AN SF340 CREW WHILE ON APCH EXPERIENCED AN AVIONICS SMOKE LIGHT ALONG WITH THE MASTER WARNING ILLUMINATING.

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CRUISE FLT TO MDW. 10-15 NM OUT OF MDW; THE AVIONICS SMOKE LIGHT AND MASTER WARNING ILLUMINATED FOR 1-2 SECONDS AND WENT OUT. WE RAN OUR MEMORY ITEMS WHICH INCLUDED PUTTING ON THE SMOKE MASK AND GOGGLES. THE AVIONICS RACK IS LOCATED DIRECTLY BEHIND THE CAPT'S SEAT ON THE SF340; AND THERE WAS NO SIGN OF SMOKE OR HEAT IN THE COCKPIT. THE CAPT (PF) XFERRED CTLS TO ME (FO/PNF); HE CALLED BACK TO THE FLT ATTENDANT WHO CONFIRMED THAT THERE WAS NO SIGN OF SMOKE OR HEAT IN THE CABIN COMING FROM THE AVIONICS RACK. WE XFERRED CTLS BACK; AND DECLARED AN EMER WITH CHICAGO APCH. THE CHKLIST CALLED FOR US TO OPEN THE ESCAPE HATCH TO THE VENTILATE POS; AND BEGIN SHUTTING DOWN ELECTRICAL EQUIP. WE DECIDED THAT THERE WASN'T ANY SMOKE AND COMPLETING ALL OF THE ITEMS ON THE CHKLIST WOULD ONLY INCREASE THE DANGER. USING OUR JUDGEMENT WITH THE AVIONICS SMOKE CHKLIST; WE ARRIVED AT END OF PROC. WE ALSO DECIDED THAT WEARING THE OXYGEN MASK AND GOGGLES COMPROMISED SAFETY WITHOUT THE SMOKE BY COMPROMISING COM AND VISIBILITY. AS WE APCHED THE ARPT IT BECAME APPARENT THAT WE NEEDED A LITTLE MORE TIME TO RUN OUR DSCNT AND APCH CHKLIST. WE TOOK A DELAY VECTOR THAT CREATED AN ADDITIONAL 1-2 MINS; WE WANTED TO GET THE ACFT DOWN AS SOON AS POSSIBLE; HAD THE ARPT IN SIGHT AND TOLD APCH WE WERE READY TO HEAD BACK. A STRAIGHT IN VISUAL APCH TO RWY 31C WITH THE TAILWIND WAS THE FASTEST WAY TO GET THE ACFT ON THE GND. THE TAILWIND WAS WELL WITHIN THE ACFT'S LIMITATIONS. WE LANDED SAFELY ON RWY 31C AND DECIDED THAT AN EMER EVAC WAS NOT NECESSARY. TWR INSTRUCTED US TO BACK TAXI AND WHILE WE DID THIS WITH THE FIRE RESCUE TRUCKS IN TRAIL; I CONTACTED THE FLT ATTENDANT ONCE AGAIN TO ENSURE SHE DIDN'T SMELL SMOKE OR FEEL HEAT FROM THE AVIONICS RACK. SHE CONFIRMED THAT THERE WASN'T ANY SMOKE OR HEAT. I CONTACTED COMPANY TO SEE WHERE THEY WANTED US TO PARK AND RAN THE AFTER LNDG CHKLIST. ONCE WE PULLED INTO THE PARKING SPOT AND SHUT DOWN; I WENT TO THE CABIN AND BRIEFED THE PAX THAT WE HAD AN ABNORMAL INDICATION AND WE WERE GOING TO DEPLANE IMMEDIATELY AS A PRECAUTION. I TOLD THE RAMP AGENT THAT WE WERE GOING TO DEPLANE THE PAX BEFORE THE VALET BAGS WERE READY. AFTER THE LAST PAX DEPLANED A FIRE OFFICIAL; ARPT OFFICIAL AND COMPANY MECH BOARDED THE ACFT. AFTER TROUBLESHOOTING; THE COMPANY MECHS FOUND NO SIGN OF SMOKE OR FIRE IN THE AVIONICS RACK.