FMCW Radar 206 - Reflections

swra705.pdf 2.9 is given in Table 3-1 as the permittivity for polycarbonate.

Material	Permitiviy	Dissipation
polycarbonate	2.9	0.012

swra705 Equation 4 is:

\begin{align} \lambda_m = \frac{c}{f \cdot \sqrt{\epsilon_R}} \tag{0} \end{align}

\[\iff \lambda_{void} = \lambda_m \cdot \sqrt{\epsilon_R}\]

Refractive index n is defined as

\(n = \frac{c}{v} \iff c = v \cdot n\)

and,

$:nbsphinx-math:lambda_{medium} = \frac {v_{medium}}{f} $

\begin{align} \frac{\lambda_{void}}{\lambda_{polycarbonate}} = \frac{\frac{v_{void}}{f}}{\frac {v_{poly}}{f}} = \frac {v_{void}}{v_{poly}} = n \iff \lambda_{void}= n \cdot \lambda_{polycarbonate} \tag{1.1} \end{align}

as per this online tutorial: https://www.tf.uni-kiel.de/matwis/amat/elmat_en/kap_3/backbone/r3_7_2.html

\[n^2 = \epsilon_R\]

from numpy import sqrt
epsilon_R = 2.9
n = 1.586
print(sqrt(epsilon_R))

1.70293863659264