In this study, a dual band band-stop filter based on split ring resonators (SRR) over a ground plane with unequal rings is proposed and characterised. The proposed SRR design method, which is demonstrated here, ensures the control of the resonance frequencies and their respective bandwidths. The lengths and coupling regions of each ring are arbitrary, making possible the control of, not only the separation between the two generated resonances, but also the bandwidth ratio between the pass-bands, or quality factors. The full characterisation of the resonators involves the computation of the resonant frequencies and the current distributions at the resonances. These current distributions are used to obtain the electromagnetic energy stored in the resonator that, in turn, is required to estimate the quality factor of each resonance. The dual band bandstop filter is composed by four proposed SRRs coupled to a transmission line showing that, indeed, both the centre frequencies and its bandwidth ratio can be controlled. The presented results confirm the reliability of the proposed method in the design of passive devices.