The utilization of power converters in a distribution network could give rise to stability problems, especially when the penetration is high. The existing literature studies the modeling and stability of converters with specific control or synchronization methods. However, the types or the control schemes of converters are normally different in an actual grid, and moreover, the line impedance plays an important role on the network stability. In this regard, this article aims at studying the modeling and stability issues of a two-bus electric network with both grid-forming (GFM) and grid-following converters. The main purpose is to provide design guidelines and solution of two-bus system with converters for stable operation. The interactions between the converters in various scenarios will be investigated by considering the effect of line impedance. More importantly, a filter-based stabilized control strategy will be proposed for the GFM converters to mitigate the oscillation in the network. Simulation and experimental results are provided to validate the effectiveness of the theoretical analysis and control strategy.