Recent advances in self-interference cancellation enable radios to transmit and receive on the same frequency at the same time. Such a full duplex radio is being considered as a potential candidate for the next generation of wireless networks due to its ability to increase the spectral efficiency of wireless systems. In this paper, the performance of full duplex radio in small cellular systems is analyzed by assuming full duplex capable base stations and half duplex user equipment. However, using only full duplex base stations increases interference leading to outage. We therefore propose a mixed multi-cell system, composed of full duplex and half duplex cells. A stochastic geometry based model of the proposed mixed system is provided, which allows us to derive the outage and area spectral efficiency of such a system. The effect of full duplex cells on the performance of the mixed system is presented under different network parameter settings. We show that the fraction of cells that have full duplex base stations can be used as a design parameter by the network operator to target an optimal tradeoff between area spectral efficiency and outage in a mixed system.