How does the noise matching network differ from the gain matching network for an LNA?

The noise matching network and the gain matching network for an LNA differ because the transistor's optimum source impedance for minimum noise figure (Z_opt or Gamma_opt) is generally different from the conjugate match impedance for maximum gain (Z_s* = Z_in* or Gamma_MS = S11*). For a typical FET or bipolar transistor, Gamma_opt is located at a different point on the Smith chart than S11*, meaning you cannot simultaneously achieve minimum noise figure AND maximum gain AND perfect input match (50 ohm return loss). The noise matching network transforms the source impedance to Gamma_opt to achieve NF_min, but this results in a deliberate input mismatch (the reflected power at the input is not zero), degrading the input return loss to typically -5 to -10 dB. The gain matching network transforms the source impedance to S11* for maximum available gain and perfect input match (return loss = infinity), but this results in a noise figure higher than NF_min. The practical solution depends on the application priority: for minimum noise (radio astronomy, satellite receivers), use noise matching and accept poor input return loss (often compensated by adding an isolator or balanced amplifier); for best return loss (measurement equipment, cascaded system), use gain matching; for a compromise, choose a source impedance between Gamma_opt and S11* that achieves acceptable noise figure (NF_min + 0.2-0.5 dB) with adequate return loss (< -10 dB), a technique called constant noise figure circles analysis on the Smith chart.