A PA28-180 COMES IN CLOSE PROX TO A C152 OR C172 IN THE TFC PATTERN AT EAU; WI. RPTR PLT CITES DISTR WITH RADIO XMITTER AND SWITCHING XMITTERS AS CAUSAL.

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WE WERE PERFORMING A RUN-UP (PA28-180) WHEN A CESSNA LANDED AND TOOK OFF (RPTING TOUCH-AND-GOES). THE RUN-UP WAS COMPLETED AND WE DEPARTED RWY 22 ANNOUNCING TOUCH- AND-GOES ON THE CTAF. #2 RADIO SEEMED TO BE HAVING XMITTING PROBS SO WE SWITCHED TO #1 (A DISTR THAT CAUSED US TO LOSE SIGHT OF THE CESSNA IN THE HAZE). DURING OUR CLBOUT THE CESSNA RPTED DOWNWIND AND WE TURNED XWIND AFTER PASSING THE DEP END OF THE RWY. A SCAN OF DOWNWIND WAS MADE; BUT WE THOUGHT THE CESSNA WOULD BE MIDWAY OR MORE DOWNWIND BY THIS TIME. THE RADIO XMITTING PROB ALSO CONTINUED TO DISTRACT US. JUST PRIOR TO TURNING DOWNWIND THE CESSNA WAS SPOTTED ABOVE AND TO OUR L ON DOWNWIND. THE CESSNA RADIOED US; ASKING WHERE (IN THE PATTERN) WE HAD COME FROM. WE REPLIED; BUT NO RESPONSE (XMITTING PROB?). AT THE SAME TIME WE MADE A R TEARDROP TURN WHICH REPOSITIONED US ON DOWNWIND. BY THAT TIME THE CESSNA WAS PAST THE APCH END OF THE RWY. AN ATTEMPT TO CONTACT THE CESSNA AGAIN BROUGHT NO RESPONSE ALTHOUGH WE COULD HEAR HIS POS RPTS! WE CONTINUED OUR TOUCH-AND-GO AND LEFT FOR 'HOME ARPT.' THE LACK OF KEEPING TRACK OF THE CESSNA (SCAN) AND THE DISTR OF THE RADIOS WERE THE MAJOR FACTORS INVOLVED IN THIS SIT. CONTRIBUTING FACTORS WERE HAZE AND THE ASSUMPTION THAT THE CESSNA WAS FURTHER DOWNWIND THAN IT ACTUALLY WAS. THIS COULD HAVE BEEN PREVENTED BY NOT ALLOWING DISTRS TO PREVENT USE OF CONSTANT AND PROPER SCAN TECHNIQUES TO KEEP TRACK OF OTHER ACFT.