Wearable Antenna Fabric Permittivity & Patch Dimensions

The formula

This is the expression the tool evaluates. Every term is named underneath, with the unit it must be supplied in.

How the result is derived

Step by step, from the values you type to the figure on screen.

1. The 4 inputs are read from the form on every keystroke: Dielectric Constant, Substrate Thickness, Compression Under Body Load and Design Frequency.
2. Each value is checked against the accepted range in the input table below. A value outside its range stops the calculation rather than producing a misleading figure — the results blank out and a message appears.
3. The validated values are substituted into the expression above, which resolves Patch Length together with every supporting figure in one pass — no value is carried over from a previous entry.
4. The supporting outputs — Patch Width, Effective Permittivity, Fringing Extension, Fractional Bandwidth, Bandwidth and Shift Under Compression — come from the same pass, so they always describe the same case as the headline figure.
5. Results are rounded for display only. The full-precision value is used throughout the chain, so reading a rounded intermediate figure back into the tool by hand can shift the last digit.

What each input means

Where to read each value on the floor, the unit it must be in, and the range the tool accepts.

What the tool returns

The headline figure and every supporting value it is built from.

Worked example

The tool loads with this case already solved — the Patch Length shown above is its answer. Change one value and the difference from this baseline is the sensitivity of the result to that variable.

How to use it

1. Work through the input groups in order — Substrate and Target Link. The defaults are a realistic case, so you can change one value at a time and watch what moves.
2. There is no calculate button. Every figure recalculates as you type or drag, which is what makes this usable for a what-if sweep rather than a single answer.
3. Read Patch Length in the dark results panel — that is the headline figure, expressed in mm.
4. Check the supporting rows underneath (Patch Width, Effective Permittivity, Fringing Extension, Fractional Bandwidth, Bandwidth and Shift Under Compression) before acting on the headline — they are where an implausible input usually shows itself first.
5. Reset to defaults returns every field to the reference case, which is the quickest way to check whether a surprising result came from the tool or from an input you had changed earlier.

Where this is used

• Process planning — establishing Patch Length before a trial is booked, so machine time and material in E-Textiles, Smart Wearables & Biomimetics are committed against a calculated figure rather than an estimate.
• Costing and quotation — Patch Length is an input to the cost sheet, and quoting from a worked number rather than a remembered one is what keeps a margin intact.
• Troubleshooting — when the floor result drifts from plan, entering the measured values (starting with Dielectric Constant) shows how much of the gap in Patch Length each variable explains.
• Teaching and study — the accepted ranges bracket normal E-Textiles, Smart Wearables & Biomimetics practice, so moving one variable at a time shows the shape of the relationship rather than a single answer.

Assumptions and limits

• Compare the compression shift against the bandwidth: if the shift is a large fraction of it, the antenna will not survive being worn, and no amount of matching at the bench will fix that. The transmission-line model used here is quick and approximate — it ignores the ground plane size, the feed and the human body underneath, and a body at a few millimetres both detunes the patch and absorbs a large share of its radiated power. Moisture is the other uncontrolled variable, since a damp substrate has a materially higher permittivity and loss than a dry one. Confirm on a vector network analyser with the antenna on a phantom, not in free space.
• Every input is bounded to the range normal practice occupies (Dielectric Constant 1.05 to 6 εr, Substrate Thickness 0.2 to 15 mm and Compression Under Body Load 0 to 70 %, and so on for the rest). Those bounds are guard rails against typing errors, not a claim that the formula fails one unit outside them.
• The calculation is deterministic: the same inputs always give the same result. It carries no allowance for machine condition, operator skill, ambient conditions or lot-to-lot material variation unless an input above explicitly represents one.
• Nothing is sent anywhere. The maths runs in your browser, so the numbers you type never leave the page.

Questions people ask