The implementation of a 0.38 V K-band low-power fully differential low-noise amplifier (LNA) in a 45 nm silicon-on-insulator (SOI) process is presented. The proposed architecture employs a two-stage approach with transformer-based interstage matching networks to minimize circuit area. The proposed LNA covers the frequency range from 20.3 to 24.1 GHz, it achieves a noise figure (NF) as low as 2.2 dB, and a gain of 12.9 dB, with a power consumption of 11.7 mW from a 0.38 V DC supply in a very compact area (0.15 mm²) excluding pads. Non-linearity simulations show the proposed circuit achieves a P_o1dB of −7.3 dBm, and an OIP3 (Output Third Order Intercept) of 7 dBm. The transformers allow improved area use since they are simultaneously used as matching networks, RF chokes to bias the active devices, baluns at the input and output terminals to convert the single-ended signal into differential mode, and vice versa, and facilitates the interconnection with the upcoming stages. We used a state-of-the-art tool that generates the desired inductances to perform impedance matching for a given frequency and coupling factor value. A comparison with similar works proves the proposed LNA achieves a very low NF and the lowest power consumption reported in a differential circuit.