What is the noise figure of a feedback amplifier compared to a matched amplifier topology?

A feedback amplifier (using resistive or reactive feedback to achieve broadband impedance matching) typically has a higher noise figure than a matched amplifier topology (using a reactive matching network optimized for minimum noise) because the feedback elements add their own thermal noise to the signal path and force the transistor to operate away from its optimum noise match condition. In a matched LNA, the input matching network transforms the source impedance to the transistor's optimum noise impedance (Z_opt or Gamma_opt), achieving the minimum noise figure (NF_min) of the transistor (typically 0.3-1 dB for modern FETs at low GHz frequencies). In a feedback amplifier, resistive feedback (typically a resistor from drain to gate in a FET, or collector to base in a BJT) sets the input impedance to approximately 50 ohms across a wide bandwidth, but the feedback resistor contributes thermal noise that raises the noise figure above NF_min by approximately 0.5-2 dB. The advantage of feedback amplifiers is extremely wide bandwidth (DC to 20+ GHz in a single design) with flat gain and good return loss, which is impossible to achieve with narrowband reactive matching networks. The trade-off is clear: use reactive matching for minimum noise figure in narrowband applications (radio astronomy, satellite receivers), and use feedback for applications requiring very wide bandwidth where moderate noise figure is acceptable (broadband test equipment, cable TV, fiber-optic receivers).