Microstrip Line Calculator
Microstrip Line Calculator
Adjust parameters to calculate line width, length, and effective dielectric constant in real-time.
Microstrip Line Layout and Calculations
The image above shows the basic layout of a microstrip line, including the width of the strip ($w$), the height of the substrate ($h$), and the ground plane.
Equations Used
Hammerstad’s Effective Dielectric Constant
The effective dielectric constant ($\epsilon_{eff}$) is given by:
$$ \epsilon_{eff} = \begin{cases} \frac{\epsilon_r + 1}{2} + \frac{\epsilon_r - 1}{2} \cdot \left( \frac{1}{\sqrt{1 + 12 \cdot \frac{h}{w}}} + 0.04 \cdot \left(1 - \frac{w}{h}\right)^2\right) & \text{if } \frac{w}{h} \leq 1 \\ \frac{\epsilon_r + 1}{2} + \frac{\epsilon_r - 1}{2} \cdot \left( \frac{1}{\sqrt{1 + 12 \cdot \frac{h}{w}}} \right) & \text{if } \frac{w}{h} > 1 \end{cases} $$Characteristic Impedance Calculation
The characteristic impedance ($Z_0$) is calculated using:
$$ Z_0 = \begin{cases} \frac{60}{\sqrt{\epsilon_{eff}}} \cdot \ln\left(\frac{8h}{w} + \frac{w}{4h}\right) & \text{if } \frac{w}{h} \leq 1 \\ \frac{120\pi}{\sqrt{\epsilon_{eff}} \cdot \left(\frac{w}{h} + 1.393 + 0.667 \ln\left(\frac{w}{h} + 1.444\right)\right)} & \text{if } \frac{w}{h} \geq 1 \end{cases} $$Explanation of Iterative Approach
The iterative approach is designed to adjust the width of the microstrip line to achieve the desired target impedance. It dynamically modifies the width based on the difference between the calculated impedance and the target impedance. The key parameters used in this approach are:
- Step Fraction: Determines how much the width is adjusted during each iteration. A smaller fraction allows for finer adjustments, which is beneficial for achieving higher impedances and narrower widths.
- Tolerance: Defines the acceptable range for the impedance calculation. A smaller tolerance can lead to more precise results but may require more iterations.
This method effectively solves for higher impedances and lower widths without error, unlike many online calculators that may not account for the complex behavior of microstrip lines.