NMAC BTWN A BEECH KING AIR CLBING OUT OF PHL AND A B747 ON ARR.

Narrative

I WAS WORKING A KING AIR OUT OF TRENTON; NJ; CLBING TO 9000 FT; FLYING TO POTTSTOWN VOR. N ARR WAS WORKING THE B747 INBOUND TO PHL. I GOT DISTR AND DIDN'T POINT THE KING AIR OUT TO N ARR. N ARR CTLR NOTICED THE 2 ACFT CONVERGING AND TURNED THE HVY TO AVOID THE KING AIR. SUPPLEMENTAL INFO FROM ACN 490910: BEING VECTORED TO PHL ARPT IN VFR CONDITIONS; ATC TURNED US FROM OUR 180 DEG HDG L TO 090 DEGS. WE WERE DSNDING AT ABOUT 1000 FPM. ATC; THEN IN A PANIC; TOLD US TO STEEPEN OUR BANK ANGLE. AS WE DID THAT; WE RECEIVED A TA FROM TCASII; FOLLOWED BY A TFC RA. TCASII SHOWED AN ACFT AT 12 O'CLOCK POS; 300 FT CLBING. WE QUICKLY INCREASED THRUST TO GAR PWR AND INCREASED BANK TO 45 DEGS AND NOSE-UP PITCH. THE AIRPLANE BEGAN TO SHUDDER AND SHAKE VIOLENTLY. WE WERE UNABLE TO MEET THE TCASII CLB REQUIREMENTS BECAUSE OF OUR BANK ANGLE AND CONFIGN. WE NEVER SAW THE TFC; BUT WITHOUT TCASII; THE CREW FELT LIKE WE PROBABLY WOULD HAVE HIT THIS AIRPLANE. WHEN ASKED; ATC SAID THEY SAW THE TFC BUT WERE NOT TALKING TO HIM. THERE WAS ALSO NO ATC HDOF TO THE NEXT CTLR. ON FOLLOW-UP; ATC ADMITTED THIS WAS A TOTAL ATC MISTAKE. THEY PROMISED THEY WOULD TAKE 'IN-HOUSE' ACTION TO PREVENT THIS FROM HAPPENING AGAIN.