Microstrip Calculator
Analyze or synthesize a zero-thickness quasi-static microstrip using Hammerstad–Jensen.
- Typical inputs
- Analyze/synthesize mode, width or target Z0, substrate height, relative permittivity, frequency, and line length.
- Calculated output
- Width, Z0, effective permittivity, guided wavelength, delay, and electrical length.
- Model status
- Release C · documented and numerically tested
What trace width produces the target impedance in this idealized stack-up?
Hammerstad–Jensen zero-thickness microstrip
Analyze a width or synthesize a target impedance by numerically inverting the same quasi-static forward model. This is not a field solver or fabrication guarantee.
- Width
- 3.11508 mm
- Calculated Z₀
- 50.00000 Ω
- Effective relative permittivity
- 3.26797
- Forward residual
- 0.000000000 Ω
- Guided wavelength
- 67.6886 mm
- One-way delay
- 180.901 ps
- Electrical length
- 159.5543°
Calculation path
- Synthesis substitutes the solved width back into the published forward equation.
Applicability: zero conductor thickness and quasi-static effective permittivity. Copper and dielectric loss, dispersion correction, solder mask, roughness, anisotropy, radiation, temperature, and fabrication tolerance are excluded. Use the actual stack-up and an appropriate field solver before production.
What this calculator is doing
The zero-thickness quasi-static Hammerstad–Jensen form maps width/height and substrate permittivity to εeff and impedance. Synthesis inverts the same forward model and reports residual.
How to read the result
Use this for first-pass geometry. Add copper thickness, mask, dispersion, roughness, tolerance, and a field solver when accuracy requires them.
Equations & conventions
- w/h is trace width divided by substrate height.
- εr is substrate relative permittivity; εeff is the quasi-static effective value.
- The model assumes zero conductor thickness.
Independently checked example
Checked example: a synthesized 50 Ω width is fed back through the forward model and reproduces 50 Ω within numerical tolerance.
Common mistakes
- Treating nominal εr as exact at every frequency.
- Claiming this model includes copper, mask, roughness, or dispersion.
Assumptions, validity & omissions
- Zero conductor thickness and homogeneous substrate parameters.
- Quasi-static model; dispersion and loss are excluded.
- Manufacturing tolerances and solder mask are not included.
Sources & model provenance
- Hammerstad & Jensen, Accurate Models for Microstrip Computer-Aided Design (1980) (opens in a new tab) — Closed-form microstrip model; this implementation uses its zero-thickness quasi-static form. Accessed 2026-09-05.
- NIST SP 330 (2019), The International System of Units (opens in a new tab) — Exact SI defining constants c and k. Accessed 2026-09-05.