Microstrip corner

The equivalent circuit of a microstrip corner is shown in fig. 11.4. The values of the components are as follows [30].

$\displaystyle C$    [pF]  $\displaystyle = W \cdot \left( (10.35\cdot\varepsilon_r + 2.5) \cdot \frac{W}{h} + (2.6\cdot\varepsilon_r + 5.64) \right)$ (11.84)
$\displaystyle L$    [nH]  $\displaystyle = 220\cdot h \cdot \left( 1 - 1.35\cdot\exp\left( -0.18\cdot \left( \frac{W}{h} \right)^{1.39} \right) \right)$ (11.85)

The values for a 50% mitered bend are [30].

$\displaystyle C$    [pF]  $\displaystyle = W \cdot \left( (3.93\cdot\varepsilon_r + 0.62) \cdot \frac{W}{h} + (7.6\cdot\varepsilon_r + 3.80) \right)$ (11.86)
$\displaystyle L$    [nH] $\displaystyle = 440\cdot h \cdot \left( 1 - 1.062\cdot\exp\left( -0.177\cdot \left( \frac{W}{h} \right)^{0.947} \right) \right)$ (11.87)

With $ W$ being width of the microstrip line and $ h$ height of the substrate. These formulas are valid for $ W/h = $ 0.2 to 6.0 and for $ \varepsilon_r = $ 2.36 to 10.4 and up to 14 GHz. The precision is approximately 0.3%.

Figure 11.4: microstrip corner (left), mitered corner (middle) and equivalent circuit (right)
\includegraphics[width=12cm]{mscorner}

The Z-parameters for the given equivalent small signal circuit can be written as stated in eq. (11.88) and are easy to convert to scattering parameters.

$\displaystyle Z = \begin{bmatrix}j\omega L + \dfrac{1}{j\omega C} & \dfrac{1}{j...
...ga C}\\ \dfrac{1}{j\omega C} & j\omega L + \dfrac{1}{j\omega C}\\ \end{bmatrix}$ (11.88)


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