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].

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

$$C_{P1} = C_1\cdot \dfrac{Q_2+Q_3}{Q_2+1}$$ (11.194)

$$C_{P2} = C_2\cdot \dfrac{Q_2+Q_4}{Q_2+1}$$ (11.195)

with

$$Q_1 = 0.04598\cdot \left( 0.03 + \left(\frac{W_1}{h}\right)^{Q_5} \right)\cdot (0.272 + 0.07\cdot\varepsilon_r)$$ (11.196)

$$Q_2 = 0.107\cdot\left( \frac{W_1}{h}+9 \right) \cdot \left( \dfrac{s}... ...t( \dfrac{s}{h} \right)^{1.05}\cdot \frac{1.5+0.3\cdot W_1/h}{1+0.6\cdot W_1/h}$$ (11.197)

$$Q_3 = \exp\left( -0.5978\cdot \left( \frac{W_2}{W_1} \right)^{1.35} \right) - 0.55$$ (11.198)

$$Q_4 = \exp\left( -0.5978\cdot \left( \frac{W_1}{W_2} \right)^{1.35} \right) - 0.55$$ (11.199)

$$Q_5 = \frac{1.23}{1 + 0.12\cdot \left( W_2 / W_1 - 1 \right)^{0.9}}$$ (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

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

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.

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