Microstrip Transmission Lines Impedance Calculator

Microstrip Line Characteristic Impedance Tool

Input Fields

Dielectric constant

εr

Relative permittivity of the PCB material

Substrate height

h

mm

Height of dielectric layer between trace and ground

Trace width

w

mm

Width of the transmission line trace

Trace thickness

t

mm

Copper thickness of the trace

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Your Results

Characteristic Impedance

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Transmission Line Impedance Formula

$$\text{If } \frac{w}{h} \leq 1: \\ Z_0 = \frac{60}{\sqrt{\varepsilon_r}} \cdot \ln\left( \frac{8h}{w} + \frac{w}{4h} \right) \\[1em] \text{If } \frac{w}{h} \geq 1: \\ Z_0 = \frac{120\pi}{\sqrt{\varepsilon_r} \cdot \left( \frac{w}{h} + 1.393 + 0.667 \cdot \ln\left( \frac{w}{h} + 1.444 \right) \right)}$$

Where:

• $$Z_0$$ = characteristic impedance (Ω)
• $$w$$ = trace width (mm)
• $$h$$ = substrate height (mm)
• $$\varepsilon_r$$ = dielectric constant

These formulas are standard for calculating impedance in microstrip transmission lines with a ground plane beneath.

Microstrip Transmission Lines Impedance – Calculation Example

Given:

• $$w$$ = 0.9 mm
• $$h$$ = 0.8 mm
• $$\varepsilon_r$$ = 4.4

Calculation:

1. $$\frac{w}{h} = \frac{0.9}{0.8} = 1.125 \Rightarrow \text{use 2nd formula}$$
2. $$Z_0 = \frac{120\pi}{\sqrt{4.4} \cdot \left(1.125 + 1.393 + 0.667 \cdot \ln(1.125 + 1.444)\right)}$$
3. $$= \frac{376.99}{2.097 \cdot \left(2.518 + 0.667 \cdot \ln(2.569)\right)}$$
4. $$≈ \frac{376.99}{2.097 \cdot (2.518 + 0.667 \cdot 0.943)}$$
5. $$≈ \frac{376.99}{2.097 \cdot 3.146} ≈ \frac{376.99}{6.598} ≈ 57.13~\Omega$$

Microstrip transmission lines are widely used in high-frequency PCB design, especially in RF and microwave circuits. This calculator allows designers to compute the characteristic impedance to ensure proper signal integrity and impedance matching. It is critical in preventing signal reflections, minimizing crosstalk, and ensuring high-performance interconnects. Whether for antennas, filters, or digital buses, impedance-controlled traces are a must in modern board layouts.