The silicon drift detector (SDD) with high quantum efficiency, energy resolution and time resolution is an advanced single photon counting detector in the fields of quantum communication, X-ray communication and pulsar navigation. In this paper we design an optimum SDD structure with circular drift rings and linear-type voltage divider, the device electric characteristics are simulated using a 3D Sentaurus TCAD computational tool including electric potential, electric field, electron concentration, voltage-divider current, leakage current and saturation capacitance. Simulation results are comparable with those of conventional spiral SDDs and other shapes of ring SDDs. The circular ring-shaped structure can generate more even and symmetrical radial electric potential and field distribution, so electrons have shorter and more distinct drift channels, and SDD has ultra-fast time response and good time resolution to detect pulsed single photon signals.