Electronic Circuits EE359A
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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
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