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Microstrip Line Calculator



This small HTML/JavaScript page provides an interactive tool for quickly estimating the physical width (W) and electrical length-based physical length (L) of a microstrip transmission line or rectangular microstrip patch antenna. Below is a walk-through of the key ideas and the workflow implemented in the code.



1. User interface

  • Front-end stack

    • Bootstrap 4 is loaded from a CDN to give the form a clean, responsive look.

    • A simple <table> holds five numeric inputs:

      1. Resonant frequency f (GHz)

      2. Relative permittivity of the substrate εr

      3. Substrate height h (mm)

      4. Desired characteristic impedance Z0 (Ω)

      5. Desired electrical length (degrees)

  • Calculate button – when clicked, it runs the function calculateMicrostripAntenna() and prints the results in millimetres under the table.


2. Core JavaScript routine

function calculateMicrostripAntenna() { … }


Step

What happens

Formula / reasoning

a. Unit handling

• Reads the five text-box values using document.getElementById(...).value.• Converts GHz → Hz, mm → m so that all later calculations stay in SI.

frequency * 10^9 ; height / 1000

b. Solve for strip width W

Uses a commonly quoted closed-form approximation (Hammerstad & Jensen, 1980) that relates Z0, εr, h and W for thin microstrip lines: A = (Z0/60)·√((εr+1)/2) + (εr−1)/(εr+1)·(0.23 + 0.11/εr)W = [8·h·e^A] / [e^{2A} – 2]

Gives a quick design-level estimate that is sufficiently accurate for most substrate heights used in RF PCBs.

c. Effective dielectric constant εeff

Because some of the electromagnetic field spreads into air, a microstrip line behaves as if it were embedded in a dielectric whose permittivity is εeff ≤ εr.  A standard expression is applied:εeff = (εr+1)/2 + (εr−1)/2 · 1/√(1+12·h/W)

d. Physical length L

The user supplies a target electrical length in degrees.  The script converts that to a true path length, using the guided wavelength inside the substrate:L = (c / (f·√εeff)) · (θ / 360°)

This lets the line behave like a series transmission-line element (e.g., a 90° phase shifter) or, for a rectangular patch, tune the resonant length.

e. Display

Results are converted back to mm, formatted to 6 decimals, and injected into the results <div> with simple HTML line breaks.


3. What the numbers mean

  • Width (W)

    Determines the characteristic impedance and the current distribution.  Wider lines on a given substrate lower Z0; narrower lines raise it.

  • Length (L)

    Controls the resonant frequency (for patch antennas) or the phase delay (for general transmission lines).  Because the calculation uses εeff, it already accounts for the influence of the dielectric/air boundary.

4. Practical notes

  • Approximations – The closed-form equations are accurate to a few percent for normal PCB substrates (h ≤ ~1 mm, 1 ≤ W/h ≤ 10).  For very thick or extremely high-εr materials, full-wave EM simulation or empirical adjustment is advisable.

  • Losses & fringing – Neither conductor loss, dielectric loss, nor patch-edge fringing extensions (ΔL) are included; these refinements can be added if tighter frequency tolerance is required.

  • Modularity – The logic is isolated to one function, so you can drop it into any framework or expand it (e.g., add a ΔL correction or export to CSV) without altering the UI.

With just a few lines of vanilla JavaScript and a Bootstrap form, this calculator gives RF designers—or hobbyists experimenting with patch antennas—a quick first-order design loop entirely in the browser, no backend required.

CALCULATOR

GITHUB

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