Because the switch must not switch into a low transient impedance.
Otherwise you lose the properties of low peak current, well defined current rate-of-rise, and controllability (PWM% ~ Vout).
For flyback, the switch turns on during one half-cycle, then only after turn-off, the secondary diode turns on. The transformer (or same inductor for the boost case, or both coupled together in SEPIC/Cuk case) stores energy, and on-state and off-state current rate is well defined, and control is effective. (Control isn't linear, in this case, mind: it actually goes as D/(1-D), indeed diverging as D --> 100%. This is why we prefer to design such converters for around 50% duty, so the expected range in duty (say, something like 20-60% under most conditions, transients included) isn't too far along the curve, and we can treat it as linear well enough.)
For forward, the switch turns on during one half-cycle, and the same voltage appears immediately at the output. If this voltage were clamped by a diode and dumped into a capacitor, only the transformer's leakage inductance (or strays alone for the buck equivalent!) would limit that current, and control would be impossible -- the output voltage would go from zero to essentially the secondary-reflected peak voltage over a tiny range of duty. Meanwhile the peak current will be massive if the capacitor voltage is far from the transformer's voltage, probably blowing the switch in the process.
So we put an inductor at the forward's secondary. But not just an inductor, we need to ensure the inductor's current itself is conserved between cycles (or for at least part of a cycle, in the case of DCM).
The LLC converter, takes these ideas and runs with them in a different direction. Suppose forward with the bad hard-rectified output, but shitty transformer (lots of leakage)? We can use that leakage as our rate-limiting inductor, but now we must 1. use a bridge / inverter (so the excess energy stored in that inductor isn't lost to snubbing...or worse), and 2. modulate frequency to control the output, and proportionally so, which... kinda really sucks (if we need a control range of 10x, we need a frequency range of 10x!).
So we make one more change: we cancel out some of that series inductive reactance, with series capacitive reactance. This causes resonance at a particular frequency, putting a sharp peak (or maybe rather shallow; depends on the load impedance) in the response, greatly reducing how much control range we need (namely: some factor above resonance, and no lower than resonance itself).
The downside is control complexity: now the gain vs. frequency response is highly nonlinear, so we expect the control will respond too quickly in some conditions, and rather slowly in others. We also want to avoid operating at or below resonance, and again, since resonance depends on load impedance, this is not straightforward to implement.
Including another inductor, gives us the LLC network, which has an inductor divider characteristic at high load impedances (light load) and high frequency, and a series resonant character at low frequencies. The resonant frequency varies with load impedance, but values can be chosen so that gain remains within certain bounds despite that change. The divider effect is convenient when we need near a nominal conversion ratio, though not very helpful if we need very different ratios (compare fixed voltage unit vs. adjustable bench supply).
The most important benefit of LLC, is that we can entirely avoid hard switching: this is a complete side-issue from the above discussion, but answers the question: how can we improve efficiency further, once we've squeezed out all the power dissipation from our otherwise-ideal components (inductors and capacitors)?
To see this, ask: what are our energy sinks in the square-wave converter case? In the forward or flyback converter, in DCM, the inverter must hard-switch on, starting from zero current and nonzero voltage, discharging at least its own capacitance, but also the rectifier's, and other strays in the circuit (there's some capacitance in the transformer itself, etc.). This energy is reactive (stored in C or L), but it's energy that is present, that must go away to complete the square wave falling edge -- we can't simply keep it ringing around (well, maybe, sort of, but we're much more likely to suffer EMI problems in that case, not to mention other unexpected energy sinks like eddy currents in the windings), so that energy must go away somehow, whether dissipated directly in the switch (intentionally slowing rise time), or in snubbers.
Conversely on turn-off, peak primary current has to go somewhere, before the secondary "knows" about it (i.e., discharging the leakage inductance). In the bridge type inverter (two-switch or half/full-bridge forward), this can be at least partially recycled into the supply, but extra voltage swing still results (the inductance discharges into the supply, then that voltage must relax back to zero -- drawing another small increment of energy).
And of those sinks, the switch turn-on self-dissipation is utterly unavoidable: the switch is the event that causes voltage to change, so there can be nothing else in the circuit to discharge its own capacitive energy but itself.
So we are fundamentally limited on switching loss, and thus efficiency, of a square-pulse type converter. Granted, we can choose arbitrarily low switching frequencies -- but this requires proportionally larger reactive components (inductor, transformer, capacitors), so gets highly cost- and size-prohibitive very quickly. (That said, I have heard of, for example, solar inverters even taking advantage of SiC MOSFETs, but doing so at 10-20kHz, damn the size (they're units installed under/beside an array of panels, who's going to notice another liter or two of volume?), to achieve very high efficiency (>98%?).)
With proper design and use (i.e. staying above resonance, but not too high so as to also manage turn-off losses), the LLC converter can fully recycle these losses due to device capacitances. Which makes LLC particularly attractive for budget-priced offerings, i.e. using Si rather than SiC MOSFETs (or even-cheaper Si IGBTs), and rather large ones indeed can be chosen as a result (reducing Rds(on) while increasing Coss). The remaining losses are due to whatever can't be managed in the reactive components, switch turn-off losses, and higher-order effects such as inverter and rectifier loop inductances.
Or, where compact size and high efficiency are paramount, the same of course applies to SiC or GaN switches, at proportionally higher frequencies.
Tim
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