Partial discharges (PD) detection is an effective method to evaluate the insulation condition of power cable joint. However, optimization of the partial discharge sensor was hard to be achieved because of the complex nature of cable joint. In this paper, the waveform and frequency characteristics of the partial discharge pulse in power cable were studied with experiment firstly. Then, the partial discharge pulses were numerical modeled to be used as excitation in cable joint simulation model. Furthermore, an electromagnetic simulation method of PD propagation in cable joint with considering the frequency dependent dielectric parameter was proposed. Afterwards, the quantitative relation between the sensor sensitivity and the sensor structure was discussed based on the developed pulse model and cable joint model. Calculations and measurements indicated the numerical sensor design can be achieved with the proposed pulse numerical model and cable joint simulation method.Index Terms -Numerical design, partial discharge, power cable joint, simulation, pulse waveform, bandwidth.Much more attention has been paid in the pulse propagation in the power cable, and many algorithms about high frequency loss Manuscript