A small band-gap carbon nanotube (SBG CNT) with a large diameter of 4 nm has been used to fabricate ambipolar field-effect transistors (FETs) with ultrahigh carrier mobility of more than 18 300 and 8300 cm(2)/V x s for holes and electrons, respectively. Using a top-gate device geometry with 12 nm HfO(2) being the gate oxide, the SBG CNT-based FET exhibits an almost perfect symmetric ambipolar transfer characteristic without any noticeable hysteresis, and a highly efficient frequency doubler is constructed based on this near perfect ambipolar FET. The SBG CNT-based frequency doubler is shown to be able to operate in a large signal mode where the input AC signal, being applied to the top-gate electrode, drives the FET operating alternatively in a p- or n-region yielding an output signal at the drain electrode with doubled frequency and high conversion efficiency. For an input AC signal of 1 kHz, detailed frequency power spectrum analysis shows that more than 95% of the output signal is concentrated at the doubled frequency at 2 kHz, with a gain of more than 0.15, and this represents the highest gain so far achieved in carbon-based devices, including graphene-based devices.