How do I design a printed inverted-F antenna for a compact wireless device?

Designing a printed inverted-F antenna (PIFA) for a compact wireless device creates a low-profile, compact antenna suitable for integration into mobile phones, IoT sensors, laptops, and wearable devices. The PIFA consists of: a rectangular or irregularly shaped radiating plate positioned above a ground plane (PCB ground), connected to the ground plane by a short-circuit pin or wall at one end, and fed by a probe at a point along the plate selected for impedance matching. The PIFA's key advantage is size: the PIFA resonates at a frequency where the antenna's total length (from the short circuit around the plate to the open end) is approximately lambda/4, which is half the length of a half-wave patch antenna. This makes the PIFA approximately half the size of a standard patch antenna at the same frequency. The design parameters are: plate dimensions (the sum of the plate width and length determines the resonant frequency: f = c / (4 × (W + L) × sqrt(epsilon_eff)); for 2.4 GHz: W + L approximately 31 mm in free space), plate height (height above the ground plane: typically 5-10 mm for smartphones; affects bandwidth: taller = wider bandwidth, but thicker device; bandwidth typically 3-8% for a standard PIFA), feed point location (the input impedance varies from 0 ohms (at the short circuit) to maximum impedance (at the open end); the feed probe is placed at the point where the impedance equals 50 ohms; this point is found by simulation or measurement), and shorting pin/wall width (a wider shorting wall provides more inductance control and affects the resonant frequency; a narrow pin provides more compact design but less bandwidth).