Question

Some of the answers are really unreadable so i would glad if you pay attention to explain clearly. (With the Barkhausen Criteria).

(a) For the oscillator shown in Figure 6, apply Barkhausen criteria to find the oscillat- ing frequency showing any necessary derivation. Then find out what is the neces- sary value of K to start the oscillator. -K + TV Stage 1 Stage 2 Stage 3 Figure 6 (b) What is the minimum number of stages for the circuit above to oscillate? If the gain of the amplifier is made positive instead of negative (that is, it is +K instead of-K), how many stages are required?

Answer 1

A. - Barkhausen criteria Starty that for assillation. BA=l that is BA12. _ ZBA714,34*78*360,00 - Bz feed back gain Az open Loop Game B = -K A is the gain of three cascaded High pass op-ang faller Towa " "R8 z k. Viz VAR Cin c iistud shot) Volwi. Rjoc = VR 2 Via Rowell lliti (lt oWeR wore three casedded stafe ار pt ای it (it | Ltd JWRC Wre JWRC Az wre (WRC)? HURC)3

AE (WRC) (WL) WRO BA = ** K 220*1fwechsel LBA = 180-L11-3 (WRO) s wre as - K gives 180 <!- BRCEt il bene che zo for 18 please tant ( urcja - 2 Juke 120 1-1 1-3 710 - 3 (WRC) (WRC)3 cor) for this - 3 =0 (WRC)3 WRC 23_ (WRC)? Wz BRC fr a oscillation frequency - 2TBRC also at d e wet (BA) 2 1 . BRC FERC hagshery part BRC o - BA 2 -K 7 BAL2 1- BURUT? Wriz?

(WRC)2 ) 11- 3 ling - at we and Ka L LB 2 + 180 BRC BA = I lo -- ----- Obz_ - of Kif tire we have to get 360° phase from Cascaded stages to proke: - LBA z 0,3601 for a single stage of it Howe I 1+ WRC LH (jwn = taill WRC feer Neteges_phose N tem 360° WRC tan gives mox go phase shift but can't take A WRC - as for go Wzo

the max phase shift we take as too Goo for proper Operation so if one grues bo - NX60 2360 6 stages required minimum
when opamp is used there is no loading of RC stages hence frequency value

In part b the maximum phase from first stage is taken 60 so that proper gain and frequency obtained