# CHAPTER 14 SIGNAL GENERATORS AND WAVEFORM SHAPING CIRCUITS

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1 CHAPTER 4 SIGNA GENERATORS AND WAEFORM SHAPING CIRCUITS Chapter Outline 4. Basic Principles of Sinusoidal Oscillators 4. Op Amp RC Oscillators 4.3 C and Crystal Oscillators 4.4 Bistable Multivibrators 4.5 Generation of Square and Triangular Waveforms using Astable Multivibrators 4.6 Generation of a Standardized Pulse The Monostable Multivibrators 4.7 Integrated Circuit Timers 4.8 Nonlinear Waveform Shaping Circuits NTUEE Electronics. H. u 4

2 Types of Oscillators 4. Basic Principles of Sinusoidal Oscillators 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 Barkhausen criterion: ( j) A( j) ( j) The phase of loop gain should be zero at The magnitude of the loop gain should be unity at The characteristic equation has roots at s = j Stability of oscillation frequency: is determined solely by the phase characteristics A steep function f () results in a more stable frequency NTUEE Electronics. H. u 4

3 Nonlinear Amplitude Control Oscillation: loop gain Ab = Growing output: loop gain Ab > Decaying output: loop gain Ab < 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 4 3

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

5 Phase Shift Oscillator The circuit oscillates at the frequency for which the phase shift of the RC network is 8 Only at this frequency will the total phase shift around the loop be or 36 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 4 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 ( s) t vo dt R o vx o dt R o x s R 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 x C o src NTUEE Electronics. H. u 4 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 ~ to khz ower limit: passive components Upper limit: frequency response and slew rate of op amp NTUEE Electronics. H. u 4 7

8 C Tuned Oscillators 4.3 C and Crystal Oscillators Colpitts oscillator: capacitive divider Hartley oscillator: inductive divider A parallel C circuit between base and collector R models the overall losses Analysis of Colpitts Oscillators / C C / / / ( ) C sc gm ( sc / R)( s C) 3 s C C s C g R C / C m / R s( C C) ( g / R) C tuned oscillators utilize the nonlinear transistor I characteristics for amplitude control (selflimiting) 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 C ( g m ) j R R / C C / / m NTUEE Electronics. H. u 4 8

9 Complete Circuit for a Colpitts Oscillator DC Analysis R E AC Analysis NTUEE Electronics. H. u 4 9

10 The Cross Coupled C Oscillator Popular C oscillator circuit suitable for IC implementation Capable of operating at high frequencies (up to hundreds of GHz) The oscillation frequency is defined by the C tank The cross couple pair is to start up the oscillation Differential oscillation output available A A / C A A g m ( R g [ g p ( R r ) o m m ( R p p r ) r )] o o NTUEE Electronics. H. u 4

11 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) / Cs s Crystals are available with resonance frequencies KHz ~ hundred MHz The oscillation frequency is fixed (tuning is not possible) NTUEE Electronics. H. u 4

12 4.4 Bistable Multivibrators Bistable Characteristics Positive feedback for bistable multivibrator Stable states: () v O = + and v + = + R /(R +R ) () v O = and v + = R /(R +R ) Metastable state: v O = and v + = 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 4

13 Transfer Characteristics of the Noninverting Bistable Circuit Initially v O = + and v + = v I R /(R +R ) + + R /(R +R ) > v O change stage to when v I decreases to a value ( T ) that causes v + = T = + (R /R ) Initially v O = and v + = v I R /(R +R ) + R /(R +R ) < v O change stage to + when v I increases to a value ( TH ) that causes v + = T = (R /R ) Application of the Bistable Circuit as a Comparator NTUEE Electronics. H. u 4 3

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

15 NTUEE Electronics. H. u 4.5 Generation of Square and Triangular Waveforms using Astable Multivibrators Operation of the Astable Multivibrator For v O = + and v + = v O R /(R +R ) > v is charged toward + through RC v O change stage to when v = v + For v O = and v + = v O R /(R +R ) < 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 4 5

16 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 4 6

17 Op Amp Monostable Multivibrators Circuit components: Trigger: C, R 4 and D Clamping diode: D R 4 >> R i D4 The circuit has one stable state: v O = + v B = D D and D on Operation of monostable multivibrator Negative step as the trigger input D conducts heavily 4.6 Generation of a Standardized Pulse The Monostable Multivibrators 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 ) e t / R C D ln C 3 ln 3 R 3 T / R C 3 NTUEE Electronics. H. u 4 7

18 4.7 Integrated Circuit Timers Monostable Multivibrator using 555 Timer Circuit S R Stable state: S = R = and Q = Q on and v C = Trigger (v trigger < T ): S = and Q = Q off and v C is charged toward CC Trigger pulse removal (v trigger > T ): S = R = and Q = Q off and v C is charged toward CC End of recovery period (v C = TH ): R = and Q = Q on and v C is discharged toward GND Stable state: v C drops to and S = R = and Q = v C ( t) CC ( e t / RC T RC ln3. RC ) NTUEE Electronics. H. u 4 8

19 Astable Multivibrator using 555 Timer Circuit v T v / ( B ) ( ) ( ) t C R A R C t CC CC T e H C T CR ln3. 69CR C( RA RB )ln.69c( RA RB ) TH e B t / CR B B T T T. 69CR H TH Duty cycle T T H B R R A A RB R B Operation of astable multivibrator Initially v C = : S/R = / and Q = Q off and v C is charged toward CC thru R A and R B v C reaches TH : S/R = / and Q = Q on and v C is discharged toward GND thru R B v C reaches T : S/R = / and Q = Q off and v C is charged toward CC thru R A and R B NTUEE Electronics. H. u 4 9

20 4.8 Nonlinear Waveform 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 4

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