The operating properties of the refractive-type optical limiting devices based on the self-focusing and defocusing phenomena are studied numerically, and the effects of both the installation position of the nonlinear refractive medium and the waist size of the incident Gaussian beam on the operating performance of the refractive-type optical limiters are examined. Our results show that the optical limiting curves of the refractive-type optical limiters exhibit a slowly attenuating oscillating waveform. The optical limiting threshold and the clamped output value of the optical limiters are dependant on the installation position of the sample and the convergence of the incident Gaussian beam to a great extent. When the sample position is given, the smaller the beam-waist radius, the better the optical limiting performance. When the beam-waist radius of the incident light is kept constant, an optimal position of the nonlinear sample can be found in the system. With fluctuating beam-waist size, however, the optimal location varies within a small range. For a self-focusing (self-defocusing) optical limiter, the optimal optical limiting effect can be obtained when the nonlinear medium is positioned at a certain location within half a Rayleigh range in the left (right) side of the focal plane.