Parties are allowed great latitude to show "any fact which would or might tend to establish ill feeling, bias, motive and animus on the part of the witness." London v. State, 739 S.W.2d 842, 846 (Tex. Crim. App.1987). the trial judge, however, has some discretion in limiting cross-examination of witnesses. See Hurd v. State, 725 S.W.2d 249 (Tex.Crim.App.1987); see also Miller v. State, 741 S.W.2d 382, 389 (Tex.Crim.App.1987), cert. denied 486 U.S. 1061, 108 S. Ct. 2835, 100 L. Ed. 2d 935 (1988). A trial judge may limit cross-examination as inappropriate for a number of reasons. See Carroll v. State, 916 S.W.2d 494, 498 (Tex. Crim. App. 1996) (citing Delaware v. Van Arsdall, 475 U.S. 673, 679, 106 S. Ct. 1431, 89 L. Ed. 2d 674 (1986) (for example, trial judge may exercise discretion to prevent harassment, prejudice, confusion of the issues, and marginally relevant interrogation)). In order to impeach a witness with evidence of outstanding warrants and child support violations, the proponent of the evidence must establish that the evidence is relevant. See Carroll, 916 S.W.2d at 494; see also London, 739 S.W.2d at 846-48. For the evidence to be admissible, the proponent must establish some causal connection or logical relationship between the warrants and support violations and the witness' "vulnerable relationship" or potential bias or prejudice for the State, or testimony at trial. See Carpenter v. State, 979 S.W.2d 633, 634-35 (Tex. Crim. App. 1998). The proponent of the evidence is not required to show actual bias. Id. at 634, n. 4. What is required is that the proponent make a showing of the witness' potential for bias. Id.