The generation of high-power electromagnetic waves is one of the major applications in the field of high-intensity pulsed power. The conventional structure of a pulsed power generator contains a primary energy source and a load separated by a power-amplification system. The latter performs time compression of the slow input energy pulse and delivers a high-intensity power output to the load. Usually, either a Marx generator or a Tesla transformer is used as a power amplifier. In the present case, a system termed "module oscillant utilisant une nouvelle architecture" (MOUNA) uses an innovative and very compact resonant pulsed transformer to drive a dipole antenna. This paper describes the ultracompact multiprimary winding pulsed transformer developed in common by the Université de Pau and Hi Pulse Company that can generate voltage pulses of up to 0.6 MV, with a rise time of less than 270 ns. The transformer design has four primary windings, with two secondary windings in parallel, and a Metglas 2605SA1 amorphous iron magnetic core with an innovative biconic geometry used to optimize the leakage inductance. The overall unit has a weight of 6 kg and a volume of only 3.4 L, and this paper presents in detail its design procedure, with each of the main characteristics being separately analyzed. In particular, simple but accurate analytical calculations of both the leakage inductance and the stray capacitance between the primary and secondary windings are presented and successfully compared with CST-based results. Phenomena such as the core losses and saturation induction are also analyzed. The resonant power-amplifier output characteristics are experimentally studied when attached to a compact capacitive load, coupled to a capacitive voltage probe developed jointly with Loughborough University. Finally, an LTspice-based model of the power amplifier is introduced and its predictions are compared with results obtained from a thorough experimental study.