Microstrip gap

A symmetrical microstrip gap can be modeled by two open ends with a capacitive series coupling between the two ends. The physical layout is shown in fig. 11.6.

Figure 11.6: symmetrical microstrip gap layout

The equivalent $ \pi $-network of a microstrip gap is shown in figure 11.7. The values of the components are according to [37] and [30].

$\displaystyle C_S \textrm{ [pF] } = 500\cdot h\cdot\exp\left( -1.86\cdot\dfrac{...
... -0.785\cdot\sqrt{\dfrac{h}{W_1}}\cdot \dfrac{W_2}{W_1} \right) \right) \right)$ (11.193)

$\displaystyle C_{P1}$ $\displaystyle = C_1\cdot \dfrac{Q_2+Q_3}{Q_2+1}$ (11.194)
$\displaystyle C_{P2}$ $\displaystyle = C_2\cdot \dfrac{Q_2+Q_4}{Q_2+1}$ (11.195)


$\displaystyle Q_1$ $\displaystyle = 0.04598\cdot \left( 0.03 + \left(\frac{W_1}{h}\right)^{Q_5} \right)\cdot (0.272 + 0.07\cdot\varepsilon_r)$ (11.196)
$\displaystyle Q_2$ $\displaystyle = 0.107\cdot\left( \frac{W_1}{h}+9 \right) \cdot \left( \dfrac{s}...
...t( \dfrac{s}{h} \right)^{1.05}\cdot \frac{1.5+0.3\cdot W_1/h}{1+0.6\cdot W_1/h}$ (11.197)
$\displaystyle Q_3$ $\displaystyle = \exp\left( -0.5978\cdot \left( \frac{W_2}{W_1} \right)^{1.35} \right) - 0.55$ (11.198)
$\displaystyle Q_4$ $\displaystyle = \exp\left( -0.5978\cdot \left( \frac{W_1}{W_2} \right)^{1.35} \right) - 0.55$ (11.199)
$\displaystyle Q_5$ $\displaystyle = \frac{1.23}{1 + 0.12\cdot \left( W_2 / W_1 - 1 \right)^{0.9}}$ (11.200)

with $ C_1$ and $ C_2$ being the open end capacitances of a microstrip line (see eq. (11.192)). The numerical error of the capacitive admittances is less than $ 0.1$mS for

\begin{displaymath}\begin{split}0.1\le W_1/h \le 3 \\ 0.1\le W_2/h \le 3 \\ 1\le...
... \le \infty \\ 0.2\text{GHz} \le f \le 18\text{GHz} \end{split}\end{displaymath}    

Figure 11.7: microstrip gap and its equivalent circuit

The Y-parameters for the given equivalent small signal circuit can be written as stated in eq. (11.201) and are easy to convert to scattering parameters.

$\displaystyle Y = \begin{bmatrix}j\omega\cdot \left(C_{P1} + C_S\right) & -j\omega C_S\\ -j\omega C_S & j\omega\cdot \left(C_{P2} + C_S\right)\\ \end{bmatrix}$ (11.201)

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