The idea of dodging the inductor sounds tempting for a variety of reasons - reduction of components and hence better reliability being only two of them !
However, there is just one reason due to which I would advise some caution with the design - DAB !! Assuming that this is going to be a broadcasting application, tampering with the transformer design has to be done with a lot of caution.
How about doing the redesign (with the air gap), making the transformer, and testing out to see if it will work ?
I think you will run into trouble. None of the literature on this type of inverter (that I have seen) suggests unifying the inductor and the transformer. They do two different things in the circuit. You may get very high switching transients, reduced primary to secondary coupling, and these lead to loss of efficiency. I suggest that you get a good circuit simulation program and experiment first before trying it in a prototype.
@Fatemeh: Please refer to the attached LC-DAB converter's schematic diagram. You can see that there is an inductor in series with the capacitor. I want to merge this inductor in transformer by increasing transformer's leakage inductance (i.e., by adding an air gap in the core).
@Sanjoy: Sir, there are few publications in which researchers have tried to do it on ferrite toroids cores (please see the attached figure), but with ETD cores increasing an air gap can also give us an increase in leakage inductance. I am thinking of testing it by comparing efficiency in both cases (i.e., with an extra inductor and by only transformer with air gap).
@Tony: Sir, there might be an increase in fringing loss along with saturation of the core and I think by increasing the number of turns can let us solve the saturation problem.
As you saw in my last message, I am not ruling out success at all ! But I am also not saying that your idea will be a sure-shot success !!
Across the past history of power electronics, researchers have attempted to reduce the number of inductors by similar tricks - the classic variations of the Cuk converter being one of the successful examples. The two motivating factors have usually been:
Reduction of the cores, which reduces cost, weight of the assembly, and makes it more portable in every respect.
Reduction of input and output ripple, which roughly speaking, plays flux ripples against each other reducing them in all fronts !
Regardless of the outcomes, I am sure the entire work will be a very interesting exercise. You may wish to be careful about an obvious challenging aspect of the design:
In a single-core configuration, whenever you attempt to increase the leakage flux, the magnetising flux tends to drop !
If you are careful about that aspect, I won't be surprised if you end up with a great design.
Putting an air gap in a magnetic circuit increases the reluctance and reduces the coupling between any two windings by increasing leakage flux. You won't get saturation effects because the gap reduces the flux not increases it. But you will then need more turns . . and it isn't a straightforward exercise - but one which you could well do and see what happens. You will get a number of effects, just be sure when analysing the circuit's behaviour either in an emulator or as a prototype, that you fully understand each effect and make sure it is helping you reach your target of an inductorless circuit! Best wishes!