It is well known that cognitive radio (CR) techniques have great potential for supporting future demands on the scarce radio spectrum resources. For example, by enabling the utilization of spectrum bands temporarily not utilized by primary users (PUs) licensed to operate on those bands. Spectrum sensing is a well-known CR technique for detecting those unutilized bands. However, the spectrum sensing outcomes cannot be perfect and there will always be some misdetections and false alarms which will affect the performance thereby degrading the quality of service (QoS) of PUs. Continuous time Markov chain (CTMC) based modeling has been widely used in the literature to evaluate the performance of CR networks (CRNs). A major limitation of the available literature is that all the key factors and realistic elements such as the effect of imperfect sensing and state dependent transition rates are not modeled in a single work. In this paper, we present a CTMC based model for analyzing the performance of CRNs. The proposed model differs from the existing models by accurately incorporating key elements such as full state dependent transition rates, multi-channel support, handoff capability, and imperfect sensing. We derive formulas for primary termination probability, secondary success probability, secondary blocking probability, secondary forced termination probability, and radio resource utilization. The results show that incorporating fully state dependent transition rates in the CTMC can significantly improve analysis accuracy, thus achieving more realistic and accurate analytical model. The results from extensive Monte Carlo simulations confirm the validity of our proposed model.