SR-22 INSTRUCTOR AND STUDENT DEPARTING SMO EXPERIENCE LOSS OF SEPARATION WITH A B737 WHEN THEY BECOME PREOCCUPIED WITH AN EQUIP PROB AND MISS A TURN ON DEP.

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I RECEIVED THE FOLLOWING CLRNC FROM SMO GND: FLY RWY HDG; UPON REACHING THE LAX VORTAC 315 DEG RADIAL R TURN TO A HDG OF 270 DEG RADAR VECTOR TO SMO VOR. I READ BACK THE DEP PROC AND TOOK 5 MINS TO SET UP MY AVIONICS FOR THE DEP PROC AND TO EXPLAIN IT TO MY STUDENT SO THAT HE COULD FLY. HE PUNCHED IN THE XPONDER CODE (I DO NOT REMEMBER THE EXACT CODE; BUT IT DID END WITH A ZERO).JUST AFTER TKOF SMO TWR ADVISED THAT HE WAS NOT RECEIVING MY SQUAWK. THE GTX-327 XPONDER IS DESIGNED TO AUTOMATICALLY SWITCH FROM STANDBY MODE TO ALT MODE AFTER REACHING 30 KIAS. I REACHED DOWN AND HIT THE 'ALT' BUTTON ON THE XPONDER AND ASKED THE TWR FOR CONFIRMATION OF THE CODE RECEIVED. HIS REPLY WAS NEGATIVE; BUT HE HANDED ME OVER TO SOCAL DEP ANYWAY. I TOLD MY STUDENT TO CONTINUE FLYING THE DEP PROC WHILE I HANDLED THE RADIOS AND TROUBLESHOT THE XPONDER. IMMEDIATELY AFTER CHKING IN WITH SOCAL AND FIXING THE XPONDER I WAS TOLD TO TURN TO HDG 270 DEGS AND EXPEDITE FOR TFC. I TOOK THE CTLS AND TURNED TO 270 DEGS. I LOOKED OVER AT THE HSI AND SAW THAT WE HAD JUST FLOWN THROUGH THE COURSE. ONCE SITUATED SO CAL GAVE ME A NUMBER TO CALL FOR A POSSIBLE PLTDEV. NOT KNOWING WHAT DEV OCCURRED; I ASKED THE REASON. HE INFORMED ME THAT A LOSS OF SEPARATION OCCURRED BTWN ME AND A B737 DUE TO MY OVERSHOOTING THE 315 DEG RADIAL FROM LAX. THE DISTR DUE TO THE XPONDER ISSUE IS WHAT LED TO THE DEV. I WILL EXPLAIN WHAT HAPPENED WITH THE XPONDER. GOING FROM A CODE OF 1200 TO XXX MY STUDENT ASSUMED THAT HE ONLY NEEDED TO PUNCH IN THE FIRST 3 DIGITS (THE LAST ALREADY BEING ZERO). AS A RESULT; THE GTX-327 DISPLAYED ALL 4 DIGITS OF THE CORRECT CODE; YET THE UNIT WAS HOLDING FOR THE LAST DIGIT TO BE ENTERED. EVEN AFTER I HIT THE 'ALT' BUTTON; IT WAS STILL ON STANDBY WAITING FOR THE FOURTH DIGIT TO BE ENTERED. NOT UNTIL I TRIED TO RE-ENTER THE CODE DID I REALIZE THE PROB AND THEN WAS ABLE TO SOLVE IT. THE DISTR WITH THE XPONDER COULD HAVE BEEN PREVENTED HAD WE PROGRAMMED IT CORRECTLY BEFORE TKOF. MORE VIGILANCE ON MY PART COULD HAVE CAUGHT THE MISTAKE. TO REDUCE THE CONFUSION WITH THE XPONDER DISPLAY; THE GTX-327 COULD BE MODIFIED SO THAT THE 4 DIGITS ON THE DISPLAY DISAPPEAR WITH THE INITIATION OF PUNCHING IN A NEW CODE. AS IT IS; THE DIGITS JUST STAY ON THE DISPLAY UNTIL YOU TYPE OVER EACH INDIVIDUAL NUMBER. ANOTHER POSSIBILITY IS FOR THE GTX-327 TO FUNCTION NORMALLY WITH THE OLD CODE UNTIL A COMPLETE NEW CODE IS ENTERED; AS OPPOSED TO FREEZING UP WHILE WAITING FOR A NEW CODE TO BE ENTERED COMPLETELY. THIS WOULD HAVE AT LEAST PUT US IN RADAR CONTACT WITH A 1200 CODE; AS OPPOSED TO FLYING IN IMC WITHOUT RADAR CONTACT. IF THAT WAS A FUNCTION; TWR AND SOCAL COULD HAVE CAUGHT THE DEV BEFORE IT BECAME A SAFETY OF FLT ISSUE. FINALLY; THERE IS A LOT GOING ON IN THE COCKPIT DURING A LESSON; LET ALONE A LESSON IN LAX AIRSPACE ON AN ACTUAL IFR FLT. THE TWR CTLR WAS ONLY TRYING TO HELP BY MAKING SURE HE WAS ABLE TO ESTABLISH RADAR CONTACT. I DO UNDERSTAND THE IMPORTANCE OF RADAR CONTACT IN THIS ENVIRONMENT AND I AM NOT PROJECTING THE BLAME FOR THE INCIDENT ONTO THE CTLR. HOWEVER; CONSIDERING THE DIFFICULTY OF THE DEP PROC; KNOWING THAT I WAS GIVING A LESSON (THIS I MENTIONED TO HIM ON THE GND); AND THE PROX TO ANOTHER ACFT THAT JUST DEPARTED LAX; IT WOULD HAVE BEEN BETTER IF THE TWR CTLR HAD NOT BROUGHT MY ATTN TO THE XPONDER ISSUE AND THEN GIVEN ME A FREQ CHANGE BEFORE WE WERE GIVEN ENOUGH TIME TO BE OUT OF HARM'S WAY. IF THE CONCERN WAS THAT I MIGHT GET TOO CLOSE TO THE OTHER TFC; THE CTLR SHOULD HAVE CONFIRMED MY ALT AND POS VERBALLY; NOT THE FUNCTIONING OF MY XPONDER.