PA46 PLT IS ALERTED BY ATC TO POSSIBLE XPONDER PROBS AFTER DEPARTING MTN; INSIDE THE DC ADIZ.

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I WAS DEPARTING OUR TWR CTLED FIELD; SQUAWKING OUR DISCRETE CODE OF XXXX. THIS IS USED ONLY BY ACFT WISHING TO DEPART (TO THE N OR SE) VFR. WE DO THIS SEVERAL TIMES A DAY. ON THIS OCCASION I WAS FOLLOWING ANOTHER COMPANY MALIBU WHICH HAD JUST TAKEN OFF AHEAD OF ME; AND AS I WAS CLBING THROUGH ABOUT 1200 FT MSL; THE MTN TWR INQUIRES IF I HAD MY XPONDER ON. I ADVISED YES AND THEY SAID THEY DID NOT SEE ME; ON THEIR 'SCOPE.' (THIS TWR HAS A BRITE SCREEN THAT FEEDS OFF OF POTOMAC'S RADAR.) THEN THEY ADVISED THAT THEY WERE NOT SURE IF IT WAS MY ACFT OR THE COMPANY MALIBU AHEAD. I REITERATED THAT MY XPONDER WAS ON XXXX AND THAT I WAS SHOWING NORMAL (WITH THE RESPONSE INDICATOR CLRLY OPERATING). THEY ADVISED THAT THEY WOULD CALL POTOMAC LANDLINE AND 'SEE WHAT THEY SAY.' AFTER ABOUT 30 SECONDS; THE TWR SAID '(CALL SIGN) THEY DON'T HAVE YOU EITHER.' THEN AT THIS POINT THE MALIBU AHEAD CALLS TOWER AND SAYS; 'I'VE HAD HIM ON MY TFC DISPLAY (A XPONDER-BASED 'SKYWATCH' SYS) SINCE HE TOOK OFF.' I THEN SWITCHED TO MY OTHER XPONDER AND THE TWR SAYS 'STILL NEGATIVE.' I ADVISED I COULD TALK TO POTOMAC APCH MYSELF; AS I WAS OUTSIDE OF CLASS D AT THIS POINT. TWR ADVISED 'FREQ CHANGE APPROVED.' NOTE: I WAS IN COM WITH THE OTHER COMPANY MALIBU ON OUR COMPANY FREQ THE ENTIRE TIME; AND THAT PLT CONFIRMED HE SAW MY XPONDER TARGET AND ALT THE ENTIRE TIME. I CALLED POTOMAC AND THE CTLR SEEMED TO NOT KNOW OF ANY PROB. I BRIEFLY EXPLAINED THAT MTN TWR'S SCREEN DID NOT SHOW MY TARGET. (I WAS STILL IN THE ADIZ; BUT NEARING THE EXIT POINT AT THAT TIME). THE CTLR HAD ME GO TO A DIFFERENT SQUAWK CODE (SIMILAR TO 'YYXX' OR SOMETHING) AND VERIFIED IT WAS WORKING AND HE 'IDENTED' ME. THEN HE HAD ME SWITCH BACK TO XXXX CODE AGAIN; AND VERIFIED HE HAD ME ON THAT CODE! SECONDS LATER; I EXITED THE ADIZ; HE HAD ME SWITCH TO AN XXZZ CODE; SAID 'I WOULDN'T BE CONCERNED; THERE SHOULDN'T BE ANY PROB; IT'S WORKING.' THEN SAID 'FREQ CHANGE APPROVED.'