In this paper, we investigate the transformation bandwidth and the thickness sensitivity of the anisotropic-slab linearly polarized (LP) to circularly polarized (CP) polarizer. The effect is represented graphically on the complex polarization ratio plane. We define a transformation bandwidth and the thickness sensitivity by using a specified axial ratio, e.g., 3 dB, as a basis. It is shown that the polarization locus for a given axial ratio leads to a circle in the polarization state diagram. When combined with the graphical description of the change in the polarization state, the transformation bandwidth and the thickness sensitivity from an initial LP wave to a desired CP wave can be obtained easily. Under the small reflection approximation, i.e., only the forward waves are considered, this method can be applied to the design of the anisotropic-slab LP to CP polarizer. This method eliminates the lengthy derivation and gives deeper physical insight to the problem. The transformation bandwidths for the anisotropic-slab polarizer with a lossless and nondispersive biaxial medium are studied. The thickness sensitivities for the anisotropic-slab polarizer with several lossless media are also investigated. The results are discussed and illustrated.