Oscillations ad Voltage Controlled Oscillators Feedback perspective A a 1 af if af 1 we get infinite gain or oscillations From EE 122 the phase shift oscillator specifically uses series parallel RC network to Make f 1 a and Guarantee exact 0 degree phase shift Timing based oscillations this can be ring oscillator type or charge discharge of C type Transistor level oscillations which we ll do now s j Reminder about s plane and poles moving into either LHP or RHP R2 Inverting R1 Gain amp Av R2 R1 Phase shift Network 0 and fo and attenuating by 1 Av Timer Circuits Schmitt Trigger 555 IC Many others dV I C dt C V Tx I S1 Control Logic S1 on S2 off Then S2 on S1 off C x x is the portion of the total period for which the respective Ix is in control Vcc S2 Colpitts Oscillator Analysis and Design Read Chapter 5 especially 5 5 in Krauss The following is a combination First order small signal analysis Dutton Improved large signal version T Lee Discussion of Krauss version ala 5 5 Common Base Amp Biasing like CE but BIG Cap at base ac ground Cap divider ala Ch 3 from collector back to emitter TANK circuit at collector ac Bottom line ground CB non inverting GAIN stage Cap divider closes loop with 0 I e oscillations ac ground C1 C2 real ground ac ground C1 ac ground C2 go sig ing na to l m sm od all el feedback to starting point real ground r gmv v L C1 C2 feedback to starting point r gmv v L An eq d c fo u i v re a wr r tra alen ting sm itte nsi t tw an a l all n g stor o p ar si en w or ge g er si or all hic t gn eq y h i al ui e s be va ith ha l e n e r vi t a or s C1 C2 V1 Vtank C1 Rin L GmV1 C2 Vo nVtank where n is Cap divider Assume a V1 Vtank Gm V1 Ztank at resonance Ztank Req RiT R where R is all other resistances and RiT comes from the impedance Transform of Rin based on C1 C2 Vo n Vtank C1 C1 C2 Vtank and if Vo V1 we will have condition for oscillations Footnote This notation follows T Lee copy from text attached Krauss uses a different notation Rt RL Rp where Rp is from inductance L and RL is an actual LOAD and Ri includes both the intrinsic transistor 1 gm and external added resistor Re At the highest level we can use simple feedback theory to emphasize a couple of points a GmReq f C1 C1 C2 af 1 denominator is zero Note this doesn t Specify where it Comes from Footnote It turns out that as shown in Fig 16 6 T Lee book the current flow in the device is highly non linear spiked in time as VBE turns on and we really can t use normal smallsignal parameters for Gm How to cope with that problem is discussed in Sect 16 3 2 of T Lee text Ch 16 R 1 2 RiT i Loading This is a highlight summary of the T Lee discussion Ch 16 Section 16 3 4 Voltage gain RiT 1 n R 1 n nG i 2 2 m Req R RiT R 1 nG 2 m at resonance 1 tan k Gm 1 R 2 n Gm R 2 tan k I bias 1 2 R n Gm the next not so obvious step uses Closing the Loop Gm 2 I bias 1 2 I bias n tan k 2 I bias R tan k n 2 R 2 I bias 1 n tan k n R 2I 2I 2 I R 1 n tan k bias tan k bias R bias Other notation C C C C C 1 2 eq 1 2 1 LC n eq C 1 C C 1 2 This is the bottom line result giving the final tank voltage in terms of the bias current R and the voltage divider ration n Incidentally if one were using the notation from Krauss then R would actually be given by RL Rp