Question

Problem 3 The circuit shown is made of an op-amp and two resistors, R1 and R2, with positive feedback, i.e. it is acting as a Schmitt trigger. An RC combination is attached so that the capacitor is charged via Vout and R. The op-amp is powered with #12V. Vout R13 a) Qualitatively discuss what this circuit is doing and what form the +12V -12V output voltage has. It might help if you think of the Schmitt trigger as a mechanical switch that alternates between +12V and -12V as shown in the circuit to the left. b) Make an attempt at a quantitative analysis, i.e. how long does it take for the output of the Schmitt trigger to change between the two output states.

Answer 1

Vout solution, a first let see Schmitt trigger circust. By potential divider rule viettege at Non enverting terminal, d'= R2 Vout = ß vont What schimnit trigger does ? - is the following. RITRE or + - Vsaturation Output Schusator bers who is either het for instance aut and when o Vin > Vink v. then. Vaut = -Is at then Vout = t us at Let's come to the actual circuit :- -Vaut R leb sul het initially supput is Your = + Vsat twerk see the graph below) ER Vout Your t & Veat Vsat

When output, Vout= + Vrat , capacitor get charged Through senistor R, Ketocole apeleye eo When the capacitor voltage reaches + B vsat then according to Schmitt Brigger circuit When Vinyl Vout - - Vset , so when capacitor voltage increasts greater than + B Vout then ouput = - Vset, And capacitor agoun started charging towards - seat and this the time, we have, v = -B vsat So when capacitor voltage, Beaches greater than v' [ I'm talking in negative sence. lie, I mean, ao v'> Vin) then Vout = + vs. at; and output looks like Shown in the previous graph. ☺ ☺ + Veat Apusat < Buset - Vsat K **

ht, thi hilly copauloy hold bangla , voltage = puso and it is charging towards the + Vent velrage. - Time period, I = titta where t, to aveart so T = ati we have to find t ti is the tine capacitor I tokes to charge from Busat - Vsol to + Pusat. From the transient analysis in vel rege acrenr, copacilor, - Velt) = Ginal it [ Venivient final ] e where, In our case, Vanal = + Usat, Venitial = - Bleat Velt) = + B Useat and t=ti -ti/RC B Vset = Vselt + [ - p Vset -- Vset se (B-1) = - EltBl IRC I simply fyting ] . [fo] - e-tee

taking natural log on both sides? & -RC en (IB -B g (t = Rc en 1 LTB V 1B Whore, B = R2 RITR2 tiin, is the time which output takes to Charge from Uscit to – vsat, which is asked in the question. Thanks!