Calculator Inputs
Example Data Table
These sample cases are generated with the same equations used by the calculator.
| Frequency (GHz) | εr | h (mm) | Z0 (ohms) | Phase (deg) | Width (mm) | Guided λ (mm) | ΔL (mm) |
|---|---|---|---|---|---|---|---|
| 2.40 | 2.20 | 0.508 | 50.0 | 45.0 | 1.565 | 91.316 | 11.415 |
| 5.80 | 3.48 | 0.813 | 50.0 | 90.0 | 1.844 | 31.258 | 7.814 |
| 10.00 | 4.40 | 1.000 | 35.0 | 180.0 | 3.312 | 16.046 | 8.023 |
Formula Used
1. Width estimate from target impedance: the calculator uses standard closed-form microstrip equations to estimate the width-to-height ratio, then converts it into width.
2. Effective permittivity: εeff = ((εr + 1) / 2) + ((εr - 1) / 2) × (1 + 12h / W)-1/2, with a narrow-line correction when W/h is below 1.
3. Guided wavelength: λg = c / (f × √εeff).
4. Required length difference: ΔL = (φ / 360) × λg.
5. Phase from known offset: φ = 360 × ΔL / λg.
6. Relative delay: Δt = ΔL / vp, where vp = c / √εeff.
These equations are idealized. Real layouts may need EM simulation, fabrication tolerance review, and connector launch verification.
How to Use This Calculator
- Choose whether you want to design a new phase shifter or evaluate an existing length difference.
- Enter frequency, substrate dielectric constant, substrate height, and target impedance.
- In design mode, enter the desired phase shift in degrees.
- In evaluate mode, enter the known physical length difference between the reference and shifted paths.
- Optionally add the reference line length to estimate the total shifted path length.
- Press calculate to see width, effective permittivity, guided wavelength, phase rate, delay difference, and final path length.
- Use the export buttons to save the result table as CSV or PDF.
Frequently Asked Questions
1. What does this calculator design?
It estimates a microstrip line width for the chosen impedance and then calculates the line length difference needed to create a desired phase shift at one frequency.
2. Why is effective permittivity important?
Microstrip fields travel partly in air and partly in dielectric. Effective permittivity captures that mixed field behavior, which directly changes guided wavelength, velocity, and phase response.
3. Can I use this for broadband designs?
Use it for first-pass sizing. Broadband phase shifters often need dispersion analysis and full-wave simulation because the phase response changes with frequency.
4. Why does substrate height affect the answer?
Substrate height changes field distribution and width-to-height ratio. That influences effective permittivity, impedance, and the final guided wavelength used in the phase calculation.
5. Does copper roughness appear in this model?
No. This page uses closed-form transmission-line equations. Copper roughness, etch bias, and plating details should be checked separately for production work.
6. What is the reference line length used for?
It lets you estimate the total shifted path length after adding the required phase offset. The phase result depends on the difference, not the absolute length.
7. How accurate is the width estimate?
It is usually good for early layout work. Final boards should still be checked with stackup data, field solvers, and manufacturing tolerances.
8. Can I export the results?
Yes. After calculation, use the CSV or PDF buttons above the result table to save a portable copy of the current design summary.