Hyeongrok Ryu Engineering Portfolio

RF · Microwave Study

Cascade Noise Figure and First-Stage Gain

I revisited Friis' equation to see why receiver noise figures cannot simply be added in dB.

Sequence
9 / 32
Track
core
Tools
RF calculators
On this page
  1. Question I started with
  2. Concept map
  3. Equations
  4. Worked example
  5. My coursework connection
  6. Next checks

Question I started with

I revisited Friis' equation to see why receiver noise figures cannot simply be added in dB.

Cascade Noise Figure and First-Stage Gain — concept flow
I redrew the relationships before returning to the equations.

Connecting the concepts

Noise factor F is a linear ratio. In a cascade, later contributions are divided by preceding available gain, which makes first-stage LNA gain and noise figure especially important.

  • noise factor
  • noise figure
  • Friis
  • LNA
  • available gain

Equations and assumptions

I write the reference impedance, units, and linear-versus-decibel domain before substituting numbers.

F_total = F1 + (F2 - 1)/G1 + (F3 - 1)/(G1 G2)NF_dB = 10 log10(F)

Worked example

For NF1=2 dB, G1=15 dB, and NF2=8 dB, linear conversion gives Ftotal≈1.753 and NFtotal≈2.437 dB, not 10 dB.

Cascade Noise Figure and First-Stage Gain — calculation relationship
This is my explanatory redraw, not an imported RFDH figure or a measurement result.

Connecting it to my coursework and projects

I connect the FMCW receiver order—antenna, LNA, mixer, IF/baseband—to this equation without claiming a measured board noise figure.

High-frequency engineering course hub

What I will check next

Available gain depends on impedance conditions. Calculations that omit passive-loss placement, temperature, and bandwidth are only initial comparisons.

Pages I read

Official references I checked

Publication first-page preview