Electronic Circuits EE359A

Transcription

1 Electronic Circuits EE359A Bruce McNair B Lecture

2 Signal Generators and Waveform-shaping Circuits Ch

3 Input summing, output sampling voltage amplifier Series voltage summing Shunt voltage sensing 406

4 Using negative feedback system to create a signal generator A Aβω ( ) 1 π Aβω ( ) = π π β 407

5 Basic oscillator structure 408

6 Basic oscillator structure With positive feedback As () Af () s = 1 As ( ) β( s) 409

7 Basic oscillator structure With positive feedback As () Af () s = 1 As ( ) β( s) Loop gain As () β() s 410

8 Basic oscillator structure With positive feedback As () Af () s = 1 As ( ) β( s) Loop gain As () β() s Define loop gain L(s) Ls () As () β() s 411

9 Basic oscillator structure With positive feedback As () Af () s = 1 As ( ) β( s) Characteristic equation 1 Ls ( ) = 0 Loop gain As () β() s Define loop gain L(s) Ls () As () β() s 412

10 Criteria for oscillation For oscillation to occur at ω o L( jω ) A( jω ) β( jω ) = 1 o o o The Barkhausen criteria: At ω o, the loop gain has a magnitude 1 and the phase shift is 0 (for positive feedback) 413

11 Criteria for oscillation For oscillation to occur at ω o L( jω ) A( jω ) β( jω ) = 1 o o o The Barkhausen criteria: x f Ax f Aβ x = β x = o Aβ = 1 x = o o x At ω o, the loop gain has a magnitude 1 and the phase shift is 0 (for positive feedback) o 414

12 Criteria for oscillation For oscillation to occur at ω o L( jω ) A( jω ) β( jω ) = 1 o o o The Barkhausen criteria: x f Ax f Aβ x = β x = o Aβ = 1 x = o o x At ω o, the loop gain has a magnitude 1 and the phase shift is 0 (for positive feedback) o If gain is sufficient, frequency of oscillation is determined only by phase response 415

13 Oscillation frequency dependence on phase response A steep phase response ( φ(ω) ) produces a stable oscillator 416

14 jω Oscillator amplitude s L(jω o ) < 1 f( t) jω t a = 0.2 s L(jω o ) > 1 f( t) t a =

15 jω Oscillator amplitude s L(jω o ) = 1 f( t) a = 0 t How do you stabilize the oscillator so the output level remains constant If the oscillator is adjustable, how is this possible across the full range? 418

16 Nonlinear oscillator amplitude control 419

17 Nonlinear oscillator amplitude control 420

18 Nonlinear oscillator amplitude control 421

19 Nonlinear oscillator amplitude control 422

20 Basic oscillator structure With positive feedback As () Af () s = 1 As ( ) β( s) Characteristic equation 1 Ls ( ) = 0 Loop gain As () β() s Define loop gain L(s) Ls () As () β() s 423

21 Nonlinear oscillator amplitude control 424

22 Wein-Bridge oscillator (without amplitude stabilization) 425

23 Wein-Bridge oscillator (without amplitude stabilization) A β(s) 426

24 Wein-Bridge oscillator (without amplitude stabilization) A β(s) Ls () = Aβ () s R A = 1+ R β () s = Z 2 1 p Z p + Z R Z 2 p Ls () = 1+ R1 Zp + Z s s 427

25 Wein-Bridge oscillator (without amplitude stabilization) A L(s) = 1+ R 2 R 1 Z p Z p + Z s β(s) L(s) = 1+ R 2 R 1 1+ Z s Z p = 1+ R 2 R 1 1+ Z s Y p L(s) = 1+ R 2 R 1 1+ R sc R + sc 428

26 Wein-Bridge oscillator (without amplitude stabilization) A β(s) Ls () = Ls () = L( jω) 1+ R2 R R + + sc sc R 1+ R2 R1 R 1 sc 1+ + scr + + R scr sc 1+ R2 R1 = j ωcr ωcr 429

27 Wein-Bridge oscillator (without amplitude stabilization) A L( jω) = 1+ R2 R j ωcr ωcr β(s) Oscillation at ω o if ω CR o 1 ωo = CR 1 = ω CR o 430

28 Wein-Bridge oscillator (without amplitude stabilization) A L( jω) = 1+ R2 R j ωcr ωcr β(s) Oscillation if 1+ R L( jω) = 3 R R = 2 + δ 2 1 R

29 Wein-Bridge oscillator (with amplitude stabilization) A β(s) stabilization 432

30 Wein-Bridge oscillator (with amplitude stabilization) ω ω f 0 o o o 1 = CR 1 = 9 3 (16 10 F)(10 10 Ω) ω = 6250 rad/sec 1000 Hz R R R 2 1 R = =

31 Wein-Bridge oscillator (with alternative stabilization) D 1 and D 2 reduce R f at high amplitudes 434

32 Phase shift oscillator -A -β(s) 435

33 Phase shift oscillator -A -β(s) Phase shift of each RC section must be 60 o to generate a total phase shift of 180 o K must be large enough to compensate for the amplitude attenuation of the 3 RC sections at ω o 436

34 Quadrature oscillator 437

35 Quadrature oscillator Limiting circuit Integrator 2 Integrator 1 438

36 Quadrature oscillator Limiting circuit 1 Ls () = scr 1 ω0 = CR Integrator 2 Integrator 1 439

37 Quadrature oscillator sin( ω0t) cos( ω t) 0 440

38 LC oscillator Colpitts oscillator 441

39 LC oscillator Hartley oscillator 442

40 LC oscillator Colpitts oscillator Frequency determining element Hartley oscillator 443

41 LC oscillator Colpitts oscillator Gain stage Hartley oscillator 444

42 LC oscillator Colpitts oscillator Feedback voltage divider Hartley oscillator 445

43 LC oscillator Colpitts oscillator ω = 0 1 CC 1 2 L C + C 1 2 Hartley oscillator ω = 0 1 ( + ) L L C

44 Practical LC (Colpitts) oscillator 447

45 Piezoelectric oscillator Quartz crystal schematic symbol 448

46 Piezoelectric oscillator Quartz crystal schematic symbol Equivalent circuit 449

47 Piezoelectric oscillator Quartz crystal schematic symbol Equivalent circuit Reactance 450

48 Piezoelectric oscillator ω = s 1 LC s Series resonance Parallel resonance ω = p 1 CC s p L C s + C p 451

49 Piezoelectric oscillator ω = s 1 LC s Series resonance Parallel resonance ω = p 1 CC s p L C s + C p r << Z L 452

50 Pierce crystal oscillator 453

51 Pierce crystal oscillator CMOS inverter (high gain amplifier) DC bias circuit (near V DD /2) LPF to discourage harmonic/overtone oscillation Frequency determining elements (but C S dominates) 454