Friis Link Budget
P_r = P_t·G_t·G_r·(λ/4πR)². Waterfall shows the dB chain from Tx to received power against sensitivity; sweep shows FSPL vs range.
Free-Space Path Loss
FSPL = 20log₁₀R + 20log₁₀f + 32.45 (km, MHz).
Gain ↔ Effective Aperture
A_e = λ²/4π·G; G = η·D.
Reflection Γ & VSWR
Γ=(Z_L−Z₀)/(Z_L+Z₀); VSWR=(1+|Γ|)/(1−|Γ|).
Phased-Array Steering
Δφ=2πd/λ·sinθ; grating lobes if d>λ/2.
Formula reference
Friis P_r=P_tG_tG_r(λ/4πR)²; FSPL=20logR+20logf+32.45 (km,MHz). A_e=λ²G/4π, θ_HPBW≈λ/D.
Γ=(Z_L−Z₀)/(Z_L+Z₀), VSWR=(1+|Γ|)/(1−|Γ|), return loss =−20log|Γ|. Array Δφ=2πd/λ·sinθ, grating lobes for d>λ/2.