An L-band high power and high efficiency solid-state power amplifier (SSPA) design is presented. This compact, lightweight GaN HEMT SSPA is designed for nano-satellite GPS applications. This paper focuses on class F to achieve high efficiency by using waveform shaping methods. The optimal magnitude and phase of the fundamental, second and third harmonics (fo, 2fo and 3fo) are optimized by harmonic load-pull to produce a half-rectified sine wave for the drain current and a square wave for the drain voltage. To realize the design, a low impedance transformer with two harmonic traps are implemented by using second and third harmonic open circuit stubs. In CW, the SSPA can achieve 49W of saturated output power with gain of 17.2dB and PAE of 46.2% at 1.575GHz.