Radar technology requires high efficiency and wide bandwidth performance at high output powers. However, new developments like using Joint Communication and Radar Sensing (JCRS), pulse shaping, and amplitude tapering provides an additional requirement: amplitude modulation. To satisfy all of these requirements, a Load-Modulated Balanced Amplifier (LMBA) using a wideband Class E is designed for 2.9-3.4 GHz using GaN transistors. First, an accurate linear model for the transistor is presented. After this, a new state-space solution for a Class-E LMBA is derived. And lastly, a LMBA using a wideband Class E is presented. Using a lossless matching network, the GaN-based amplifier has an average drain efficiency of 81 % over the full 10 dB power back-off. However, the final design has an average drain efficiency of 45 % with a peak output power of 44 dBm.