CAPT OF A B737-300 DSNDED BELOW ILS FAF DUE TO CAPTURING THE GS TOO HIGH AND FOLLOWING A FALSE GS. ATC ADVISED OF LOW ALT ALERT.

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WE WERE APCHING OAK ARPT AND THE CURRENT ATIS WAS RPTING THE FIELD TO THE 300 FT OVCST AND 2 MI VISIBILITY; AND THE GS FOR RWY 29 WAS RPTED TO BE INOP. THIS WOULD PUT THE CEILING APPROX 60 FT BELOW OUR MINIMUMS FOR THE EXISTING RWY CONDITIONS. OUR OTHER ALTERNATIVE WAS TO USE RWY 27R WHICH IS 5400 FT; WHICH I CONSIDERED TO BE ADEQUATE; BUT NEVERTHELESS A SHORTER RWY THAN WE ARE USED TO USING. MINIMUMS FOR RWY 27R ARE 250 FT AND 3/4 MI VISIBILITY; AND WE WERE INFORMED THAT WE WOULD BE USING RWY 27R AS HAD OTHER CARRIERS. I BRIEFED THE FO ON THE APCH TO RWY 27R; BUT AFTER SEVERAL MINS HAD ELAPSED AND A HDOF TO BAY APCH; WE WERE INFORMED THAT THE RWY WOULD NOW BE RWY 29. WE CHKED ATIS ONLY TO GET THE SAME WX WE HAD BEFORE; IE; 300 FT OVCST AND 2 MI VISIBILITY. WE THEN CALLED OAK TWR AND WERE INFORMED THAT THE CEILING WAS NOW 800 FT OVCST. THIS WAS A LAST MIN CHANGE FOR US WHILE BEING VECTORED FOR THE APCH TO RWY 29. WE WERE HIGH FOR THE PROFILE DUE TO ATC TFC AND THEREBY HAD TO REMAIN AT ALT AND IT PREVENTED OUR NORMAL DSCNT. IN ADDITION TO THIS; APCH WAS TURNING US CLOSE TO THE FAF; COMPOUNDING OUR PROB OF THE NEED FOR A HIGHER THAN NORMAL DSCNT RATE. WE WERE CLRED FOR THE APCH TO RWY 29 WHEN ESTABLISHED ON THE LOC. AT THIS POINT I INCORRECTLY SELECTED 'GS' ON THE MCP. THE ACFT CAPTURED A FALSE GS AND BEGAN DSCNT. AT FIRST; THE RATE OF DSCNT APPEARED NORMAL BUT AS WE APCHED THE FIX I COULD SEE THAT IT WAS INDEED TOO HIGH A RATE OF DSCNT. I THEN DISCONNECTED THE AUTOPLT AND HAND FLEW THE APCH. DURING THIS TIME OF BRIEF CONFUSION; I REALIZED THAT I MIGHT BE AT AN ALT THAT WAS LOWER THAN CALLED FOR. I QUERIED THE FO AS TO WHAT THE ALT WAS SUPPOSED TO BE; BUT DID NOT HEAR A RESPONSE. WHEN I WAS ABLE TO XCHK THE ALT; I VERIFIED THAT I WAS TOO LOW. I BELIEVE THIS WAS ABOUT 800-600 FT MSL AT ABOUT 2 MI PRIOR TO THE FAF. I BEGAN TO CORRECT; BUT BY THE TIME THIS OCCURRED; I WAS AT THE FAF AND MINIMUMS FOR US WERE 400 FT MSL. I THEREFORE CONTINUED TO HOLD THIS ALT; AND IT WAS AT THIS POINT INSIDE THE FAF THAT APCH CTL OR TWR (I'M NOT SURE WHICH AT THIS POINT) CALLED 'LOW ALT ALERT.' I THEN QUERIED THE FO AGAIN AS TO THE CORRECT ALT; AND HE VERIFIED THAT 400 FT MSL WAS CORRECT FOR INSIDE THE FAF. WE BROKE OUT ON SCHEDULE AND LANDED UNEVENTFULLY. I FELT THE LAST MIN CHANGE OF RWYS; BOTH WITH MARGINAL SETS OF CONDITIONS; EACH DIFFERENT IN ITS OWN WAY; CONTRIBUTED TO THE CONFUSION DURING THE HIGH RATE OF DSCNT; AND THE EVENTUAL CAPTURE OF A FALSE GS. I FEEL THAT I SELECTED THE 'GS' UNDER THE IDEA THAT I WAS USING RWY 27R FOR A BRIEF MOMENT; THEN REALIZING MY ERROR TRIED TO CORRECT FOR THE ALT WHEN MY ERROR WAS REALIZED.