This paper describes an ultra-low-power low-noise amplifier (LNA) targeting the 617-652 MHz narrowband-IoT (NB-IoT) frequency band. The design breaks the trade-off in practice between the input matching, minimum required DC current, and minimum NF by using a step-down transformer with an equivalent turns ratio of less than 1, resulting in input impedance boosting and noise attenuation of the main transistor. A local feedback loop is also employed to use the LNA current source transconductance to further attenuate the main transistor noise without additional power cost. The LNA power consumption scales efficiently with the required overall transconductance without being limited to the input matching condition, in practice, while enabling a sub-3dB minimum NF, making it a suitable option for a wide range of applications. A comparison between the proposed, conventional, and state-of-the-art low-power LNA structures is presented with both analytical and simulation models, while measurement results of a prototype designed in a 65 nm technology show a sub-3dB minimum noise figure (NF), −8.8 dBm IIP3, 15 dB gain, and a state-of-the-art FoM of 39.74 dB while consuming only 36 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{W}$ </tex-math></inline-formula> from a 0.55 V supply.