Microstrip corner

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

$$C = W \cdot \left( (10.35\cdot\varepsilon_r + 2.5) \cdot \frac{W}{h} + (2.6\cdot\varepsilon_r + 5.64) \right)$$ (11.84)

$$L = 220\cdot h \cdot \left( 1 - 1.35\cdot\exp\left( -0.18\cdot \left( \frac{W}{h} \right)^{1.39} \right) \right)$$ (11.85)

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

$$C = W \cdot \left( (3.93\cdot\varepsilon_r + 0.62) \cdot \frac{W}{h} + (7.6\cdot\varepsilon_r + 3.80) \right)$$ (11.86)

$$L = 440\cdot h \cdot \left( 1 - 1.062\cdot\exp\left( -0.177\cdot \left( \frac{W}{h} \right)^{0.947} \right) \right)$$ (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)

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.

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