What Is the Microstrip Characteristic Impedance Calculator (Wheeler & Hammerstad)?
A microstrip is a flat metallic conductor trace fabricated on a thin dielectric substrate backed by an electrical ground plane.
Controlled impedance (typically 50 Ω single-ended or 100 Ω differential) is critical for preventing signal reflections and signal integrity degradation in modern electronics.
How Does the Microstrip Characteristic Impedance Calculator (Wheeler & Hammerstad) Work?
Because electromagnetic fields fringe through both the PCB dielectric substrate below and the open air above, the signal travels in an effective dielectric medium: 1 < εeff < εr.
Wider traces increase capacitance to ground, reducing characteristic impedance Z₀.
Microstrip Characteristic Impedance Calculator (Wheeler & Hammerstad) Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Computes effective dielectric constant εeff accounting for fringing fields in air, then calculates characteristic impedance and flight time.
How to Use the Microstrip Characteristic Impedance Calculator (Wheeler & Hammerstad)
- Enter the trace width W, substrate thickness H, and laminate dielectric constant εr.
- Adjust W until Z₀ matches your target system impedance (e.g. 50 Ω).
- Use the propagation delay (ps/mm) to match high-speed bus trace lengths (e.g. DDR memory routing).
Step-by-Step Example Calculation
Standard 50 Ω Trace on 0.8 mm FR4 PCB
Input Values:
Understanding Your Result
Z₀ is the instantaneous impedance seen by traveling signal wavefronts.
Propagation delay gives the flight time in picoseconds per millimeter (typically ~6 to 7 ps/mm on FR4).
Factors That Affect the Result
- W/H aspect ratio: Doubling trace width roughly cuts impedance in half.
- Dielectric tolerance: FR4 permittivity varies from 4.0 to 4.6 across vendors and frequency.
When Should You Use This Calculator?
- Routing 50-ohm RF antenna feeds and high-speed clock / PCIe / USB data lines.
- Stackup planning in Altium, KiCad, and Cadence Allegro PCB tools.
Assumptions & Limitations
- Valid for microstrips where W/H > 0.1 and εr < 16.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Hammerstad-Jensen equations are accurate to within ±1% of full numerical electromagnetic field solvers.