Question
Download Solution PDFA lossless microstrip transmission line consists of a trace of width π€. It is drawn over a practically infinite ground plane and is separated by a dielectric slab of thickness π‘ and relative permittivity ππ > 1. The inductance per unit length and the characteristic impedance of this line are πΏ and π0, respectively.
Which one of the following inequalities is always satisfied?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
A lossless microstrip transmission line consists of a trace of width ‘w’ as shown:
The characteristic impedance of the transmission line is given as:
\({Z_0} = \sqrt {\frac{L}{C}} \) , where \(C = \frac{{\varepsilon A}}{d}\)
Application: As we know \({Z_0} = \sqrt {\frac{L}{C}} \) where \(C = \frac{{\varepsilon A}}{d}\)
here d = t, A ≅ w, and ε = εeff
\(\therefore C = \frac{{{\varepsilon _{eff}}w}}{t}\)
The above is the actual capacitance, with no fringing taken into account.
\(\therefore {Z_0} = \sqrt {\frac{L}{{\frac{{{\varepsilon _{eff}} \cdot w}}{t}}}} = \sqrt {\frac{{L.t}}{{w\;{\varepsilon _{eff}}}}} \)
Let the characteristic impedance of a practical transmission line be Z0’.
Since in practice, the capacitance C will be smaller than the actual capacitance due to the fringing effects, i.e.since εeff < ε0 εr, we can write:
Z0’ > Z0, i.e.
\({Z_0} < \sqrt {\frac{{Lt}}{{{\varepsilon _0}{\varepsilon _r}w}}} \)
This is because the capacitance is inversely related to the characteristic impedance, i.e. smaller the C, larger is the impedance.
Last updated on Jan 8, 2025
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