Microstrip open

A microstrip open end can be modeled by a longer effective microstrip line length $ \Delta l$ as described by M. Kirschning, R.H. Jansen and N.H.L. Koster [35].

$\displaystyle \frac{\Delta l}{h} = \frac{Q_1\cdot Q_3\cdot Q_5}{Q_4}$ (11.185)

with

$\displaystyle Q_1$ $\displaystyle = 0.434907\cdot \dfrac{\varepsilon_{r,eff}^{0.81}+0.26}{\varepsil...
...\dfrac{\left( W/h \right)^{0.8544} + 0.236}{\left( W/h \right)^{0.8544} + 0.87}$ (11.186)
$\displaystyle Q_2$ $\displaystyle = 1 + \dfrac{\left( W/h \right) ^{0.371}}{2.358\cdot \varepsilon_r + 1}$ (11.187)
$\displaystyle Q_3$ $\displaystyle = 1 + \dfrac{0.5274}{\varepsilon_{r,eff}^{0.9236}} \cdot \arctan\left( 0.084\cdot\left( W/h \right) ^{\tfrac{1.9413}{Q_2}} \right)$ (11.188)
$\displaystyle Q_4$ $\displaystyle = 1 + 0.0377\cdot \left( 6-5\cdot\exp{\left(0.036\cdot\left(1-\va...
...)\right)} \right)\cdot \arctan\left( 0.067\cdot\left(W/h\right)^{1.456} \right)$ (11.189)
$\displaystyle Q_5$ $\displaystyle = 1 - 0.218\cdot \exp{\left( -7.5\cdot W/h \right)}$ (11.190)

The numerical error is less than $ 2.5$% for $ 0.01 \le
W/h \le 100$ and $ 1\le\varepsilon_r\le 50$.

Another microstrip open end model was published by E. Hammerstad [36]:

$\displaystyle \dfrac{\Delta l}{h} = 0.102\cdot \dfrac{W/h+0.106}{W/h+0.264} \cd...
..._r+1}{\varepsilon_r}\cdot \left(0.9+\ln{\left(W/h+2.475\right)} \right) \right)$ (11.191)

Here the numerical error is less than $ 1.7$% for $ W/h < 20$.

In order to simplify calculations, the equivalent additional line length $ \Delta l$ can be transformed into an equivalent open end capacitance $ C_{end}$:

$\displaystyle C_{end} = C'\cdot \Delta l = \dfrac{\sqrt{\varepsilon_{r,eff}}}{c_0\cdot Z_L} \Delta l$ (11.192)

With $ C'$ being the capacitance per length and $ c_0$ = 299 792 458 m/s being the vacuum light velocity.


This document was generated by Stefan Jahn on 2007-12-30 using latex2html.