This paper is devoted to the Cramer Rao bound (CRB) on the azimuth, elevation and range of a narrow-band near-field source localized by means of a uniform circular array (UCA), using the exact expression of the time delay parameter. After proving that the conditional and unconditional CRB are generally proportional for constant modulus steering vectors, we specify conditions of isotropy w.r.t. the distance and the number of sensors. Then we derive very simple, yet very accurate non-matrix closed-form expressions of different approximations of the CRBs