First, I'd like to say that I appreciate your disassembly and drawing up of various components like this; these are things that few people do and even fewer ever post up, and they can help tremendously when diagnosing problems in some cases (as they may show exactly how a particular thing works and what behavior can be expected under various failure modes).
More below:
LewTwo said:
And yes that LED is connected to the signal line via the 10K Ohm resistor (not a mistake).
The resistor is just a voltage dropping resistor to limit current thru the LED (since it can't take more than about a volt and a half or less across it, before current exceeds it's ability to handle and it overheats and fails).
It's also (LED+resistor) a pullup from ground to 5v, so that there is a voltage when the hall sensor is not triggered, for the controller to read. (the controller may also have an internal pullup, but if it doesn't, this does the job).
Then I connected a DMM between ground and the signal line. The DMM was set to read the voltage.
As Private Gomer Pyle used to say “Surprise, surprise, surprise”! When a magnet is passed over the hall sensor the signal line “TOGGLES” between zero volts and 3.1 volts.
Depending on the sensor type (other than for throttles), on ebikes hall sensors are usually just open-collector. This means that when in their active state, they ground the output, but otherwise the output will be in a floating state. That's why there is a pullup (resistor+LED in this case) to 5v. (basically they act like a switch between ground and the signal wire--if the switch is on, it's grounded, otherwise it's no connection, so it reads whatever is connected to the signal line outside the hall sensor).
So when the magnet passes, it changes the state of the sensor to active, the sensor grounds the output so it goes to (about) zero volts (often no lower than about 0.3-0.8v).
During this time current now flows thru the LED and resistor and it lights the LED.
When the magnet is not passing it, the state is inactive, and the output floats so a voltage reading there will be whatever the pullup is connected to. In this case that's likely to be the supply voltage minus the LED's forward-voltage-drop, usually 1.2-1.4v or so. Since you're supplying 4.5v, and the LED drops 1.4v, you get 3.1v at the hall signal output pin.
The same process happens in motor UVW hall sensors (one for each phase, vs things like SIN/COS encoders, etc), except most of the motors use latching halls, so they remain in the state they are in until the opposite polarity field passes thru them (when they change to the other state), or power is cycled (when they reset to inactive state).
Speedo sensors probably aren't latching, and respond to *any* field polarity/direction as long as it is strong enough, but otherwise behave the same.
PAS sensors would be similar, except that they may use two sensors and may they have logic in them to take two sensors and detect the output direction by the timing between the two, and vary the output waveform to tell the controller about it.
