Expiation of a broken Ramadan fast by masturbation

In this case, one would first have to repent and then make up the fast. Therefore, one only needs to make up the actual day of fasting that was invalidated and the major expiation of two months' consecutive fasting would not be obligatory in this case.

Invalidating one's obligatory fast is not a small matter for the Prophet, may Allah bless him and give him peace, said,

"Whoever breaks a fast-day of Ramadan without an excuse or dispensation could not requite it by fasting a lifetime, were he to do so [A: meaning that making up that day, while obligatory, does not remove the sin, though repentance does.]" (Reliance of the Traveler, p10.0).

In addition to this, if the fast was broken by something unlawful, such as masturbation, one should be more fearful of the consequences of his action and repent to Allah sincerely. One should intend never to repeat this again, and to avoid the things that lead him to this.

And Allah knows best.