Series Resonant Converter (SRC)

A bridge inverter drives a series Lr–Cr tank in series with the load, so the tank behaves like a frequency-controlled valve. Sweep the switching frequency near resonance and the output follows — with soft switching, low EMI and near-sinusoidal currents. This is the simplest member of the resonant-converter family and the gateway to LLC.

Table of Contents:

Introduction — switching softly, not squarely

Every hard-switched converter on this site — buck, boost, forward, the bridges — shares one problem: the switch turns on and off while it is carrying current and blocking voltage at the same instant. That overlap is switching loss, and it grows with frequency. It is the wall you hit when you try to shrink the magnetics by switching faster.

A resonant converter ducks around that wall. Instead of feeding the transformer a hard square wave, it feeds a square wave into an L–C resonant tank. The tank rings, so the current handed to the switches is a smooth near-sinusoid that naturally passes through zero. Time the switching to those zero crossings and the switch changes state while its current or voltage is (almost) zero — soft switching. Losses fall, EMI falls, and the converter can run at hundreds of kilohertz with a small, cool transformer.

The series resonant converter (SRC) is the simplest of the family: the tank inductor Lr and tank capacitor Cr sit in series with the load. That single choice explains everything the SRC does well and badly. This page builds it from the ground up — the circuit, the six switched modes, the waveforms, why it is run above resonance, the frequency-controlled gain curve, and the one weakness (light-load regulation) that led engineers to the LLC converter.

What is a Series Resonant Converter?

A series resonant converter is an isolated DC-DC converter in which a switching bridge drives a series Lr–Cr resonant tank that sits in the path between the source and the load. Output voltage is regulated by changing the switching frequency, not the pulse width. It is built from these parts:

  • A switching bridge (inverter). A full bridge (Q1–Q4) or a half bridge chops the DC input Vg into a square-wave voltage vs of ±Vg (or 0 to Vg for a half bridge).
  • A series resonant tank: Lr then Cr. This is the defining element. In series with the load, the tank forms a frequency-dependent divider — it passes energy easily at its resonant frequency and blocks it away from resonance.
  • An isolation transformer. Provides galvanic isolation and scales the voltage by its turns ratio n. The tank current flows through the primary.
  • An output rectifier + filter. A diode bridge (or synchronous rectifier) turns the near-sinusoidal tank current into DC, smoothed by a filter capacitor Cf across the load R.

The tank is characterised by two numbers. Its resonant frequency fr = 1 / (2π√(LrCr)) is where it rings; its characteristic impedance Zo = √(Lr/Cr) sets how hard it pushes back. The ratio of Zo to the (reflected) load resistance is the quality factor Q, which decides how sharply the output responds to frequency.

The one-sentence version. A series resonant converter puts an Lr–Cr tank in series with the load and slides the switching frequency around the tank’s resonance to control the output — buying soft switching and low EMI, at the cost of being a step-down-only converter that struggles to regulate at light load.

Block Diagram

Block diagram of a series resonant converter: a DC input feeds a four-switch bridge inverter driven by a variable-frequency controller, then a series Lr-Cr resonant tank, then an isolation transformer, then a diode-bridge rectifier, then an output filter capacitor, then the load, with isolated feedback that adjusts the switching frequency.
Figure 1: Series resonant converter block diagram — a bridge inverter feeds a series Lr–Cr tank, transformer and rectifier; feedback regulates by adjusting the switching frequency

Read it left to right: the DC input is chopped by the bridge inverter into a square wave, filtered by the series resonant tank into a near-sinusoid, passed through the transformer, rectified and smoothed for the load. The control loop is what marks this as a resonant converter — feedback does not adjust a duty cycle; it adjusts the switching frequency, sliding the operating point along the tank’s gain curve.

Circuit Diagram & Construction

Circuit diagram of a series resonant converter: four MOSFETs Q1 to Q4 with body diodes form a full bridge across the DC input Vg, producing nodes a and b. A series resonant inductor Lr and capacitor Cr connect node a to the transformer primary; node b returns the primary. The single secondary feeds a four-diode bridge rectifier D1 to D4 into a filter capacitor Cf and load R, giving the output voltage Vo.
Figure 2: The dc-dc series resonant converter power circuit — MOSFET bridge (output Vs) → series tank L, C (tank current x1, tank-cap voltage x2) → transformer → diode rectifier → filter capacitor Cf (voltage x3) and load R

This is the power stage of the series resonant converter. What matters is not just the parts, but the three state variables the whole model is built on — so read the circuit in terms of them:

x1 — tank inductor currentThe current in the series resonant inductor L. It is the main resonating variable, and (as the next section shows) its sign decides which output diodes conduct.
x2 — tank capacitor voltageThe voltage across the series resonant capacitor C. The tank current x1 charges and discharges it every cycle.
x3 — filter capacitor voltageThe voltage across the output filter capacitor Cf — i.e. the output voltage delivered to the load R.
Vs — MOSFET-bridge outputThe voltage the switching bridge applies to the tank. The switches set it to +Vg, 0 or −Vg; it is varied by frequency (and, in some designs, symmetrical-duty) control.

Reading the power path from the input: a dc source Vg feeds a MOSFET bridge whose output Vs is a switched voltage; that drives the series resonant tank (inductor L and capacitor C in series); the tank current x1 passes through the transformer to the output diode rectifier, whose forward drop is written Vf; and the rectified current feeds the filter capacitor Cf and the load R.

Taking the converter to run in continuous conduction mode (CCM), the whole circuit can be written as a single nonlinear state-space model:

L · dx1/dt = s·Vg − x2 − rLoss·x1 − sgn(x1)·(x3 + 2Vf)
C · dx2/dt = x1
Cf · dx3/dt = |x1| − x3/R

Each line is one physical law of the circuit above — worth reading term by term:

  • Inductor equation. The tank current x1 is pushed by the bridge voltage s·Vg, opposed by the tank-capacitor voltage x2, by the loss drop rLoss·x1 (rLoss is the inductor resistance plus the capacitor’s series resistance), and by the reflected output term sgn(x1)·(x3+2Vf) — the output voltage plus two diode drops, with a polarity that follows the direction of the current.
  • Tank-capacitor equation. C·dx2/dt = x1: the resonant capacitor simply integrates the tank current.
  • Output equation. Cf·dx3/dt = |x1| − x3/R: the filter capacitor is charged by the rectified tank current |x1| and discharged by the load current x3/R.
  • The logic input s. s ∈ {−1, 0, +1} is the logic input: it represents the state of the input switches and so fixes the bridge output Vs = s·Vg — +Vg, zero, or −Vg.
Two direction-dependent terms. Notice the sgn(x1) and the |x1| in the model — both flip with the direction of the tank current. They are exactly what make this a switched circuit rather than a single fixed linear one, and, as the next section shows, sorting them by the sign of x1 together with the three values of s is what produces the six switched modes of operation.

Principle of Operation

Think of the tank as a frequency-selective filter standing between the square-wave bridge and the load. A square wave is really its fundamental sine plus a stack of harmonics. A series Lr–Cr tank has its lowest impedance right at resonance, so it lets the fundamental through and heavily attenuates the harmonics. What reaches the transformer and load is therefore an almost pure sine wave at the switching frequency — this is the basis of the standard “first-harmonic approximation” used to analyse the SRC.

Now the key idea — how the frequency sets the output:

  • At resonance (fs = fr), Lr and Cr cancel: the tank is a plain wire (just its small resistance). Almost the entire fundamental reaches the load, so the gain is at its maximum, M = 1. The current is exactly in phase with the square wave.
  • Away from resonance (either side), the tank’s net reactance grows, dropping more of the voltage across Lr–Cr and less across the load. The gain falls. So moving the switching frequency away from fr turns the output down.
  • The converter is normally operated above resonance (fs > fr). There the tank looks inductive, the current lags the voltage, and the switches get zero-voltage switching — the low-loss, low-EMI sweet spot for MOSFET bridges.

Because the tank passes only near-resonant energy, an SRC is a step-down converter: the best it can do is deliver the full fundamental at resonance (M = 1). It cannot boost. To raise or lower the output within that ceiling, the controller simply slews the frequency up (less output) or down toward fr (more output).

Modes of Operation (six switched states)

The cleanest way to describe the modes is to treat the converter as a switched system made of affine subsystems. The reason is simple: because the model above contains the two direction-dependent terms sgn(x1) and |x1|, the single nonlinear model splits into a set of ordinary linear pieces — one for every combination of the tank-current sign and the switch state. Counting them gives exactly six modes, shown as the six sub-circuits in the figure below. Each one is fixed by just two things:

  • the sign of the tank current x1 (x1 > 0 or x1 < 0), which sets the sign of the reflected output term ±(x3+2Vf) and of the charging term ±x1 in the output equation; and
  • the logic input s ∈ {+1, 0, −1}, which fixes the bridge voltage Vs = s·Vg. Here s = 0 is the dead-time state in the switching between the two switches.
The six switched modes of a series resonant converter, arranged as six small bridge circuits. Each mode is fixed by the sign of the tank current x1 and the logic input s, which is plus one, zero, or minus one. Mode 1: x1 positive, s plus one, bridge output Vs equals plus Vg. Mode 2: x1 positive, s zero, the dead-time state, Vs equals zero. Mode 3: x1 positive, s minus one, Vs equals minus Vg. Mode 4: x1 negative, s plus one. Mode 5: x1 negative, s zero, dead time. Mode 6: x1 negative, s minus one. The conducting devices are highlighted in green and the orange arrow shows the direction of the tank current x1; the output diode pair that conducts is set by the sign of x1.
Figure 3: The six switched modes of the SRC — each fixed by the sign of the tank current x1 and the logic input s ∈ {+1, 0, −1} (s = 0 is the dead-time state); green = conducting device, orange arrow = direction of x1

Writing the model out for each of the six conditions gives six affine (linear-plus-constant) systems. Only two things change from row to row — the s·Vg term (set by s) and the sign of the reflected output (x3+2Vf) and of the charging term (set by the sign of x1) — while the tank- capacitor equation C·dx2/dt = x1 is the same throughout:

ModeConditionVsL·dx1/dt =Cf·dx3/dt =
1x1 > 0, s = +1+Vg+Vg − x2 − rLossx1 − (x3+2Vf)+x1 − x3/R
2x1 > 0, s = 0  (dead time)0−x2 − rLossx1 − (x3+2Vf)+x1 − x3/R
3x1 > 0, s = −1−Vg−Vg − x2 − rLossx1 − (x3+2Vf)+x1 − x3/R
4x1 < 0, s = +1+Vg+Vg − x2 − rLossx1 + (x3+2Vf)−x1 − x3/R
5x1 < 0, s = 0  (dead time)0−x2 − rLossx1 + (x3+2Vf)−x1 − x3/R
6x1 < 0, s = −1−Vg−Vg − x2 − rLossx1 + (x3+2Vf)−x1 − x3/R

Reading the table by the two halves of the switching cycle:

  • Modes 1–3 (x1 > 0). The tank current is positive, so the reflected output term is −(x3+2Vf) and the filter capacitor is charged by +x1 (one output-diode pair conducts). Within this half the logic input steps the bridge through Vs = +Vg (mode 1), the dead-time state Vs = 0 (mode 2), and Vs = −Vg (mode 3).
  • Modes 4–6 (x1 < 0). The current has reversed, so the other output-diode pair conducts: the reflected term flips to +(x3+2Vf) and the capacitor is charged by −x1 (= |x1|). Again s runs the bridge through +Vg, 0 and −Vg (modes 4, 5, 6).
Why split it into six. The single state-space model carries the sgn(x1) and |x1| nonlinearities, which are “hard” and awkward to work with directly. Fixing the sign of x1 and the value of s removes them: inside each of the six modes the converter is an ordinary linear (affine) circuit, ẋ = Aix + bi. Those six affine states are the complete switched-mode picture of the converter.

Waveforms Explained in Detail

Series resonant converter waveforms over two switching periods at above-resonance operation: the two diagonal gate pairs firing alternately; the bridge output voltage vs as a bipolar square wave; the tank inductor current iLr as a near sinusoid lagging the square wave so it is still in the diodes at each turn-on, giving zero-voltage switching; the tank capacitor voltage vCr as a larger sinusoid lagging the current by ninety degrees; the rectified output current as sine humps at twice the switching frequency; and the smooth output voltage Vo held nearly constant by the filter capacitor.
Figure 4: SRC waveforms (above resonance, fn = 1.2, Q = 1.5) — gate pairs, square-wave vs, near-sinusoidal tank current iLr (lagging → ZVS), tank-capacitor voltage vCr, rectified output current, and the smooth output Vo

Read the traces together and the converter’s whole behaviour is in one picture:

  • Gates. The two diagonal pairs fire alternately, each for about half the period, 180° apart, with a small dead time. Crucially, the controller regulates by changing the frequency of this pattern, not its width.
  • Bridge voltage vs. A clean bipolar ±Vg square wave — the raw drive the tank has to filter.
  • Tank current iLr. A near-sinusoid, because the tank passes essentially only the fundamental. Above resonance it lags vs (about 29° here). Look at each switching instant (marked): the current is still flowing the “old” way through the body diodes, so the incoming switches turn on at zero volts.
  • Tank-capacitor voltage vCr. Cr integrates the current, so vCr lags iLr by 90° and swings a large sinusoid. It stores and returns energy every cycle; its peak sets the voltage rating of Cr and can exceed Vg.
  • Rectified output current. The diode bridge folds iLr into a train of sine humps at twice the switching frequency. Their average is the load current Io.
  • Output voltage Vo. Nearly flat, with only a small ripple at 2·fs that Cf smooths. Its level is set by how far fs sits from fr.

These are the fundamental (quasi-sinusoidal) waveforms — the standard way to picture an SRC. In a real converter the current is a slightly distorted sine, but the phase relationships and the soft-switching story are exactly as drawn.

Resonance, ZVS & ZCS — the three regions

Whether the SRC switches softly — and how — depends entirely on which side of resonance you operate. The tank current’s phase relative to the bridge voltage tells the whole story:

Three panels comparing tank-current phase in a series resonant converter. Below resonance the current leads the square-wave voltage, the tank is capacitive and gives zero-current switching but risks hard diode reverse recovery. At resonance the current is in phase and the gain is at its maximum. Above resonance the current lags, the tank is inductive and gives zero-voltage switching, the preferred region for MOSFET bridges.
Figure 5: The three operating regions — below resonance (capacitive, ZCS), at resonance (maximum gain), and above resonance (inductive, ZVS, the region MOSFET bridges use)
  • Below resonance (fs < fr) — capacitive, ZCS. The net tank reactance is capacitive, so the current leads the voltage. Switches turn off near a current zero (zero-current switching). The catch: at turn-on the MOSFET body diode is forced to recover hard, which is lossy and noisy — so this region is generally avoided with MOSFETs (it can suit thyristor or IGBT designs).
  • At resonance (fs = fr) — maximum gain. The tank is purely resistive, current and voltage are in phase, and the output is at its ceiling, M = 1.
  • Above resonance (fs > fr) — inductive, ZVS. The current lags. During each dead time the tank current charges/discharges the switch capacitances and forces the incoming body diode to conduct, so the switch turns on at zero voltage. This is the region almost every MOSFET-based SRC (and LLC) is designed to live in.
Stay above resonance. Because the gain curve is nearly symmetric about fr, the same output can often be produced just below or just above resonance — but only the above side gives clean ZVS. Straying below resonance during transients or startup can trigger hard reverse-recovery of the body diodes and destroy the bridge, so practical controllers include a hard lower-frequency clamp.

Voltage Gain & Frequency Control

Using the first-harmonic approximation, the tank plus reflected load behaves like a series R–L–C driven by the fundamental of the square wave. That gives the SRC’s signature gain curve:

M(fn) = 1 / √( 1 + Q² · (fn − 1/fn)² )    where fn = fs/fr,   Q = Zo/Rac
Voltage-gain curves of a series resonant converter versus normalised frequency fn for several load quality factors Q. Every curve peaks at gain one at fn equal to one and falls off both sides, so the converter always steps down. Higher Q gives a sharper, taller peak. As Q tends to zero at no load, the gain stays near one for all frequencies, which is why the series resonant converter cannot regulate its output down at very light load. The region above resonance, fn greater than one, is inductive and gives zero-voltage switching.
Figure 6: The SRC voltage-gain family M(fn) for several load factors Q — always ≤ 1 (step-down), peaking at resonance; the flat Q→0 curve shows the no-load regulation problem

Three things to read off this curve, each a design consequence:

  • It is always a step-down. Every curve tops out at M = 1 at resonance. An SRC cannot make its output larger than the input reflected through the turns ratio — it can only reduce it. To raise the output toward the ceiling, move fs down toward fr; to lower it, move fs up.
  • Load changes the curve. Higher Q (lighter load impedance / higher load current) sharpens the peak; lower Q (heavy load) flattens it. A fixed frequency therefore gives different gains at different loads, so the controller must retune fs as the load moves.
  • The no-load problem. As the load falls to zero, Q → 0 and the curve becomes almost flat at M ≈ 1 for every frequency. No frequency can pull the output down — to regulate a no-load SRC you would need an infinitely high frequency. This single limitation is the reason the LLC converter (which adds a parallel magnetising inductance to keep control at light load) largely replaced the plain SRC in modern supplies.

Key Formulas

Resonant frequencyfr = 1 / (2π√(LrCr))
Characteristic (surge) impedanceZo = √(Lr/Cr) = ωrLr = 1/(ωrCr)
Loaded quality factorQ = Zo / Rac
AC-equivalent load (full-bridge rectifier, cap filter)Rac = (8/π²) · n² · R
Normalised frequencyfn = fs / fr
Fundamental voltage gain (tank)M = 1 / √(1 + Q²(fn − 1/fn)²)
Output voltage (approx.)Vo ≈ n · M · Vg  (full bridge);   ½ that for a half bridge
Peak gain / operating limitMmax = 1 at fn = 1; run at fn > 1 for ZVS

Rac is the trick that makes the linear gain formula work: the diode rectifier plus its constant-voltage load do not look like a plain resistor to the tank, but to the fundamental they behave like an equivalent resistance Rac = (8/π²)·n²·R. Feeding that into a textbook series-RLC divider gives the gain curve above.

Worked Example

One consistent tank, used by every figure on this page. Follow the numbers and the curve checks out.

GivenVg = 400 V, Lr = 47 µH, Cr = 53 nF, full bridge
Resonant frequency   fr = 1/(2π√(LrCr))1 / (2π√(47µ × 53n)) ≈ 101 kHz
Characteristic impedance   Zo = √(Lr/Cr)√(47µ / 53n) ≈ 30 Ω
Operating frequency   fs = 1.2·fr≈ 121 kHz (above resonance → ZVS)
Chosen load factor   Q = Zo/Rac1.5
Tank phase lag   φ = atan(Q(fn−1/fn))atan(1.5 × (1.2 − 0.833)) ≈ 29° (current lags → inductive)
Voltage gain   M = 1/√(1+Q²(fn−1/fn)²)1/√(1 + 1.5²×0.367²) ≈ 0.88
To raise the outputlower fs toward fr (M → 1); to lower it, raise fs

At fn = 1.2 the tank passes about 88 % of the fundamental to the (reflected) load, the current lags by ~29° so the bridge switches at zero voltage, and if the load lightens the controller must push fs higher to hold Vo — until, near no load, it simply runs out of room. Slide fs down toward 101 kHz and the gain climbs toward 1; that is the entire control law.

Advantages & Disadvantages

Advantages

  • Soft switching. Run above resonance, the bridge turns on at zero voltage — low switching loss and high efficiency, especially at high frequency.
  • Low EMI. The tank current is a near-sinusoid, not a hard-edged square, so high-frequency noise is far lower than in a hard-switched converter.
  • Small, cool magnetics. Soft switching allows very high frequency, which shrinks the transformer; Lr can even be the transformer’s leakage.
  • Inherent DC blocking. The series capacitor Cr stops any DC reaching the transformer, so the core can’t walk into saturation — no flux-balancing circuit needed.
  • Natural short-circuit tolerance. Above resonance the tank impedance limits the current; a shorted output is a manageable, not catastrophic, condition.

Disadvantages

  • Step-down only. The gain never exceeds M = 1; the SRC cannot boost.
  • Poor light-load / no-load regulation. As Q → 0 the gain flattens near 1, so the output can’t be pulled down at light load without impractically high frequency — the SRC’s defining weakness.
  • Variable-frequency control complicates EMI filtering and magnetic design (the operating frequency is a moving target) and can demand a wide frequency range.
  • Large circulating current. Energy sloshes in the tank each cycle (big vCr), adding conduction loss even at light load.
  • Output ripple. With only a capacitor filter and pulsed diode current, output ripple current in Cf is high — the capacitor must be rated for it.

Applications

  • High-voltage DC supplies (X-ray, electrostatic, laser, CRT) — the tank naturally handles the transformer’s large leakage and parasitic capacitance, and limits fault current.
  • Induction heating and ultrasonic drives, where a resonant load is the point.
  • Battery chargers and telecom rectifiers that run at a fairly constant load, where the no-load weakness doesn’t bite.
  • The conceptual parent of the LLC converter — today’s dominant isolated DC-DC topology for PC, server and adapter supplies, which is a series resonant converter with an added parallel inductance to fix light-load regulation.
  • Teaching and analysis — the SRC is the cleanest place to learn resonant conversion, ZVS/ZCS and frequency control before tackling LLC or LCC.

In short: the SRC is the foundation of soft-switched conversion. Where the load is steady it is used directly; where the load swings from full to zero, its close relative the LLC converter takes over — but LLC only makes sense once you understand the series resonant converter first.

Frequently Asked Questions – FAQs

A series resonant converter is an isolated DC-DC converter that puts an inductor and capacitor (the resonant tank) in series with the load. A switching bridge feeds a square wave into the tank; the tank rings and passes mainly a sine wave to the transformer and rectifier. Because the tank is a frequency-selective filter, the output is controlled by changing the switching frequency, not the pulse width. Operated above resonance, the switches turn on at zero voltage, so the converter is efficient and quiet. Its main limits are that it can only step the voltage down and it struggles to regulate at very light load.

By varying the switching frequency. The series tank has its lowest impedance at its resonant frequency fr, so the gain is highest (equal to one) when the switching frequency equals fr, and it falls as the frequency moves away. To raise the output, the controller moves the switching frequency down toward resonance; to lower the output, it moves the frequency up. This is called frequency modulation or frequency control, and it replaces the pulse-width modulation used in hard-switched converters.

The resonant frequency is fr = 1 / (2 pi times the square root of Lr times Cr). It is the frequency at which the inductor and capacitor reactances cancel, leaving the tank at its lowest impedance. The characteristic impedance is Zo = square root of (Lr divided by Cr); it measures how strongly the tank reacts off resonance and, divided into the reflected load resistance, defines the quality factor Q. For example, Lr = 47 microhenry and Cr = 53 nanofarad give fr of about 101 kHz and Zo of about 30 ohm.

Above the resonant frequency the tank looks inductive, so the tank current lags the bridge voltage. That lag means the current is still flowing through a switch's body diode at the moment the switch is told to turn on, so it turns on with zero voltage across it. This zero-voltage switching almost eliminates turn-on loss and keeps EMI low. Below resonance the tank is capacitive and the current leads, which forces the body diodes to recover hard at turn-on, causing loss and noise. So MOSFET-based SRCs are always designed to operate above resonance.

Zero-voltage switching (ZVS) means the switch turns on while the voltage across it is zero; it happens above resonance where the current lags and the body diode conducts just before turn-on. Zero-current switching (ZCS) means the switch turns off while the current through it is zero; it happens below resonance where the current leads. MOSFET bridges prefer ZVS because their body diodes recover badly, so the above-resonance region is used. ZCS suits devices like thyristors and some IGBTs where turn-off loss dominates and body-diode recovery is not an issue.

The shape of the gain curve depends on the load through the quality factor Q. Under heavy load Q is high and the curve is sharp, so frequency has strong control over the output. As the load lightens, Q falls, and the gain curve flattens out near a value of one for every frequency. At no load the gain stays close to one no matter how high the frequency goes, so there is no frequency that pulls the output down to the target. In practice the converter would have to run at an impractically high frequency. This is the classic no-load regulation problem of the SRC and the main reason the LLC converter, which adds a parallel magnetizing inductance, replaced it in most modern supplies.

It is step-down only. The tank gain reaches its maximum value of one exactly at resonance and falls below one at every other frequency, so the converter can never deliver more than the full input reflected through the transformer turns ratio. To get a higher output voltage you must use a larger turns ratio, not a higher tank gain. If you need a converter that can both step up and step down while keeping soft switching, the LLC converter, which can achieve gain above one below its main resonance, is the usual choice.

Over one switching period the converter passes through six switched states, each defined by the sign of the tank current and the bridge state s, which is plus one, zero, or minus one. With positive tank current: s plus one has the diagonal MOSFETs delivering power; s zero is a dead time where the body diodes freewheel; s minus one has the incoming switches gated on while their diodes still carry the current, giving zero-voltage turn-on. The next three modes are the mirror image with negative tank current. In every mode the output rectifier pair is picked by the sign of the current. Each of the six is an affine (linear) state, which is why the converter is described as a switched affine system.

Because the resonant tank already shapes the current into a sinusoid, the rectifier delivers smooth sine humps rather than the chopped square pulses a hard-switched converter produces. A simple capacitor across the load is enough to average those humps into DC, so no bulky output inductor is required. This also keeps the tank current genuinely resonant: the output looks like a constant-voltage load in series with the tank, which is exactly what the first-harmonic gain analysis assumes. The trade-off is that the filter capacitor sees a large ripple current and must be rated for it.

The LLC converter is a series resonant converter with one extra element: a magnetizing (parallel) inductance across the transformer primary, which adds a second, lower resonance. That parallel inductance keeps the gain controllable even at no load, curing the SRC's biggest weakness, and it lets the converter reach a gain above one below the main resonance, so it can both step up and step down. Everything else, the bridge, the series Lr and Cr, the rectifier, the frequency control, and the above-resonance ZVS, carries straight over from the SRC. That is why the SRC is the right place to start before studying LLC.

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