Electronic – Difference series resonant and LLC DC/DC converter

The Q and M curves show that the resonant frequency is a property of the transformer, the load and the series capacitor. \$f_o\$ isn't necessarily a 'shorted' resonant frequency but a mostly-load-independent second resonant point predominantly controlled by the leakage inductance and series capacitor.

The switching frequency is indeed controlled by the some form of control IC (usually a PWM). The frequency of operation will vary as a function of input line and load, and should stay above the worst-case (minimum load) resonant peak to ensure ZVS over the whole range. You are correct in that operation below the worst-case peak gain forces the converter into an uncontrolled region and should be avoided.

LCD TV and laptop adapters are usually < 24V. If the designer was able to use a schottky diode for the output rectifier, you don't have to rely on forced commutation from the primary to reduce losses. The best way to tell if you're suffering from excessive reverse recovery loss is to put a current probe in the secondary and measure the reverse recovery current. Operating this 70V converter above resonance means they're not soft-commutating the secondary (which isn't necessarily bad) to reduce conduction losses (less circulating current in the primary).

With the schematic posted as is, when Q1 turns off, in the ideal case, there is no current path available as you said. In the real world, a large positive voltage would appear at the drain of the Q1. Unless D1 breaks down first, the most likely current path is through Q1 under Vds breakdown. I think the circuit can actually work under this condition because a MOSFET can survive Vds breakdown if the power being dissipated is low enough.

By the way, infinite inductor means infinite impedance. Therefore an infinitesimal amount of current corresponds to a voltage approaching infinity. So the assumption such a (unloaded) transformer as being a short is not right.

In the real world, a common scheme of resetting the magnetizing current is by an extra reset winding on the transformer.

Going back to the diagram post, with the schematic as is, the current would not behave as illustrated. In order for the current to behave as illustrated, the transformer needs to be shorted by something when Q1 is off. One easy way to do something close to that is to put a diode (sometimes called a flyback diode in some applications) across the primary. Such a diode would not produce a working design in this application.