VFR SMA ACFT EQUIP PROB ERRONEOUS MODE C ALT CAUSED ACR X TCASII RA DSND NON ADHERENCE TO ATC CLRNC.

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ACR X WAS UNDER RADAR VECTORS BY FAY APCH CTL FOR ASR 10 APCH. THE ILS 4 WAS UNUSABLE DUE TO TSTMS ON THE FINAL APCH COURSE. WE WERE ON A SOUTHERLY VECTOR WHEN ALL OF A SUDDEN THE TCASII GAVE US AN ALERT OF TFC AT 12 O'CLOCK AT 100 FT ABOVE US. RIGHT AFTER THE ALERT WENT OFF; THE CTLR CALLED THE TFC OUT TO US. WE WERE JUST BELOW A CLOUD LAYER AND THEREFORE WERE UNABLE TO VISUALLY SEE THE TFC. WE ADVISED THE CTLR OF THIS AND JUST BEFORE HE GAVE US A VECTOR; THE TCASII GAVE US A DSCNT COMMAND. WHEN WE ADVISED HIM OF THE TCASII MANDATED DSCNT; HE GAVE US A HDG OF 270. OUR DSCNT TOTALED TO ABOUT 600 FT AND AFTER THE CONFLICT WAS OVER; HE CLBED US BACK UP TO 4000 FT. AFTERWARDS; I TALKED WITH THE RADAR SUPVR AND HE TOLD ME THAT THEY HAD TRACKED THE TARGET FOR A WHILE; WHICH GAVE A CONSTANT ALT READOUT OF 4100 FT AND CALLED THE CTLING FACILITY WHOSE AIRSPACE HE ENTERED; TO TRACK HIM AND IF HE EVER TALKED TO THEM TO GIVE FAY A CALL BY PHONE. THE NEXT FACILITY; BY THE WAY; ALSO GOT AN ALT READOUT OF 4100 FT. WHEN THE PLT CALLED FAY APCH AND WAS TOLD WHAT HAPPENED; HE TOLD THE CTLR THAT HE WAS AT 9500 FT AND LEVEL. BEING TOLD THAT 3 INDEPENDENT SYS TRACKED HIM AT 4100 FT; HE INSISTED HE WAS AT 9500 FT. IT IS LIKE THE CTLR TOLD ME; IT'S THE PLT'S WORD AGAINST OURS AND IF HE WAS INDEED AT 9500 FT HE DID NOT VIOLATE ANY AIRSPACE. I HAVE HEARD OVER THE YRS OF ALT ENCODERS BEING OFF BY A LOT; BUT 5400 FT IS EXTREME. BUT THIS WAS A CASE WHERE I WAS GLAD THAT TCASII HAS BEEN DEVELOPED. SUPPLEMENTAL INFO FROM ACN 221495: I AM AN AIR TFC CTLR AT FAY ATCT; NC. WHILE WORKING RADAR CONDUCTING OJT; I BEING THE INSTRUCTOR. I ISSUED TFC TO ACR X ON AN UNIDENTED VFR SMA WHOSE ALT INDICATED 4100 FT. ACR X WAS AT 4000 ON A CONVERGING COURSE. TFC ISSUED WAS: TFC 12 O'CLOCK; 3 MI; OPPOSITE DIRECTION; ALT INDICATES 4100 FT. PLT RESPONSE WAS 'ROGER WE'RE DSNDING.' MY RESPONSE WAS 'ACR X; TURN R HDG 270 ADDITIONAL TFC 12 O'CLOCK 3 MI SMT AT 3000.' PLT RESPONSE WAS: 'ROGER; TURN R HDG 270.' MY RESPONSE WAS; 'PREVIOUSLY ISSUED TFC IS NOW 12 O'CLOCK LESS THAN A MI ALT INDICATES 4000.' PLT RESPONSE WAS; 'WE'RE HDG 270 AND TFC NOT IN SIGHT.' AT THIS TIME APPROX 20 SECONDS AFTER THE INITIAL TFC CALL; ACR AND THE VFR TAG CROSSED AND ACR X WAS CLBED BACK TO 4000; AND GIVEN A HDG OF 220 UPON REACHING 4000. PRIOR TO THAT LAST XMISSION THE SMT WHO WAS IFR AT 3000 HDG 220 WAS TURNED L TO 180. WHEN THE SIT WAS OVER I ASKED ACR X IF HE DSNDED BECAUSE OF A TCASII ALERT. PLT RESPONSE WAS AFFIRMATIVE. I THEN ASKED IF ACR X EVER SAW THE ACFT. PLT RESPONSE WAS 'NEGATIVE AND; IF THE ACFT WAS AT 4000 HE HAD TO BE IN IMC CONDITIONS.' ACR X AND THE UNIDENTED SMA PASSED LESS THAN A MI AND 400 FT APART. ACR X AND THE SMT NEVER LOST SEPARATION.