Maybve I'm taking this too far:
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So, I did some basic power analysis on the keyfob. When it's "awake," and the car is about 40ft away, it seems to ping once a second. When it does that, it draws up to 48mA.
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After about one minute, it seems to go to sleep. At which point I see spikes of current draw of about 9mA on average every one to two seconds.
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On the spectrum analyzer, you can clearly see a beacon every second when the key is awake, right at 2.4Ghz. So, that is probably some sort of Bluetooth beaconing. I looked up the FCC ID for the fob, and it appears to support ultra-wideband communications at 6.5 GHz, 7.5 GHz, and 8.5 GHz. I should have some time next week to try to analyze that and see if there is any TX on those bands when it's sleeping. The next step is to do the same analysis on my Subaru fob, which seems to last forever.
I also noticed it does not take much to "wake" the key. Simply tapping on my desk was enough to wake it.
I let the fob sit for an hour and tracked its power consumption. Based on that, it should last years. (~70 µWh per hours sleeping) So, at some point, when I'm not looking, something is draining the battery.
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I've also watched when the car wasn't home, and it doesn't seem to matter. The pattern is the same. This is with the latest firmware on the fob and car.
My battery seems to die within 7 to 10 days.