Not realizing the output voltage of the GPS we are using, I wired it directly up to our new Arduino. After three hours of it not working, it occurred to me that the voltage output may be at RS232 levels (plus or minus 3 to 15 volts) instead of TTL (0 through 5 volts) levels. A quick check on the oscilloscope confirmed that the Garmin unit we are using outputs at plus and minus 6 volts. I ordered a sample of an ADM232 which converts between RS232 levels and TTL levels. Temporarily, we are using an OPA2350 rail to rail op amp to limit the output from 0-5 volts. This solution works, and we are now able to read NMEA data through the Arduino.
Here is the schematic of the circuit that we are using:
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