Electronic Circuits EE359A

Transcription

1 Electronic Circuits EE359A Bruce McNair B Lecture

2 Signal Generators and Waveform-shaping Circuits Ch

3 Stability in feedback systems Feedback system Bounded input Is output bounded? 381

4 Stability measures 382

5 Using negative feedback system to create a signal generator A Aβω ( ) 1 π Aβω ( ) = π π β 383

6 Basic oscillator structure 384

7 Basic oscillator structure With positive feedback As () Af () s = 1 As ( ) β( s) 385

8 Basic oscillator structure With positive feedback As () Af () s = 1 As ( ) β( s) Loop gain As () β() s 386

9 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 387

10 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 388

11 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) 389

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 390

13 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 391

14 Oscillation frequency dependence on phase response A steep phase response ( φ(ω) ) produces a stable oscillator 392

15 jω Oscillator amplitude σ L(jω o ) < 1 f( t) jω t a = 0.2 σ L(jω o ) > 1 f( t) t a =

16 jω Oscillator amplitude σ 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? 394

17 Nonlinear oscillator amplitude control 395

18 Nonlinear oscillator amplitude control 396

19 Nonlinear oscillator amplitude control 397

20 Nonlinear oscillator amplitude control 398

21 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 399

22 Nonlinear oscillator amplitude control 400

23 Wein-Bridge oscillator (without amplitude stabilization) 401

24 Wein-Bridge oscillator (without amplitude stabilization) A β(s) 402

25 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 403

26 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 404

27 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 405

28 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 406

29 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

30 Wein-Bridge oscillator (with amplitude stabilization) A β(s) stabilization 408

31 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 = =

32 Wein-Bridge oscillator (with alternative stabilization) D 1 and D 2 reduce R f at high amplitudes 410

33 Phase shift oscillator -A -β(s) 411

34 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 412

35 Quadrature oscillator 413

36 Quadrature oscillator Limiting circuit Integrator 2 Integrator 1 414

37 Quadrature oscillator Limiting circuit 1 Ls () = scr 1 ω0 = CR Integrator 2 Integrator 1 415

38 Quadrature oscillator sin( ω0t) cos( ω t) 0 416

39 LC oscillator Colpitts oscillator 417

40 LC oscillator Hartley oscillator 418

41 LC oscillator Colpitts oscillator Frequency determining element Hartley oscillator 419

42 LC oscillator Colpitts oscillator Gain stage Hartley oscillator 420

43 LC oscillator Colpitts oscillator Feedback voltage divider Hartley oscillator 421

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

45 Practical LC (Colpitts) oscillator 423

46 Piezoelectric oscillator Quartz crystal schematic symbol 424

47 Piezoelectric oscillator Quartz crystal schematic symbol Equivalent circuit 425

48 Piezoelectric oscillator Quartz crystal schematic symbol Equivalent circuit Reactance 426

49 Piezoelectric oscillator ω = s 1 LC s Series resonance Parallel resonance ω = p 1 CC s p L C s + C p 427

50 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 428

51 Pierce crystal oscillator 429

52 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) 430