This paper presents the analysis of a bidirectional series-resonant converter (SRC) for light loads working above or below resonance. In normal operation (heavy load), it is well known that the SRCs have a maximum voltage conversion ratio (m) equal to one. This occurs when the switching frequency (f(S)) equals the resonant frequency (f(0)) and power losses are neglected. This maximum can also be obtained for f(S) < f(0) when the switches are turned ON during a half-resonant period. Thus, zero-current switching can be achieved at both the turn-ON and turn-OFF processes. However, anomalous step-up behavior is found when the converter is attached to light loads. A comprehensive analysis of this phenomenon in the time-domain and in the state plane is presented. Based on the latter, an expression that estimates m and shows the influences of the parameters is obtained. With the aid of this expression, a solution that mitigates that effect is presented and implemented in a prototype, which is part of a bidirectional power chain for supercapacitors. This solution can be implemented for both f(S) > f(0) and f(S) < f(0).