We designed an ultra-high frequency (UHF: 300MHz to 3 GHz) ferrite circulator to investigate magnetic parameters, which are suitable for a self-biased GHz circulator design. The size of the ferrite disk was 1.58 mm in thickness and 13.5 mm in diameter. The saturation magnetization ($4{pi}M_s$) of 3900 Gauss, internal magnetic field ($H_{in}$) of 1 kOe, and ferromagnetic linewidth (${Delta}H$) of 354 Oe were used in circulator performance simulation. The simulation results show the isolation of 36.4 dB and insertion loss of 2.76 dB at 2.6 GHz and were compared to measured results. A Ni-Zn ferrite circulator was fabricated based on the above design parameters. An out-of-plane DC magnetic field ($H_0$) of 4.8 kOe was applied to the fabricated circulator to measure isolation, insertion loss, and bandwidth. Experimental magnetic parameters for the ferrite were $H_{in}$ of about 1.33 kOe and $4{pi}M_s$ of 3935 Gauss. The isolation 43.9 dB and insertion loss of 5.6 dB measured at 2.5 GHz are in close agreement with the simulated results of the designed ferrite circulator. Based on the simulated and experimental results, we demonstrate that the following magnetic parameters are suitable for 2 GHz self-biased circulator design: $4{pi}M_r$ of 3900 Gauss, $H_a$ of 4.5 kOe, $H_c$ greater than 3.4 kOe, and ${Delta}H$ of 50 Oe.