Using substrate of ɛr=3.38, h=1.6, find the width of microstrip sections that implement the above circuits as well as t...

Given, 

$$\begin{gathered} {\epsilon }_r = 3.38 \\ h = 1.6 \end{gathered}$$

The width of the microstrip substrate is ,

$w = \frac{1}{2f_{r\sqrt{{\mu }_0{\epsilon }_0}}}\sqrt{\frac{2}{{\epsilon }_r+1}} = \frac{v_0}{2f_r}\sqrt{\frac{2}{{\epsilon }_r+1}}$ 

Velocity of light in space,

 $$\begin{gathered} v_0 = 3\times {10}^8 m/s \\ let resonant frequency , f_r = 5Hz \end{gathered}$$

$$\begin{gathered} w = \frac{v_0}{2f_r}\sqrt{\frac{2}{{\epsilon }_r+1}}= \frac{3\times {10}^8}{2\times 5\times {10}^9}\sqrt{\frac{2}{3.38+1}} = 0.02027 m \\ = 2.027 cm \\ ie., \\ w = 2.027 cm \end{gathered}$$  

Then the corresponding length is 

$$\begin{gathered} L \approx 0.47 \frac{{\lambda }_0}{\sqrt{{\epsilon }_r}}\approx 0.47 \frac{v_0}{f_r\sqrt{{\epsilon }_r}} \\ ie., \\ L = 0.47 \frac{3\times {10}^8}{5\times {10}^9\sqrt{3.38}}=0.01533 m =1.533 cm \end{gathered}$$ 

 Therefore the corresponding length is 1.533 cm