A C172 VFR TRAINING FLT IS OVERTAKEN ON FINAL APCH TO RWY 16; EXPERIENCING AN NMAC BY A WESTWIND JET WHO HAD NOT CALLED THE TWR AT PWK; IL.

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I DEPARTED BURLINGTON (C52) AT ABOUT XA05 AFTER REFUELING. THIS WAS A TRAINING FLT WITH A CFI; A DIRECT FLT TO PWK HOME BASE FOR AIRPLANE X. AFTER PASSING CAMPBELL ARPT; I LISTENED TO ATIS: WINDS 230 DEGS AT 10 KTS; 16/24; ALTIMETER 29.93. I THEN CALLED TWR ON 119.9 AT ABOUT 11 NM OUT; 'PWK TWR THIS IS SKYHAWK X; 11.2 MUNDLEIN LNDG PWK GOING TO THE TEES.' TWR; 'ACFT X SQUAWK XXXX RPT 2 OUT FOR 16.' ACFT X; 'RPT 2 OUT 16 SQUAWK XXXX.' I BEGAN A DSCNT FROM ABOUT 2700 FT TO 2200 FT AND WAS ABOUT 1 MI TO THE W OF THE EXTENDED CTRLINE. I NOTICED ANOTHER AIRPLANE (CESSNA Y) WAS SLIGHTLY HIGHER AND TO MY L. HE APPEARED TO BE ON THE EXTENDED CTRLINE ILS OF RWY 16. I CALLED TWR 'PWK TWR; ACFT X HAS TFC TO OUR L PARALLEL TO US. HOW ABOUT WE DO A R 360 FOR SPACING?' TWR; 'R 360 APPROVED FOR SPACING CESSNA ACFT X. YOU WILL BE #2 FOR LNDG.' I REPLIED; 'ACFT X; R 360.' I PERFORMED A R 360 DEG TURN AND THEN BEGAN TO TRACK THE LOC; MAINTAINING ABOUT 2200 FT MSL. AT ABOUT 5 MI OUT; A WESTWIND JET (ACFT Y) PASSED JUST ABOVE ME ABOUT 120 FT; I WOULD GUESS; AND SLIGHTLY TO THE R. THE JET CONTINUED ON THE APCH AND WAS ALMOST ON THE NUMBERS WHEN TWR CALLED HIM AND INSTRUCTED HIM TO EXECUTE A MISSED APCH. I DO NOT RECALL HEARING AT ANY TIME THE TWR CLRING THE JET FOR LNDG AT RWY 16. I DO NOT RECALL HEARING ANY XMISSION FROM TWR TO THE JET UNTIL HE CALLED THE TWR AND RPTED THE NMAC. THE JET THEN MADE A MISSED APCH. I WAS CLRED TO LAND ON RWY 16. I PROCEEDED TO LAND ON RWY 16 AND WHEN DOWN WAS INSTRUCTED TO TAXI TO THE HANGARS. AFTER ABOUT 5 MINS AFTER STOPPING AT THE HANGARS; I GOT OUT OF THE PLANE AND WATCHED THE WESTWIND LAND ON RWY 16. IT WAS INSTRUCTED TO BACK-TAXI TO FBO AT THE N END OF THE FIELD. AS TO THE QUESTION OF WHAT CAUSED THE NMAC IT APPEARS THAT THERE WAS SOME SORT OF DELAY IN THE HDOF FROM APCH CTL TO THE TWR. OR THERE WAS AN UNACCEPTABLE DELAY FROM THE TIME THE JET WAS TOLD TO CONTACT TWR AND THE TIME HE ACTUALLY DID. IN FACT; AS STATED ABOVE; HE DID NOT TALK TO THE TWR UNTIL HE WAS WELL LONG THE ILS AND HAD ALREADY PASSED ABOVE ME. AS TO WHAT CAN BE DONE TO PREVENT THIS FROM HAPPENING AGAIN; I CAN ASSURE YOU THAT I WILL MAKE IT A POLICY TO STAY AWAY FROM A STRAIGHT-IN APCH TO RWY 16 EVEN THOUGH I AM CLRED TO DO SO. THE HVY IRON COMES DOWN ALMOST TWICE AS FAST AS I CAN GO. IT IS APPARENT THAT RELYING ON ATC IS NOT A 100% GUARANTEE THAT THERE IS NO ONE CLOSING BEHIND ME. I THINK A CHANGE SHOULD BE MADE TO THE AIM; SUGGESTING A PARALLEL ENTRY TO A BASE LEG IN LIEU OF A STRAIGHT-IN ENTRY FOR TWR CTLED VFR APCHS TO RWYS WITH ALS THAT JET TFC ROUTINELY UTILIZES. THIS WILL HELP TO KEEP THE TURTLES AND RABBITS APART!