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The question is from GATE 2016-ECE-paper 2.

Here in the question, we need to comment on the characteristics impedance of Microstrip line and we are given 4 options: enter image description here The ANSWER GIVEN IS (B),

My Approach for the problem is as follows:

  1. Since the width of the microstrip line is smaller than the grounded plate, there will be some leakage of the Electric field to the air from the microstrip line, i.e. not all the field lines are bounded between the dielectric material and the microstrip line.

  2. Therefore effective permittivity (\$ \epsilon_{eff} \$) of the transmission line will be less than (\$ \epsilon_{r} \$)[ dielectric] but more than \$ \epsilon_0 \$ [air].

  3. The characteristic impedance of the lossless line is given by \$ Z_0 \$ = \$ \sqrt{\frac{L}{C}} \$, where L is the inductance per unit length and C is the capacitance per unit length.

  4. Also, Capacitance= \$ (\frac{\epsilon_{eff}*Area} {length}) \$

  5. Hence the characteristic impedance will be more than the impedance, I.e My Answer is Coming as option (A)

So where I get wrong, Since the answer given is option (B)?

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1 Answer 1

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not all the field lines are bounded between the dielectric material and the microstrip line.

This is true. However, the formula \$C=\frac{\varepsilon_0\varepsilon_R A}{t}\$ applies to the case of quasi-infinite plates. That is, the case where all the field lines are strictly vertical from one plate to the other. This formula neglects fringing fields altogether.

The field lines that "escape" the dielectric into the air are part of the fringing field, not accounted for in the parallel plate capacitance formula. Thus they (and the other fringing fields that are confined to the dielectric) can only add to the capacitance, not subtract from it.

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