1. Oscillators Fixed Frequency, Controlled Power Transmitters Receivers/Tuners Clock Circuits AvAv B(j  ) + + V out V in System poles @ A v B(s) = 1

2. Barkhausen Criteria System poles @ A v B(s) = 1 Pole in RHP: Oscillation amplitude grows until amplifier starts to clip, then A v ’ < A v. 00 Root locus for A v ’ < A v

3. Oscillator Design AvAv B(j  ) + + V out V in Common Base: r in = r e A v = R c ’/r e Common Emitter: r in = (  +1)r e A v = -R c ’/r e Frequency Selective Feedback Network LC Network Quartz Crystal

4. Amplifier Gain A v = + R c ’/r e r e = 26 mV/I E (from DC Analysis) R c ’ : Parallel Combination of 1.Transformed Load: R L ’ = R L /  v 2 2.Parasitic Loading (finite Q): R coil = Q u X T 3.Feedback Network: R e ’ =..... 4.Collector Dynamic (AC) Resistance: r c ~ 20 k 5.Any other resistances in Collector Circuit

5. Hartley Oscillator (common base, autotransformer feedback) E C

6. R1R1 R2R2 R3R3 R4R4 RLRL n1n1 n2n2 n3n3 CTCT LTLT, Q u BP V CC, r c + - R2R2 R3R3 IBIB V CC R1R1 I C  I B R3R3 rere I E  I B ieie rcrc R4R4 n2n2 n1n1 + v e - B C E B C E rere Hartley Oscillator DC Equivalent AC Equivalent 

7. R3R3 rere ieie rcrc RPRP R4R4 n2n2 n1n1 + v e - B C E + v c - B1vcB1vc v e = B 1 B 2 v c R3R3 rere ieie rcrc RPRP + v e - B C E + v c - B=B 1 B 2 v e = Bv c Ideal

8. rere ieie rcrc RPRP + v e - B C E + v c - B v e = Bv c rere ieie + v e - B C E + v c - B v e = Bv c Note: any additional resistance placed across the tank circuit must be included as an additional parallel contribution.

9. B AVAV Barkhausen: is A V B > 1 ? Book Example : f = 1 Mhz I C ~ I E = 1 ma n 1 = 10, n 2 = 100, n 3 = 5 (subscripts changed) L T = 53 uH, Q u = 50, X T = 333  R L = 50  R 3 = 1 k  R 4 = 0  therefore, B 2 = 1  r c = 50 k  R1R1 R2R2 R3R3 R4R4 RLRL n1n1 n2n2 n3n3 CTCT LTLT, Q u BP V CC, r c rere 

10. Maximum Power Considerations The maximum 0-pk collector AC voltage is: The maximum power to the load is: V CC was not given for this problem, but we can determine a minimum value required to prevent saturation at max power by recalling that...

11. Colpitts Oscillator (common base, capacitive feedback) E C