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For classical resistive-based signal transduction methods, constant-power (CP) and constant-current (CC) activation methods have been utilized since the 1970s. However, since the discovery of carbon nanotube (CNT) in 1991, not much has been done in the past 20 years in terms of comparing how these transduction methods affect CNT-based sensor output. In this paper, we compare the responsivity, sensitivity, transient response, and instantaneous power consumption of CNT sensors activated by CC and CP modes. As an application example, multiwall CNTs were functionalized with COOH groups and used as ethanol (alcohol) vapor sensors. A CP control circuit has been built in order to test the CNT-based ethanol vapor sensors. A commercial source meter was used to activate the CNT sensors under CC mode. The CP configuration was shown to be effective in minimizing the self-heating effect, which is a significant factor that affects sensor performance, especially for resistive-based sensors. Compared to CC mode, CP mode of sensor activation demonstrated not only shorter transient response time but also larger responsivity, especially when the input activation power is low or ethanol concentration is relatively high.