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I'm not quite satisfied with the explanation in the article -- maybe someone with radio signal experience can help me out?

Assuming that the unlock is accomplished over 2-way communication (car calls to key, key responds), I can understand how an amplifier could boost the car signal to a key that was far away, but how does it boost the key's response to accomplish the second half of the process?

The general theory is the amplification works both ways. The device listens for any signal on a certain band and re-transmits it at a higher power. Signals from the car to the keyfob are amplified as are signals from the keyfob to the car. Noise canceling circuitry prevents it from getting into a feedback loop. This sort of thing exists for garage door openers[1].

In practice, I have found the keyfobs tend to transmit with enough power that 50ft isn't a problem, provided they get an activation ping from the car.

[1] http://www.ebay.com/itm/Signal-Repeater-Enhance-wireless-ran...

Exactly: It's not simply an amplifier, it's a repeater. It's similar to two-way radio repeaters used by amateur radio and emergency communications, with the major difference being that this sounds like a full duplex device on one frequency, whereas radio communication repeaters generally use two sets of frequencies in a half-duplex configuration.

I can see this boosting the signal going from the car at 315MHz or 433MHz but what about boosting the response back from the key at 125KHz or 130KHz?

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