Abstract Digital-driven scaling poses significant problems to analog circuits because scaling severely deteriorates transistor current saturation, significantly degrading the intrinsic gain. Special material properties of emerging low-dimensional semiconductors trigger the possibility of providing solutions. We report complementary carbon nanotube thin-film transistors with negative differential resistance-induced current super-saturation for high, exponentially variable intrinsic gain with immunity against degradation during scaling. Current super-saturation at the negative-to-positive differential resistance transition boundary provides intrinsic gain singularities. The large-window, gate-modulated negative differential resistance behavior derived from carbon nanotube’s characteristics enables its practical utilization in circuits. When approaching the singularity, we record that the intrinsic gain varies by orders of magnitude, ranging from 102 to 106 at different operation points. We further demonstrate high and exponentially variable gain in an operational amplifier, showing a tunable single-stage gain ranging from 35 to 60 decibels.