## 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     =    $\frac{speed of light}{frequency of signal}$

voltage standing wave ratio = VSWR =

Reflection Coefficient = Γ = $\frac{\mathrm{{V}_{\mathrm{0-}}}}{\mathrm{{V}_{\mathrm{0+}}}}$ * -2jβl = $\frac{{Z}_{L}-{Z}_{0}}{{Z}_{L}+{Z}_{0}}$    ,   0 ≤ Γ ≤ 1
where l => length from ZL,ZL = impedance of the load, Z0 = impedance of the source

Normalized Γ:Γ0 =  $\frac{{Z}_{L}-1}{{Z}_{L}+1}$

scalar reflection coeffient р = |Γ| = $VSWR-1 VSWR+1$

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

VSWR = $1+р 1-р$

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- ${р}^{2}$ ) for a lossless coaxial line

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