In this work, an analytical model describing the quasi-static operation of a monolithically integrated SiC solid-state circuit breaker (SSCB) device is rederived and refined. This SSCB is based on a 4H-SiC JFET technology offering a self-sensed blocking mechanism. The proposed model is solely based on physical parameters including the SSCB design parameters. With respect to the refinement, the proposed model is not limited to one-sided pn-junctions, considers incomplete ionization of dopants, and is able to represent breakdown characteristics. In this regard, the JFET gate breakdown characteristics are derived taking thermionic emission, space-charge-limited current and impact ionization into account. To calculate the SSCB output characteristics, a bisection-based optimization algorithm is applied carefully considering individual JFET operating states.