How to build a Schmitt trigger using transistors?
The schmitt trigger part (Q1 and Q3) actually works. What doesn't work is your output stage. Check the possible voltages at Q3 collector:


When Q3 is off, it is obviously close to the supply voltage. Therefore, there will be current through R3 and Q4 will conduct.
When Q3 conducts, the current through RC2 will go through RE and, although it will be a bit closer to ground, the voltage across RE still makes it much closer to the supply than ground. Q4 actually still conducts. The current path is: RC2 -> (R3 || RE).


To quickly fix this, you can use a PNP at the output, instead of a NPN. You'll also have to increase RC2 because with 1k, you're still too close to the supply voltage (which then changes the thresholds, yes, but anyway...). Also, you can remove R3 since RE is already here to limit current through Q4 base.

Here is the new schematic:







simulate this circuit &ndash; Schematic created using CircuitLab

With this new circuit, simulation show the thresholds are 3V and 4.5V (I'm way too lazy to confirm this by formulas). Here is the LTspice (which I find waaaay more productive than circuitlabs) asc file pastebin.