Spectrum detection technology in cognitive radio includes two processes: channel sensing and channel monitoring. For each process, longer detection time may result in fewer opportunities for cognitive radios to fill in spectrum holes, while shorter sensing time may make cognitive radios miss the chance to detect the presence of primary users which will bring harmful interference to primary users. However, to make sure the detection time has a great relationship with the prior probability of the existence of the primary user in authorized channel, a general and universal authorized channel model is needed for cognitive radios' spectrum detection. In this paper, the duration of primary user's presence and absence is modeled as an exponential distribution, and energy detection method is adopted to detect the channel modeled above. By Monte Carlo simulation, we obtain that the receiver operating characteristic curves for the modeled channel is very similar with the theoretical curve. Therefore, the model is very effective for analyzing the performance of the spectrum detection algorithms in cognitive radio networks.