: ZVS of primary MOSFETs (operating above series resonant frequency) and ZCS of secondary diodes (operating at second resonant frequency involving Lm).
• Variable frequency control is the standard regulation method. Output voltage decreases as frequency increases above fr and increases as frequency approaches fr from above in LLC topology.
• Peak switch current in ZCS is higher than in PWM converters for the same average output, which is a trade-off against the reduction in switching loss.

Quick Revision

• ZCS: Resonant tank in series with switch. Current swings to zero. Switch turned off at zero current.
• ZVS: Resonant capacitor in parallel with switch. Voltage swings to zero. Switch turned on at zero voltage.
• Resonant frequency: fr = 1 / (2 x pi x sqrt(Lr x Cr)).
• Characteristic impedance: Zr = sqrt(Lr / Cr). Controls peak current or voltage stress.
• LLC converter achieves ZVS of primary and ZCS of secondary simultaneously at resonant frequency.
• Regulation is done by varying switching frequency, unlike fixed-frequency PWM converters.
• Exam trap: Confusing which topology achieves ZVS vs ZCS, or applying fixed-frequency PWM equations to resonant converter problems.