Some Useful RF Equations

speed of light in free space (vacuum) = c = 229979245.8 meters per second

1 second is defined as 9192631770 vibrations of a cesium 133 atom ≡ 1s

1 meter is defined as the length of the path travelled by light in a vacuum during a time interval of $\frac{1}{299792458}$ of a second

wavelenght of an RF signal,    λ = c/f     =    $\frac{\mathrm{speed\; of\; light}}{\mathrm{frequency\; of\; signal}}$

voltage standing wave ratio = VSWR =

Reflection Coefficient = Γ = * ℮^-2jβl = $\frac{Z_{\mathrm{L}}-Z_0}{Z_{\mathrm{L}}+Z_0}$    ,   0 ≤ Γ ≤ 1
where l => length from Z_L,Z_L = impedance of the load, Z₀ = impedance of the source

Normalized Γ:Γ₀ =  $\frac{Z_{\mathrm{L}}-1}{Z_{\mathrm{L}}+1}$

scalar reflection coeffient р = |Γ| = $\frac{\mathrm{VSWR}-1}{\mathrm{VSWR}+1}$

return loss =S₁₁=-20log₁₀(р),  0  ≤  RL  <  ∞

VSWR = $\frac{1+\mathrm{<i>р</i>}}{1-\mathrm{<i>р</i>}}$

insertion loss = S₂₁ = -20log₁₀(|1+gamma|),  0  ≤  IL  <  -∞

angular momentum, ω  =  2 π f

β  =  ω  $\sqrt{\mathrm{\mu \epsilon }}()$  =  ω $\sqrt{\mathrm{LC}}()$ for a lossless coaxial line

mismatch loss (logarithmic)  = -10Log₁₀(1- ${\mathrm{<i>р</i>}}^2$ ) for a lossless coaxial line

Convert dBm to Watts:
$\frac{{\mathrm{10}}^{\frac{\mathrm{dBm}}{\mathrm{10}}}}{\mathrm{1000}}$ Convert Watts to dBm:
$dBm=\mathrm{10}{\log }_{10}\mathrm{(1000*Watts)}$