Question

3) For the Bistable circuit shown, a) Derive expressions for the threshold voltages VTL and Vth in terms of the op- amp's saturation level L+, L_, R1, R2, R3, and V. b) Let L+ = -L_ = 7.5 V, V = 12.5 V, and R1 = 2 k.2. Find the values of R2 and R3 that result in VTL = +4.75 V and Vth = +5.25 V. OV R3 R2 w R w vo

Answer 1

Bis tables circuit It is the circuit, whose output have two stable states and those two stable states directed wag by the giving input signal to that circuit Given circuit diagram: qR3 w Ri m + Vp ovo a ܐܕ Here I am the non-inverting terminal considering node as Up f inverting terminal node as V.

we che of Here having positive feedback, tihenewa, op amp was connected in positive feedback, it works comparator of Up & VN Comparator Working Op-amp Actually, the positive feed back eksfects the total system, gain . We know that initially op-amp high gain and feedback having positive a ausalt we are having high gain. High gain leads to high voltage of output. in teams of both positive & negative But the maximum volt output voltage output voltage op-amp = to increase its have some сле 290. in addition this of of op-amp = +Vec minimum - Voc The thee is also called as positive Saturation level (+Visset -Vcc ich also called as negative saboration kvel Ekset Condition : of up >VN, then Vo goes to tv sat vo= tvsat Condition 2 to - Vsat of Vn>Up, then to goes Vor – Vsot

Threshold VoHage: al is the voltage level of which Voot from the changes One slate to another state. Given circuit diagram R3 R2 W Ri M + Vp ovo V VN By applying kch at Vp node: Vo R + Vp-V R3 + Vp-Vo = 0 R2 + I Ra Riz up R, R2 + Rq Rg + R, R3 **o - V. Rg+ Vo. R3 R, RR R2 Ri Vp = V. Rg + Vo R3 R, Rq + R2 R3 + R, RS

This up is also known as Threshold voltage because it is vollage avel , where to changes when y Cinped) changes changes for V > Vp ķ<vp to Corl Vy svp to V – VP In this circuit of Vo. We are having too type 0 Vo: tvsat 2 Vo=- Vsat Condition : When 1 Vo = tsat, then Vp is known as Higher Threshold Vollage (V R. : VTH = [V.Rg+ (+vsat). R3 |R, R21 R₂ R₂ + R, R3 Condition : When. Vo=-Usat, then up is known as Lower Threshold Voltage (VT) VTL = [v Pat Evione) ed] Ri R, R2 + R₂ R₂ + R, R3

Given that tvsat : L+ & Voal L- By substi from ituting these values in en o & ev en 0 : "TH= [viret 4. R, Ri (3 R, R2 + Rq R₂ + R, R3 from (2 * [vo R+ L-R] RiRq+ Rg Rg+ R, Rz 6 Given that L+ = -h_= 7.50, V=12.5V, R, = 262, V7 = +4.75V & VTE = +5.25V. from eqreation VTIL Ri Rę + Rarzt R, Ry] =(V. Rşk) + (2 +) Ry R₂ R, VTH [R, Re] + R3VTu[ Retri] = [v. Rg. RT + [2 + . R3 Ri] Rg VTH [Retri] - R3 [24. Ri] V.Rg.R, -V That (Rp.Ri) R: [ Vry(2:48) - (L4-R) [v=Van] [ Rg. Ri

Roz -VTH (5 VTH (R+R)) -(+R) from quation ☺ : VT2(R, Rat RyR3+ RiR3) = [v. Rg + L-R3][ki] (V.R.R.)+ (L-R3.R) - VT (R, Rq) + R3 [Vth (R, +Ro) R3 I VIL [VIE CR, PR ))+ (R.L.-P.) (RS. L. Ri) = V. Rr.Rg -V2 CRRa) - Ro-Rg (V-VT2) R3 RI RE (V-Vru) VIL CR, +R2) + Lari 6

By dividing ev 6 with ew Rafal V-Vra)(wra (812) - (LR) 14. (V-V.) [va Cerita) - [..] Ro R V-VTE V-VTH 1 VALCR, ARG) - Lei Ri VTH (R+R) - LR (v_vn) [ty (R+R) – L+R V=UTH (VIZ (Ritra). LERI (V_V1a) (UTH R.) + (V-vn) (HR) – (V-Vnz) (4) (V-V1H) (VTZRI) +(V-VTH) (UTZ R2) -(V-V71)(L-RI Rą (VHCV-vn) – Re(v=við vn) = (v-V1) (11R) +(v=vn2{fri) +(V-VTA)CUTZ R.) - (v-vm)_0R1) (v.vn) – (wvwWra) = R. [(v=V72)L+ – (V-VT2] VITA Seven Chap t. (V-VT4)7 -(V-VTAL

Rear VTAV - OTAK-VVTL + Pour = R./ (V-V72) L+ V-VTH + TL VTH + V. VTZ VTH VTL - (V-VT4) L- Ro[VTHV - VZV) L+ (V-VTC) - V.VTH + V.VTL - L-CV-V1) 1 )-ven -2-cv -m? A[vcvorn)[ Locum) - Locate) av (en (V TH -VTL) R2 = Ri v CVTH VIL) L+(V-VTL) -L-CV-VTH) V(VT2 - VTD) VENTH VIL 1+ (V-VT2) - L-(V-VTH) Ra " RI -1 v (VTH-V1)

By substituting their Gespective values: R2 = (x103)| (7.5) (12.5-4.75) – (-75) (19.5-525) ons Gale -1 (19.5) (525 -4.75) R$ =@x103] 7.5(7.75) + (7.5) (2:29) -1 (12.5) (05 Rg = (2x103) 58.125+ 54.375 Bor (2 -1 6.25 Ra ī (2000) 112.5 1 - 2000 18- 6.25 poſle-2 [17] Ra = 2000 & R2 = 34ks

By substituting this value in ea a. Rg = (34ks) (R.) (V-VTH) VTH (Ritra) – (LIR) By Substita tituting their values: R3 = (34x102) (2010>) (2.5 -525) (525) Que) +(34x103)) - (4-5 X 9x0>) (68x100) (7.25 525 ( 36x103) a (15x103) 4934 106 (189x103)-(15x103) 493x1063 (189-15) x Long 4 493x103 2.83x103 174 R2-2.83X1032