An integrated generator-rectifier system has been shown to be beneficial in reducing ac-to-dc conversion loss at megawatt power level. The architecture incorporates passive and active rectifiers into a multi-port permanent magnet synchronous generator. With a conventional sinusoidal back emf, filter capacitors are required on passive rectifiers to create a low-ripple-voltage dc bus. These capacitors are bulky, unreliable, and reduce the power factor on the ac ports. Consequently, the generator must be over designed to accommodate high peak ac current. This paper proposes an alternative back emf shape, relying on the trapezoidal waveform. The proposed back emf accomplishes debus ripple voltage of less than 5% at a high power factor using a capacitor-less passive rectifier. In addition, the generator torque ripple is reduced compared to a sinusoidal-back-emf machine. This opens an opportunity for compact generator design while further reducing the power electronics size, weight, and cost. The relationship between the dc-bus ripple voltage and the trapezoidal back emf is developed analytically. The findings are used to shape the generator back emf and select the range of the synchronous inductance. Simulation and experimental results corroborate the proposed approach.