Electronic Circuits EE359A Bruce McNair B206 bmcnair@stevens.edu 201-216-5549 Lecture 16 404
Signal Generators and Waveform-shaping Circuits Ch 17 405
Input summing, output sampling voltage amplifier Series voltage summing Shunt voltage sensing 406
Using negative feedback system to create a signal generator A Aβω ( ) 1 π Aβω ( ) = π π β 407
Basic oscillator structure 408
Basic oscillator structure With positive feedback As () Af () s = 1 As ( ) β( s) 409
Basic oscillator structure With positive feedback As () Af () s = 1 As ( ) β( s) Loop gain As () β() s 410
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
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
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
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
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
Oscillation frequency dependence on phase response A steep phase response ( φ(ω) ) produces a stable oscillator 416
jω Oscillator amplitude s L(jω o ) < 1 f( t) 2 0 2 jω 0 1 2 3 4 5 t a = 0.2 s L(jω o ) > 1 f( t) 2 0 2 0 1 2 3 4 5 t a = 0.2 417
jω Oscillator amplitude s L(jω o ) = 1 f( t) 2 0 2 0 1 2 3 4 5 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
Nonlinear oscillator amplitude control 419
Nonlinear oscillator amplitude control 420
Nonlinear oscillator amplitude control 421
Nonlinear oscillator amplitude control 422
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
Nonlinear oscillator amplitude control 424
Wein-Bridge oscillator (without amplitude stabilization) 425
Wein-Bridge oscillator (without amplitude stabilization) A β(s) 426
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
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 + 1 1 sc R + sc 428
Wein-Bridge oscillator (without amplitude stabilization) A β(s) Ls () = Ls () = L( jω) 1+ R2 R1 1 1 1+ R + + sc sc R 1+ R2 R1 R 1 sc 1+ + scr + + R scr sc 1+ R2 R1 = 1 3 + j ωcr ωcr 429
Wein-Bridge oscillator (without amplitude stabilization) A L( jω) = 1+ R2 R1 1 3+ j ωcr ωcr β(s) Oscillation at ω o if ω CR o 1 ωo = CR 1 = ω CR o 430
Wein-Bridge oscillator (without amplitude stabilization) A L( jω) = 1+ R2 R1 1 3+ j ωcr ωcr β(s) Oscillation if 1+ R L( jω) = 3 R R = 2 + δ 2 1 R 2 1 431
Wein-Bridge oscillator (with amplitude stabilization) A β(s) stabilization 432
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 2 1 2 = 20.3 10 = 2.03 433
Wein-Bridge oscillator (with alternative stabilization) D 1 and D 2 reduce R f at high amplitudes 434
Phase shift oscillator -A -β(s) 435
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
Quadrature oscillator 437
Quadrature oscillator Limiting circuit Integrator 2 Integrator 1 438
Quadrature oscillator Limiting circuit 1 Ls () = scr 1 ω0 = CR 2 2 2 Integrator 2 Integrator 1 439
Quadrature oscillator sin( ω0t) cos( ω t) 0 440
LC oscillator Colpitts oscillator 441
LC oscillator Hartley oscillator 442
LC oscillator Colpitts oscillator Frequency determining element Hartley oscillator 443
LC oscillator Colpitts oscillator Gain stage Hartley oscillator 444
LC oscillator Colpitts oscillator Feedback voltage divider Hartley oscillator 445
LC oscillator Colpitts oscillator ω = 0 1 CC 1 2 L C + C 1 2 Hartley oscillator ω = 0 1 ( + ) L L C 1 2 446
Practical LC (Colpitts) oscillator 447
Piezoelectric oscillator Quartz crystal schematic symbol 448
Piezoelectric oscillator Quartz crystal schematic symbol Equivalent circuit 449
Piezoelectric oscillator Quartz crystal schematic symbol Equivalent circuit Reactance 450
Piezoelectric oscillator ω = s 1 LC s Series resonance Parallel resonance ω = p 1 CC s p L C s + C p 451
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
Pierce crystal oscillator 453
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