Basic Principles of Sinusoidal Oscillators Linear oscillator Linear region of circuit: linear oscillation Nonlinear region of circuit: amplitudes stabilization Barkhausen criterion X S Amplifier A X O X f Frequency-selective network Loop gain L(s) = β(s)a(s) haracteristic equation -L(s) = Oscillation criterion L(jw ) = A(jw ) β(jw ) = Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6
Basic Principles of Sinusoidal Oscillators (ont.) At w, the phase of the loop should be zero and the magnitude of the loop gain should be unity Oscillation frequency w is determined solely by φ Δφ Δω dφ dω Δφ ω ω A steep phase response results in a small given change in phase w for a Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6
Nonlinear Amplitude ontrol o sustain oscillation: βa a. Overdesign for βa variations b. Oscillation will grow in amplitude Poles are in the right half of the s-plane c. Nonlinear network reduces βa to when the desired amplitude is reached Poles will be pulled to jw-axis Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -4 郭泰豪, Electronics(), 6 Nonlinear Amplitude ontrol (ont.) Limiter circuit for amplitude control Linear region O A B ( f ) 4 i 4 5 O O 4 5 5 I D D f A 4 B 5 O -
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6-5 Nonlinear Amplitude ontrol (ont.) Nonlinear region ) ( L similarly, ) ( ) ( L 5 4 D 5 4 O D D - O D B D A f ) ( Slope L L 4 f ) ( Slope O I f Slope
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -6 郭泰豪, Electronics(), 6 Wien-bridge oscillator L ) L s jω) ω L s OPAMP- Oscillator ircuits Z S S j ω ω For phase,ω p Z Z ) p s d ω Z P _ Z S O
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -7 郭泰豪, Electronics(), 6 OPAMP- Oscillator ircuits (ont.) Wien-bridge oscillator with a limiter 5 D k a.k k _ 4 k O k 6nF 6nF k 5 k D b 6 k 5
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -8 郭泰豪, Electronics(), 6 OPAMP- Oscillator ircuits (ont.) v O 5k p b k a - 6nF 6nF k k
Phase-Shift Oscillator Without amplitude stabilization -K ------- phase shift of the network is 8 degrees. otal phase shift around the loop is or 6 degrees. Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -9 郭泰豪, Electronics(), 6
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6 Phase-Shift Oscillator (ont.) With amplitude stabilization k t 5k x 6nF 6nF 6nF k k _ D vo D 4
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6 OP : inverting integrator with amplitude control OP : noninverting integrator 4 - Quadrature Oscillator v O v - f v O Equivalent circuit at the input of OP Set v(t) v v f O O (t) (s) t vo(t) dt t vo(t) dt vo(s) s _ v O X _ OP v O v OP f (Nominally )
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6 Quadrature Oscillator (ont.) ------ Break the loop at X, loop gain L(s) = O oscillation frequency X (s) (s) = - s w s - s ------ o is the integral of o 9 phase difference between o and o quadrature oscillator
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6 Block diagram Active-Filter uned Oscillator f PSD - t PSD t 5f o f o f o... Frequency - f o Frequency High-distortion v High-Q bandpass low-distortion v
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -4 郭泰豪, Electronics(), 6 Active-Filter uned Oscillator (ont.) Practical implementation Q - -
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -5 郭泰豪, Electronics(), 6 A General Form of L-uned Oscillator onfiguration Many oscillator circuits fall into a general form shown below O ˆ - A I Z Z Z O O - A ˆ v Z Z Z O Z L Z L Z, Z, Z : capacitive or inductive
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6-6 A General Form of L-uned Oscillator onfiguration (ont.) v v v O v O v O L v O L O O L L v O X X A X X X A ) X (X X X X A X X X oscillation, for ) X (X X ) X X (X j X X A capacitance for ω X inductance ωl for X jx Z, jx Z jx, Z if ) Z (Z Z ) Z Z (Z Z Z A, Z Z Z Z A Z Z Z A ˆ ˆ ˆ
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -7 郭泰豪, Electronics(), 6 A General Form of L-uned Oscillator onfiguration (ont.) With oscillation = and i.e. = =, 6, 7, degree. (X =ωl or X = - ) ω X & X must have the same sign if A v is positive X & X are L, X = -(X + X ) is or X & X are, X = -(X + X ) is L ransistor oscillators.ollpitts oscillator -- X & X are s, X is L.Hartley oscillator -- X & X are Ls, X is
L-uned Oscillators wo commonly used configurations olpitts (feedback is achieved by using a capacitive divider) DD L L Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -8 郭泰豪, Electronics(), 6
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -9 郭泰豪, Electronics(), 6 L-uned Oscillators (ont.) Hartley (feedback is achieved by using an inductive divider) DD L L L L
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6 olpitts oscillator Equivalent circuit L-uned Oscillators (ont.) s π L c π s L ) sπ π g m π π ( gs for a FE) can be considered to be a part of = loss of inductor + load resistance of oscillator + output resistance of transistor
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6 - L-uned Oscillators (ont.) For oscillations to start, both the real and imaginary parts must be zero Oscillation frequency ) + L( = ω S=jw ] ) ( [ ) ( ) ( ) ( ) ( ) )( ( L j L g g s L s L s L s s g s sl s m m m c w w w
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6 Gain g m L-uned Oscillators (ont.) (Actually, g Oscillation amplitude.l tuned oscillators are known as self limiting oscillators. (As oscillations grown in amplitude, transistor gain is reduced below its small signal value).output voltage signal will be a sinusoid of high purity because of the filtering action of the L tuned circuit Hartley oscillator can be similarly analyzed m )
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6 Symbol of crystal rystal Oscillators ircuit model of crystal L S P r
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -4 郭泰豪, Electronics(), 6 rystal Oscillators (ont.) eactance of a crystal assuming r = Z(s) s ω Let ω If Z jω) P S P P sl s L L S S S ω ω j ω P ω ω, then ω ω P S P s S S P P s s L ) P L S S P S rystal reactance (rystal is high Q device) inductive ωs capacitive ω p ω
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -5 郭泰豪, Electronics(), 6 rystal Oscillators (ont.) he crystal reactance is inductive over the narrow frequency band between ω s and ω p olpitts crystal oscillator onfiguration Equivalent circuit L P crystal π S v S - w P, L, S w S w P
Pierce oscillator rystal Oscillators (ont.) Almost all digital clock oscillators are Pierce oscillators Derived from olpitts oscillator Inverter with feedback resistor as an inverting amplifier eplacement of the E amplifier f o DD o = i crystal D operation point i Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -6 郭泰豪, Electronics(), 6
Multivibrators Multivibrators bistable: two stable states ( types) monostable: one stable state astable: no stable state Bistable Has two stable states an be obtained by connecting an amplifier in a positive-feedback loop having a loop gain greater than unity. I.e. βa> where β= /( + ) Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -7 郭泰豪, Electronics(), 6
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -8 郭泰豪, Electronics(), 6 Bistable Multivibrators (ont.) Bistable circuit with clockwise hysteresis v o v + L v I - - v O L - L H v I lockwise hysteresis (or inverting hysteresis) L + :positive saturation voltage of OPAMP L - :negative saturation voltage of OPAMP H L βl βl L L Hysteresis width = H - L
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -9 郭泰豪, Electronics(), 6 Noninverting Bistable ircuit ounterclockwise hysteresis onfiguration v I - v + - v O L L v o H v I L - v v I v O For v For v O O L L,, v v,, v v I I L H L H L L
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6 Noninverting Bistable ircuit (ont.) omparator characteristics with hysteresis an reject interference Input Output Hysteresis buffer Signal corrupted with interference Input H L t Multiple Zero crossings Output t
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6 Generation of Square and riangular Waveforms Using Astable Multivibrators an be done by connecting a bistable multivibrator with a circuit in a feedback loop. v o L v v L H v I H βl t L - L t L βl L -
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6 Generation of Square and riangular Waveforms Using Astable Multivibrators (ont.) v O t) L t v + - v - L - ) t o L v - v O - H βl t - L H βl v t) βl o L - ime constant t = L βl
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan - 郭泰豪, Electronics(), 6 Generation of Square and riangular Waveforms Using Astable Multivibrators (ont.) During (t) if L ( ) L βl ) βl e t where, L L ) β ln β β During (t) if ( L ) L βl ) βl ln e β ; β (t ) L L ) β ln β L L is assumed)
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -4 郭泰豪, Electronics(), 6 Generation of riangular Waveforms v o t _ L L H L - v I t Bistable Slope -L H L t t L Slope L L
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -5 郭泰豪, Electronics(), 6 Generation of riangular Waveforms (ont.) During L L i dt where i H L L L H ; L During Similarily L H L Period = + o obtain symmetrical waveforms L L
Monostable Multivibrators Alternative name one shot Has one stable state (βl+ D) v E (t) an be triggered to a quasi-state v A (t) t L E D 4 L - _ A βl v (t) B βl - D D v B (t) o L βl - o L Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -6 郭泰豪, Electronics(), 6
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -7 郭泰豪, Electronics(), 6 During Monostable Multivibrators (ont.) B B For (t) L () βl D (L L βl ln( βl D D )e L L L t ) (L D )e ln( ) β βl + is greater than D Stable state is maintained
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -8 郭泰豪, Electronics(), 6 Monostable Multivibrators (ont.) Monostable multivibrator using NO gates v in in O X + DD O DD v O t NO NO DD DD X t DD DD v O t DD t
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -9 郭泰豪, Electronics(), 6 Monostable Multivibrators (ont.) - - O DD v X - - O - DD DD v X - () v t v (e ) x DD v ( ) ( e ) x DD DD ln ln.69 DD DD where ; is NO gate threshold voltage v v x ( ) DD e t
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -4 郭泰豪, Electronics(), 6 Monostable Multivibrators (ont.) Monostable multivibrator with catching diode DD in o D O NO x NO X 5.6 forward resistance of diode 5 D ime constant f ime constant t
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -4 郭泰豪, Electronics(), 6 Astable Multivibrator Using NO(or Inverter) Gates v o X O O DD v _ v o DD t ransient behavior () < t < (i) v : when t= o DD (ii) v : when t= o DD (iii)v =( + )e x DD -t (iv)v =v - =- +( + )e c x O DD DD -t DD v X DD v t DD t t
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -4 郭泰豪, Electronics(), 6 Astable Multivibrator Using NO(or Inverter) Gates (ont.) () < t < ( + ) (i) v : when t= (ii) v : o DD o DD x DD DD when t= (iii)v = -( + )e (t- ) (iv)v =v - =v = -( + )e c x O x DD DD (t- )
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -4 郭泰豪, Electronics(), 6 Astable Multivibrator Using NO(or Inverter) Gates (ont.) Oscillation frequency v ( )= x t DD ( + )e = DD+ =ln DD If =, then =ln and =ln.455 oscillation frequency f = ln
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -44 郭泰豪, Electronics(), 6 Astable Multivibrator Using NO(or Inverter) Gates (ont.) With catching diode at X X O O v _ f ln ln.7 Asymmetrical square wave DD (i) (ii) DD X O D D v _ O
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -45 郭泰豪, Electronics(), 6 c + - eading Assignment: he 555 I imer Widely used as both a monostable and astable multivibrator n Used as a monostable multivibrator hreshold c rigger t H L omparator S Q omparator Q Q O v t (t) v c (t) H v O (t) v(t) S n Q n+ Q n N/A H L vt L ( e n t ) Dischargetransistor
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -46 郭泰豪, Electronics(), 6 eading Assignment: he 555 I imer (ont.) For t v (t) [ ()]e t ( () E(sat) ) For t =, v ln ( ) H () ln ( () )
Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan -47 郭泰豪, Electronics(), 6 eading Assignment: he 555 I imer (ont.) Used as an astable multivibrator cc H= cc L = ( ) A B cc c S, cc c S, cc cc c S ln, ( )ln B A B Oscillation frequency t A B f hreshold c rigger t H L (A omparator omparator B )ln 555 timer chip S Q Q Q O Dischargetransistor
Sine-wave shaper Precision rectifier circuits Precision full-wave rectifiers Peak rectifier rystal oscillators Appendix APP- -48 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
Sine-Wave Shaper Shape a triangular waveform into a sinusoid Extensively used in function generators Note: linear oscillators are not cost-effective for low v O v f t frequency application not easy to time over wide frequency ranges t APP- -49 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
Sine-Wave Shaper (ont.) Nonlinear-amplification method For various input values, their corresponding output values can be calculated ransfer curve can be obtained and is similar to _ vo (Sine wave) v i (riangular wave) Q Q I I - EE APP- -5 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
Sine-Wave Shaper (ont.) Breakpoint method Piecewise linear transfer curve Low-valued is assumed and are constant in in in D D D out ( in in ison(voltage drop D 5 ) ison limit 5 to 4 D ) D APP-4-5 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
Sine-Wave Shaper (ont.) D in out D 5 5 in 4 D 5 4 out D 4 APP-5-5 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
Precision ectifier ircuits Precision half-wave rectifier --- superdiode "Superdiode" O i _ A O i An alternate circuit O D _ D O i i APP-6-5 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
Precision ectifier ircuits (ont.) Application:Measure A voltages D 4 i _ A D _ A O Average π P ;where p is the peak amplitude of an input sinusoid APP-7-54 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
Precision ectifier ircuits (ont.) If ω 4 π P min 4 ;ω min is the lowest expected frequency of the input sine wave APP-8-55 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
Precision Full-Wave ectifiers A D A A B D B B or L APP-9-56 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
Precision Full-Wave ectifiers (ont.) i A _ A E D O O _ A D P i F L APP- -57 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
With load Peak ectifier Super diode v i - _ L v O - Buffered D _ A D _ A v O - v i - APP- -58 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
rystal Oscillators - + gd MHz XAL L 6~ uh stray M.kΩ D N68 S =pf.μf Bias circuit L - (For A,- and ground are the same=) APP- -59 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
rystal Oscillators (ont.) AX v Since return ratio = X then X must be large for the loop gain to be greater than one. X is very large when ω closes to ω ωs ω ωp p and X +X +X = & X = X &X are inductive ω j Z =L//= = jω + ω + jω L ω L X = > ωl> ω> ω+ ω L ωl For MHz crystal, =pf L 84.4μH π L MHz APP- -6 Prof. ai-haur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6