In this paper, we describe an analytical model developed to investigate the performance limitations of admittance-based haptic interfaces. The model is used to investigate the effects that position control bandwidth and outer loop delay have on the stability and rendering range of an admittance-based interface. We show that the performance, as defined by both the minimum renderable mass and the rendering frequency range, is directly related to the closed-loop bandwidth of the inner-position loop and the amount of additional delay in the outer rendering loop. In addition, we show that the minimum renderable mass is directly proportional to the damping provided by the user which implies a stronger grip, with a higher damping, decreases the stable rendering region of the admittance-based haptics device as opposed to an impedance-based device where increased damping enhances stability. Our results are validated using a one degree-of freedom admittance-based device.