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A lossless microstrip transmission line consists of a trace of width $w$. It is drawn over a pratically infinite ground plane and is separated by a dielectric slab of thickness $t$ and relative permittivity $\varepsilon _{r}> 1.$ The inductance per unit length and the characteristic impedance of this line are $L$ and $Z_{0}$, respectively.


Which one of the following inequalities is always satisfied?

  1. $Z_{0}> \sqrt{\frac{Lt}{\varepsilon _{0}\varepsilon _{\gamma}w}} \\$
  2. $Z_{0}< \sqrt{\frac{Lt}{\varepsilon _{0}\varepsilon _{\gamma}w}} \\$
  3. $Z_{0}> \sqrt{\frac{Lt}{\varepsilon _{0}\varepsilon _{\gamma}t}} \\$
  4. $Z_{0}< \sqrt{\frac{Lt}{\varepsilon _{0}\varepsilon _{\gamma}t}}$
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