I think the servo wants a fixed-frequency PWM pulse train, where the duty cycle corresponds to the position. I think it's monopolar, so 0= hard over one way, 100% equals hard over the other way, 50%=center.
Actually the servo expects a pulse train, with pulses ranging from 1ms to 2ms, at a nominal frame rate of 50Hz. For most transmitters 1ms is stick back and 2ms is stick forward, although Fred Cronenwett can cite a counterexample. The frame rate can vary somewhat.
You used to be able to test 72MHz transmitters by putting your TV on an unoccupied channel around 4, and looking at the bright bands moving around.
(Servo workings put at the end of the post)
I think you are only get a string of pulses out of the encoder, you would need something to count them, and I don't think it is what a servo needs.
Yes, you would need to count pulses, and to know where center (or some other absolute position) is you'd need an index pulse which mice don't have. Moreover, the angular resolution of the wheel depicted is much worse than the accuracy attainable with a pot or magnetic device.
Of course, someplace in a transmitter it probably generates the duty cycle from a pot position, so some fraction of a transmitter would probably serve the purpose.
Modern transmitters run the pots straight into an analog input on a microcontroller, which does all the rest in code. It would be hard to whack the thing in two.
The appropriate circuit to use with a potentiometer input would be a 555 timer chip of one flavor or another connected as an astable multivibrator. I could have designed the circuit in the time it's taken to respond with this post.
I think the servo wants a fixed-frequency PWM pulse train, where the duty cycle corresponds to the position. I think it's monopolar, so 0= hard over one way, 100% equals hard over the other way, 50%=center. Run that through a low-pass filter and you get a voltage proportional to the duty cycle, which drives the servo loop.
In an analog servo the pulse is stretched, and compared to a pulse that is generated by the servo amplifier, and whose duration depends on the position of the pot wiper (and, hence, the servo position). If the pulses match the motor is powered down; if the pulses differ then the motor is powered in the correct direction to make the difference less. One consequence of this is that the control loop sampling rate is dependent on the transmitter's frame rate. Another consequence is that if you use too high of a frame rate the servo will misbehave badly. Alas, the TUT's frame rate is slightly over 120Hz.
In a digital servo the pulse width is measured and fed as a command to the controller, which operates at a fixed sampling rate which is considerably higher than the pulse frame rate. This is but one of the reasons that digital servos work better.