SMA POSSIBLY PENETRATED CLASS B AIRSPACE WITHOUT CLRNC.

Narrative

I HAD JUST FINISHED 3 HRS OF INST TRAINING. I DROPPED OFF THE INSTRUCTOR AT 47N AND I DEPARTED KUPPER ARPT RWY 25 FOR THE RETURN TO MY BASE ARPT. TO CONTINUE PRACTICING INST FLYING; I DECIDED TO INTERSECT THE SBJ VOR IN THE 060 RADIAL DIRECT TO CDW. THERE WAS STRONG WIND FROM THE SW AND I BEGAN TO TRACK A HDG THAT I THOUGHT WOULD INTERCEPT THE DESIRED COURSE. I DO NOT KNOW WHAT MAY HAVE GONE WRONG; BUT BEFORE I KNEW IT I COULD SEE MMU ARPT AHEAD; MAYBE 12 MI; AND TO MY L. I KNEW THAT I WAS CLOSE TO THE NEW YORK TCA AND THAT AT 2000 FT CRUISE ALT COULD GET INTO TROUBLE BECAUSE THE FLOOR OF THE CLASS B AIRSPACE IN THIS AREA BECOMES 1800 FT AND 1500 FT. I TURNED NW AND CONTACTED MMU; A CLASS D AIRSPACE; TO TRANSITION THE AREA. THE COM WITH MMU TWR WAS SHORT BUT THEY MADE A FEW INQUIRIES. THAT IS WHAT I AM WORRIED ABOUT. AFTER GIVING THEM MY N-NUMBER; THE TWR BEGAN QUESTIONING THE HDGS THAT I HAD BEEN FLYING; THE DIRECTION THAT I WAS APCHING THE AREA AND THE ALT. AFTER A MIN OF SILENCE THE TWR ONCE AGAIN ASKED FOR MY N-NUMBER BUT THEY NEVER CLRED ME TO ENTER THE CLASS D AIRSPACE. I SIMPLY CIRCLED AROUND IT TO MY DEST. IN RETROSPECT; I ASSUME THAT I SHOULD HAVE BEEN MORE ALERT TO PILOTAGE IN AN AREA SO CLOSE TO A TCA INSTEAD OF PRACTICING NAV AND LOOKING FOR TFC WITHOUT A SAFETY PLT. IT IS ALSO MY BELIEF THAT I DID NOT BREAK THE TCA. IMMEDIATELY UPON REALIZING MY POS I LOOKED FOR FAMILIAR LANDMARKS AND I RECOGNIZED THE HOSPITAL IN S BERKELEY HEIGHTS. THAT IS WHERE I TURNED TOWARD THE NW. EITHER WAY; I DID NOT MEAN TO CAUSE ANY VIOLATIONS; IF I DID. AND; THAT WAS MY IMPRESSION FROM THE EXCHANGE WITH MMU TWR.