# CHAPTER 12 SIGNAL GENERATORS AND WAVEFORM-SHAPING CIRCUITS

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1 CHAPTER SIGNA GENERATORS AND WAEFORM-SHAPING CIRCUITS Chapter Outline. Basic Principles of Sinusoidal Oscillators. Op Amp-RC Oscillators.3 C and Crystal Oscillators.4 Bistable Multivibrators.5 Generation of Square and Triangular Waveforms using Astable Multivibrators.6 Generation of a Standardized Pulse-The Monostable Multivibrators.7 Integrated-Circuit Timers.8 Nonlinear Waveform-Shaping Circuits.9 Precision Rectifier Circuits NTUEE Electronics. H. u -

2 Types of Oscillators. BASIC PRINCIPES OF SINUSOIDA OSCIATORS inear oscillator: Employs a positive feedback loop consisting of an amplifier and a frequency-selective network. Some form of nonlinearity has to be employed to provide control of the amplitude of the output. Nonlinear oscillator: Generates square, triangular, pulse waveforms. Employs multivibrators: bistable, astable and monostable. The Oscillator Feedback oop and Oscillation Criterion Positive feedback loop analysis: xo A( ( s ) Af ( s) loop gain : ( s) A( s) ( s) x A( s) ( s) i ( j0) A( j0) ( j0) Barkhausen criterion: The phase of loop gain should be zero at 0. The magnitude of the loop gain should be unity at 0. The characteristic equation has roots at s = j 0. Stability of oscillation frequency: 0 is determined solely by the phase characteristics. A steep function () results in a more stable frequency. NTUEE Electronics. H. u -

3 Nonlinear Amplitude Control Oscillation: loop gain A = Growing output: loop gain A > Decaying output: loop gain A < Oscillation mechanism: Initiating oscillation: loop gain slightly larger than unity (poles in RHP). Gain control: nonlinear network reduces loop gain to unity (poles on j-axis). imiter Circuits for Amplitude Control For small amplitude (D off, D off) incremental gain (slope) = R f /R For large negative swing (D on, D off) incremental gain (slope) = (R f R 4 )/R For large positive swing (D off, D on) incremental gain (slope) = (R f R 3 )/R v R R 3 A v O R R3 R R3 R R4 R R R D v B R4 R5 R R R R 4 R R R R R D 5 v O NTUEE Electronics. H. u -3

4 Wien-Bridge Oscillator R Z p s) R Z p Z s j) 3. OP AMP-RC OSCIATOR CIRCUITS R / R j( RC / RC) ( R / R ( s) 3 src / src ( For = 0 =/RC and R /R =. To initiate oscillation R /R = +. imiter is used for amplitude control. NTUEE Electronics. H. u -4

5 Phase-Shift Oscillator The circuit oscillates at the frequency for which the phase shift of the RC network is 80. Only at this frequency will the total phase shift around the loop be 0 or 360. The minimum number of RC sections is three. K should be equal to the inverse of the magnitude of the RC network at oscillation frequency. Slightly higher K is used to ensure that the oscillation starts. imiter is used for amplitude control. NTUEE Electronics. H. u -5

6 Quadrature Oscillator Based on the two-integrator loop without damping. R, R, R 3, R 4, D and D are used as limiter. oop gain: v v O O v C C t 0 ( s) t vo dt R o 0 o vx o dt R o x s R x C src src Poles are initially located in RHP (decreasing R f ) to ensure that oscillation starts. Too much positive feedback results in higher output distortion. v O is purer than v O because of the filtering action provided by the second integrator on the peak-limited output of the first integrator. NTUEE Electronics. H. u -6

7 Active-Filter Tuned Oscillator The circuit consists of a high-q bandpass filter connected in a positive-feedback loop with a hard limiter. Any filter circuit with positive gain can be used to implement the bandpass filter. Can generate high-quality output sine waves. Have independent control of frequency, amplitude and distortion of the output sinusoid. Final Remark Op amp-rf oscillators ~ 0 to 00kHz. ower limit: passive components. Upper limit: frequency response and slew rate of op amp. NTUEE Electronics. H. u -7

8 C Tuned Oscillators.3 C AND CRYSTA OSCIATORS Colpitts oscillator: capacitive divider. Hartley oscillator: inductive divider. Utilize a parallel C circuit between base and collector. R models the overall losses. Analysis of Colpitts Oscillators / C C 0 / / 0 / ( ) C sc gm ( sc / R)( s C) 0 3 s C C s C g R C / C m / R s( C C) ( g / R) 0 C-tuned oscillators utilize the nonlinear transistor I- characteristics for amplitude control (self-limiting). Collector (drain) current waveforms are distorted due to the nonlinear characteristics. Output voltage is a sinusoid with high purity because of the filtering action of the C tuned circuit. 3 ( C C ) C C 0 C ( g m ) j R R / C C 0 / / m NTUEE Electronics. H. u -8

9 Complete Circuit for a Colpitts Oscillator DC Analysis R E AC Analysis NTUEE Electronics. H. u -9

10 Crystal Oscillators Crystal impedance: Z( s) / sc Z s) sc ( p s s / C s s / scs s / Cs [( C C ) / C C p p s p s ] / p (/ C s / C ) p s Z( j) j C p p Crystal reactance is inductive over very narrow frequency ( s to p ). The frequency band is well defined for a given crystal. Use the crystal to replace the inductor of the Colpitts oscillators. Oscillation frequency is dominated by C s (much smaller than other C s). / 0 Cs s Crystals are available with resonance frequencies KHz ~ hundred MHz. The oscillation frequency is fixed (tuning is not possible). NTUEE Electronics. H. u -0

11 .4 BISTABE MUTIIBRATORS Bistable Characteristics Positive feedback is used for bistable multivibrator. Stable states: () v O = + and v + = + R /(R +R ). () v O = and v + = R /(R +R ). Metastable state: v O = 0 and v + = 0. Transfer Characteristics of the Inverting Bistable Circuit Initially v O = + and v + = + R /(R +R ) v O change stage to when v I increases to a value of + R /(R +R ). Initially v O = and v + = R /(R +R ) v O change stage to + when v I decreases to a value of R /(R +R ). The circuit exhibits hysteresis with a width of ( TH T ). Input v I is referred to as a trigger signal which merely initiates or triggers regeneration. NTUEE Electronics. H. u -

12 Transfer Characteristics of the Noninverting Bistable Circuit Initially v O = + and v + = v I R /(R +R ) + + R /(R +R ) > 0 v O change stage to when v I decreases to a value ( T ) that causes v + = 0 T = + (R /R ) Initially v O = and v + = v I R /(R +R ) + R /(R +R ) < 0 v O change stage to + when v I increases to a value ( TH ) that causes v + = 0 T = (R /R ) Application of the Bistable Circuit as a Comparator NTUEE Electronics. H. u -

13 imiter Circuits for Precise Output evels ) ( D Z D Z D D Z NTUEE Electronics. H. u -3 ( 4) D3 D Z

14 .5 GENERATION OF SQUARE AND TRIANGUAR WAEFORMS USING ASTABE MUTIIBRATORS Operation of the Astable Multivibrator F d R /(R +R ) 0 NTUEE Electronics. H. u -4 For v O = + and v + = v O R /(R +R ) > 0 v is charged toward + through RC v O change stage to when v = v + For v O = and v + = v O R /(R +R ) < 0 v is discharged toward through RC v O change stage to + when v = v + ) / ( ln ) ( ) ( / / T e e v t RC t ln T ) / ( ln ) ( ) ( / / T e e v t RC t

15 Generation of Triangular Waveforms Triangular can be obtained by replacing the low-pass RC circuit with an integrator. The bistable circuit required is of the noninverting type. TH T T RC T RC TH T TH T T RC T RC TH T NTUEE Electronics. H. u -5

16 .6 GENERATION OF A STANDARDIZED PUSE THE MONOSTABE MUTIIBRATORS Op-Amp Monostable Multivibrators Circuit components: Trigger: C, R 4 and D Clamping diode: D R 4 >> R i D4 0 The circuit has one stable state: v O = + v B = D 0 D and D on Operation of monostable multivibrator Negative step as the trigger input D conducts heavily v C is pulled below v B v O changes state to and v C becomes negative D and D off and C is discharged toward v O changes state to as v B = v C Stays in the stable state Positive trigger step turns off D (invalid trigger) v ( t) B v ( T ) B T C R ( ( D ) e ) D t / R C 3 T / R C D ln C 3 ln 3 R e 3 NTUEE Electronics. H. u -6

17 .7 INTEGRATED-CIRCUIT TIMERS Monostable Multivibrator using 555 Timer Circuit S R Stable state: S = R = 0 and Q = 0 Q on and v C = 0 Trigger (v trigger < T ): S = and Q = Q off and v C is charged toward CC Trigger pulse removal (v trigger > T ): S = R = 0 and Q = Q off and v C is charged toward CC End of recovery period (v C = TH ): R = and Q = 0 Q on and v C is discharged toward GND Stable state: v C drops to 0 and S = R = 0 and Q = 0 v C ( t) CC ( e t / RC T RC ln3. RC ) NTUEE Electronics. H. u -7

18 Astable Multivibrator using 555 Timer Circuit v T v t / C( R B ) ( ) ( ) A R C t CC CC T e H C T CR ln CR C( RA RB )ln 0.69C( RA RB ) TH e B t / CR B B T T T 0. 69CR H TH Duty cycle T T H B R R A A RB R B Operation of astable multivibrator Initially v C = 0: S/R = /0 and Q = Q off and v C is charged toward CC thru R A and R B v C reaches TH : S/R = 0/ and Q = 0 Q on and v C is discharged toward GND thru R B v C reaches T : S/R = /0 and Q = Q off and v C is charged toward CC thru R A and R B NTUEE Electronics. H. u -8

19 .8 NONINEAR WAEFORM-SHAPING CIRCUITS Nonlinear Amplification Method Use amplifiers with nonlinear transfer characteristics to convert triangular wave to sine wave. Differential pair with an emitter degeneration resistance can be used as sine-wave shaper. Breakpoint Method R 4, R 5 >> R, R and R 3 to avoid loading effect. < v IN < : v O = v IN < v IN < or < v IN < v O = + (v IN ) R 5 / (R 4 + R 5 ) v IN < or < v IN v O = NTUEE Electronics. H. u -9

20 .9 PRECISION RECTIFIER CIRCUITS Precision Half-Wave Rectifier (Superdiode) Operation of super diode: v O = v I for v I > 0 v O = 0 for v I < 0 The offset voltage (~0.5) can be eliminated. Nonideal characteristics are masked by the loop gain. Disadvantages: Reverse bias may damage the input terminals. Op saturation (open loop) degrades the speed. Improved Precision Half-Wave Rectifier Rectifier operation: v I > 0 : D off, D on v O = 0 v I < 0 : D on, D off v O = (R / R ) v I The feedback loop remains closed at all times. The op amp remains in its linear operation region. Can prevent the delay due to saturated op amp. NTUEE Electronics. H. u -0

21 AC oltage Measurement The circuit consists of a half-wave rectifier and a first-order low-pass filter. Dc component of v is ( p /)(R /R ). The PF corner frequency should be much smaller than the input sine wave to reduce error by the harmonics. Precision Full-Wave Rectifier Full-wave rectifier is implemented by combining two rectifiers with a common load. Diode A is replaced by a superdiode. Diode B is replaced by the inverting precision half-wave rectifier. NTUEE Electronics. H. u -

22 Precision Peak Rectifiers Buffered Precision Peak Detector Precision Clamping Circuit NTUEE Electronics. H. u -

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