A fuel injector includes a forward end wall and an aft end wall. The fuel injector further includes side walls that extend between the forward end wall and the aft end wall. The forward end wall, the aft end wall, and the side walls collectively define an opening for passage of air. At least one fuel injection member is disposed within the opening and extends between the end walls. A fuel circuit is defined within the fuel injector. The fuel circuit includes an inlet plenum defined within the forward end wall of the fuel injector. The fuel circuit further includes a fuel passage that extends from, and is in fluid communication with, the inlet plenum. The fuel passage is defined within the at least one fuel injection member. The fuel passage has a cross-sectional area that varies along a length of the fuel injection member.