Two multi-band filters operating in the 1-10 GHz range are designed, analytically studied and experimentally verified. The filters are developed by making modifications to a series capacitively coupled, microstrip line filter. The middle section of the microstrip line is widened and rectangular slots are etched on it. Widening increases the effective dielectric constant which helps in miniaturization of the circuit. On the other hand, the rectangular slot cause various longitudinal, transverse and slot mode resonances to be excited resulting in multi-band operation. An extensive parametric analysis with respect to the physical parameters of the filter leading to the development of a semi-empirical model is presented. The model can be used to predict the resonant frequencies with sufficient accuracy for a given geometrical structure. The model also predicts the limit of miniaturization achievable with the presented design. The proposed filters besides being compact have good out of band rejection and are easy to design and fabricate without the need of additional matching circuits.