A lossless microstrip has trace width w over a practically infinite ground plane, separated by a slab of thickness t and relative permittivity r>1. Its inductance per unit length is L and characteristic impedance is Z 0. Which inequality is always satisfied?

$Z_0>\sqrt{Lw/(\epsilon_0\epsilon_rt)}$

$Z_0<\sqrt{Lw/(\epsilon_0\epsilon_rt)}$

GATE 2016 EC (EC2) – Question 63

Electromagnetics · Transmission Lines · 2 marks · Multiple choice

A lossless microstrip has trace width w over a practically infinite ground plane, separated by a slab of thickness t and relative permittivity $\epsilon_r>1$. Its inductance per unit length is L and characteristic impedance is $Z_0$. Which inequality is always satisfied?

Diagram for GATE 2016 EC (EC2) question 63

$Z_0>\sqrt{Lt/(\epsilon_0\epsilon_rw)}$
$Z_0<\sqrt{Lt/(\epsilon_0\epsilon_rw)}$
$Z_0>\sqrt{Lw/(\epsilon_0\epsilon_rt)}$
$Z_0<\sqrt{Lw/(\epsilon_0\epsilon_rt)}$

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Correct answer: (B) $Z_0<\sqrt{Lt/(\epsilon_0\epsilon_rw)}$

Explanation

The parallel-plate contribution to capacitance per unit length is $C_{pp}=\epsilon_0\epsilon_rw/t$. The microstrip also has fringing electric fields outside the rectangular region under the trace, so its total capacitance C exceeds this contribution.

For a lossless line, $Z_0=\sqrt{L/C}$. A larger C makes this smaller than $\sqrt{L/C_{pp}}=\sqrt{Lt/(\epsilon_0\epsilon_rw)}$. Thus **B**.

GATE 2016 EC (EC2) – Question 63

Explanation

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