The exploitation of slight imperfections of transmitters' hardware for identification of wireless devices has recently emerged as an effective method for security enhancement in wireless access networks. Previously, we introduced a model-based approach for device identification based on the imperfections of two main wireless transmitter components: 1) the digital-to-analog converter and 2) the power amplifier. Here, motivated by applications with transmit power control mechanisms, we analyze the degree to which a device can be identified from the unique, power mode independent characteristics of a third main component: the RF oscillator. The model-based device identification method introduced here allows for effective device identification even from short time records at relatively low signal-to-noise ratios when exploiting imperfections of commercially used RF oscillators.