Hi, I'm trying to find the high (Vth) and low(Vtl) threshold voltages on this schmitt trigger circuit:
 The first thing I did was to asume that Q1(off)  Q2(on) so I wrote this ecuation to find Ve2 (emiter voltage of Q2):
I wrote those equations to find the emiter voltage:
Once I found the emiter voltage of Q2, then I found the condition to turn on the transistor Q1, Q1 turns on when it's base emiter junction is forward biased, so with the inequality above, I found the high threshold voltage.
 Now I asume that Q1(On)  Q2(off)
I wrote those equations to find the emiter voltage:
As you can see the emiter voltage of Q1 depends of the imput voltage, I have tried to find the lower threshold voltage of the schmitt trigger, finding the input voltage to cut off Q1 and turn on Q2 again, but I have not succeed, , What should I do, I don't understand how to find Vtl?
I did a simulation, Vin is the triagle wave and the blue one is the output,
Vth is about 6.32V and Vtl is about 4.77V, but I have to find Vtl analytically, and without using approximations as say that the collector and emitter currents are the same, the only approximations I have used is to fix the colector emiter saturation voltage to 0.3V and the base emiter voltage as 0.7V
 The first thing I did was to asume that Q1(off)  Q2(on) so I wrote this ecuation to find Ve2 (emiter voltage of Q2):
I wrote those equations to find the emiter voltage:
Once I found the emiter voltage of Q2, then I found the condition to turn on the transistor Q1, Q1 turns on when it's base emiter junction is forward biased, so with the inequality above, I found the high threshold voltage.
 Now I asume that Q1(On)  Q2(off)
I wrote those equations to find the emiter voltage:
As you can see the emiter voltage of Q1 depends of the imput voltage, I have tried to find the lower threshold voltage of the schmitt trigger, finding the input voltage to cut off Q1 and turn on Q2 again, but I have not succeed, , What should I do, I don't understand how to find Vtl?
I did a simulation, Vin is the triagle wave and the blue one is the output,
Vth is about 6.32V and Vtl is about 4.77V, but I have to find Vtl analytically, and without using approximations as say that the collector and emitter currents are the same, the only approximations I have used is to fix the colector emiter saturation voltage to 0.3V and the base emiter voltage as 0.7V
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