This paper presents the design of a SiC-based photoconductive semiconductor switch (PCSS) in which a picosecond laser pulse generates excess free electrons and holes that are rapidly separated by applying a lateral electric field across the switch. Due to the high velocity and low recombination rate of carriers in high-quality, semi-insulating SiC, the PCSS can potentially operate at terahertz frequency at 10's of watts of output power, thereby improving the frequency-power-size tradeoff of high-electron mobility transistors and traveling wave tubes. The key contributions of this paper are as follows. First, we quantify the impact of material properties, doping, traps, laser spot size, and electric field on the transient response of the switch. Second, we develop a new compact model that can describe the performance of the PCSS over broad operating conditions. Excellent agreement of the model against numerical data is demonstrated. Finally, we identify an upper bound on the frequency of operation of the switch and obtain 'frequency versus length' and 'frequency versus laser spot size' scaling under low optical generation conditions.