CL600 FLT CREW HAS TCASII TFC ALERT DURING APCH TO DFW.

Narrative

I WAS PF AT 4000 FT ON R BASE TO RWY 35C AT DFW INTL. APCH CTL ASKED US IF AN MD80 ON FINAL WAS IN SIGHT ALONG WITH THE ARPT. AT THE TIME OF THIS REQUEST I WAS IN A R TURN JOINING BASE; SO MY FO COULD SEE THE ARPT; I COULDN'T; BUT HE POINTED THE TFC OUT TO ME. AFTER ROLLING OUT; I SAW THE ARPT AND WE STATED AS SUCH TO THE CTLR. HE CLRED US FOR A VISUAL. BY THE TIME I BEGAN MY TURN; WE WERE 1 MI FROM FINAL; BUT I CONTINUED A 30 DEG BANK ANGLE TURN TO JOIN FINAL. ATC TOLD US 'TURN NOW;' CLRED VISUAL. SINCE I WAS ALREADY IN THE TURN; I HAVE OVERSHOT FINAL; CROSSED ON FINAL FOR RWY 35L; BUT CONTINUED TO TURN BACK TOWARDS RWY 35C. AT THIS TIME; WE RECEIVED A TA FOR AN ACFT JOINING FINAL ON RWY 36L. THERE WAS 600 FT ALT CLRNC AND WE DID NOT RECEIVE AN RA; SINCE I HAD CONTINUED THE TURN. THE APCH WAS CONTINUED WITHOUT ANY FURTHER PROBS AND ATC DID NOT HAVE ANY PROBS WITH US JOINING FINAL AND CONTINUING THE VISUAL APCH. DUE TO THE FACT THAT WE WERE CLOSE IN ON THE MD80; WHEN ON BASE; I DECIDED TO SQUARE OUT JOINING FINAL; TO AVOID BEING TOO CLOSE IN SINCE WE HAD TO MAINTAIN A HIGHER AIRSPD TO FAF (180 KTS). IT WAS THAT DECISION; SINCE ONCE CLRED FOR VISUAL; I AM RESPONSIBLE FOR TFC SEPARATION; THAT CAUSED ME TO OVERSHOOT FINAL. IN THE FUTURE; I WILL COORDINATE BETTER WITH ATC EVEN IN A CLASS B ENVIRONMENT.