NUMERICAL CALCULATION OF STRIPLINE IMPEDANCE Evaluate the above expressions for a stripline having εr = 2.55 and a = 100b to find the characteristic impedance for W/b = 0.25 to 5.0. Compare with the results from (3.179).

Question

NUMERICAL CALCULATION OF STRIPLINE IMPEDANCE

Evaluate the above expressions for a stripline having [latex]\ \epsilon _{r}=2.55[/latex] and a = 100b to find the characteristic impedance for W/b = 0.25 to 5.0. Compare with the results from (3.179).

[latex]Z_0=\frac{30\pi }{\sqrt{\epsilon _r} }\frac{b}{W_e+0.441b}[/latex] (3.179a)

[latex]\frac{W_e}{b}=\frac{W}{b}- \begin{cases} 0 & ext{for}\frac{W}{b} \gt 0.35 \ (0.35-W/b)^2& ext{for}\frac{W}{b} \lt 0.35. \end{cases}[/latex] (3.179b)

Accepted Answer

A computer program was written to evaluate (3.192). The series was truncated after 500 terms, and the results for Z0 are as follows.

[latex]\ C=\frac{Q}{V_{avg}} =\frac{W}{\sum\limits_{n=1\ odd}^{\infty}{A_{n}\left(\frac{2a}{n\pi W} ight)\sin \frac{n\pi W }{2a} \sin \frac{n\pi b }{2a} } }F/m.[/latex] (3.192)

[latex]\ Z_{0}.\Omega [/latex]
W/b	Numerical Eq. (3.192)	Formula, Eq. (3.179)	Commercial CAD
0.25	90.9	86.6	85.3
0.5	66.4	62.7	61.7
1.0	43.6	41.0	40.2
2.0	25.5	24.2	24.4
5.0	11.1	10.8	11.9

We see that the results are in reasonable agreement with the closed-form equations of (3.179) and the results from a commercial CAD package, particularly for wider strips where the charge density is closer to uniform. Better results could be
obtained if more sophisticated estimates were used for the charge density.

Question 3.6: NUMERICAL CALCULATION OF STRIPLINE IMPEDANCE Evaluate the ab...

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