A planar inverted-F antenna (PIFA) is still the workhorse for cellular and Wi-Fi handsets when you need a low-profile element over a grounded chassis. The textbook L and W formulas are a start; the ground plane, battery and plastic stack decide whether you ship.

1. What a PIFA actually is
A rectangular (or meandered) top plate shorted to ground at one edge and fed a short distance from that short. The short sets a low-impedance feed region; the open end is the high-voltage radiator. Height h above ground and the open-end length dominate the lowest resonance.

2. First-cut dimensions (sub-GHz example ~900 MHz)
- Target quarter-wave length on the plate path ≈ lambda/4 ≈ 83 mm in free space; dielectric loading and folding shorten this.
- Height h of 5 to 8 mm is common in phones; below ~4 mm bandwidth collapses fast on FR4-like stacks.
- Plate width affects radiation resistance and Q more than a simple resonant-length calculator admits.

Start in a parametric EM sweep (L, W, feed-to-short distance s, h) rather than locking CAD from a closed-form guess.

3. Ground plane rules of thumb
- Chassis length under ~0.4 lambda at the low band makes the ground a co-radiator; hand/head loading shifts resonance several percent.
- Clear keep-out under the open end; copper pour under the whole plate kills bandwidth.
- USB / speaker / camera metal within ~0.1 lambda of the open end is a common "lab good, factory fail" cause.

4. Matching and multi-band
- Single-band PIFAs often need a series L or a shunt C near the feed after the chassis is frozen.
- Dual-band (e.g. 0.9 / 1.8 GHz) uses slotted plates or dual resonators; slot length is as sensitive as the outer outline.
- Do not tune only S11 on a fixture without the battery and LCD; the lid is part of the antenna.

5. Bench checklist
- Measure on the real PCB + battery + rear cover, not a bare FR4 coupon
- Check efficiency (or at least total radiated power) not only S11
- Repeat with hand phantom / head phantom if the product is held
- Watch CTIA or carrier TRP/TIS gates early; a -6 dB S11 with poor efficiency still fails

Design the clearance and ground first. The copper rectangle is the easy part.