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There is an often cited PDF of a supposedly 50% duty cycle 555 configuration. (http://www.aldinc.com/pdf/time_15002.0.pdf) This unfourtunately does not work. I have built the circuit in real life using various 555 versions, and all exibited the behavior which EveryCircuit simulates in this model.
Essentially, the theory of operation for 50% duty assumes the 555 is a "rail to rail" device. The internal reference voltages are 1/3 and 2/3 rail to rail voltage. However, the output has a voltage drop. At lower voltages, the 1-2 volts is significant, and the cap takes longer to charge to 2/3 rail voltage than it takes to drop to 1/3 voltage, resulting in a duty cycle greater than 50%. At very high voltages (far beyond actual capacity of physical chips), the drop is negligible, and the duty is only barely larger than 50%.
A true 50% duty square wave can be created with a true rail-to-rail op amp, a double ended supply with the two voltages exactly opposite of each other, a voltage divider, and a timing resistor-capacitor pair. If you want to use a single ended supply, use a second op-amp to create a voltage follower (gain of 1), and a 1:2 voltage divider for the positive input. Use the output as a virtual ground point.
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