Basic Principles of Sinusoidal Oscillators


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1 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 Frequencyselective network Loop gain L(s) = β(s)a(s) haracteristic equation L(s) = Oscillation criterion L(jw ) = A(jw ) β(jw ) = Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan  郭泰豪, Electronics(), 6
2 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. aihaur Kuo, EE, NKU, ainan ity, aiwan  郭泰豪, Electronics(), 6
3 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 splane c. Nonlinear network reduces βa to when the desired amplitude is reached Poles will be pulled to jwaxis Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan  郭泰豪, Electronics(), 6
4 Prof. aihaur 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 I D D f A 4 B 5 O 
5 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 65 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
6 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 6 郭泰豪, Electronics(), 6 Wienbridge 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
7 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 7 郭泰豪, Electronics(), 6 OPAMP Oscillator ircuits (ont.) Wienbridge oscillator with a limiter 5 D k a.k k _ 4 k O k 6nF 6nF k 5 k D b 6 k 5
8 Prof. aihaur 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
9 PhaseShift Oscillator Without amplitude stabilization K phase shift of the network is 8 degrees. otal phase shift around the loop is or 6 degrees. Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 9 郭泰豪, Electronics(), 6
10 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan  郭泰豪, Electronics(), 6 PhaseShift Oscillator (ont.) With amplitude stabilization k t 5k x 6nF 6nF 6nF k k _ D vo D 4
11 Prof. aihaur 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 )
12 Prof. aihaur 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
13 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan  郭泰豪, Electronics(), 6 Block diagram ActiveFilter uned Oscillator f PSD  t PSD t 5f o f o f o... Frequency  f o Frequency Highdistortion v HighQ bandpass lowdistortion v
14 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 4 郭泰豪, Electronics(), 6 ActiveFilter uned Oscillator (ont.) Practical implementation Q  
15 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 5 郭泰豪, Electronics(), 6 A General Form of Luned 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
16 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 66 A General Form of Luned 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
17 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 7 郭泰豪, Electronics(), 6 A General Form of Luned 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
18 Luned Oscillators wo commonly used configurations olpitts (feedback is achieved by using a capacitive divider) DD L L Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 8 郭泰豪, Electronics(), 6
19 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 9 郭泰豪, Electronics(), 6 Luned Oscillators (ont.) Hartley (feedback is achieved by using an inductive divider) DD L L L L
20 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan  郭泰豪, Electronics(), 6 olpitts oscillator Equivalent circuit Luned 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
21 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6  Luned 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
22 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan  郭泰豪, Electronics(), 6 Gain g m Luned 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 )
23 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan  郭泰豪, Electronics(), 6 Symbol of crystal rystal Oscillators ircuit model of crystal L S P r
24 Prof. aihaur 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
25 Prof. aihaur 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
26 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. aihaur Kuo, EE, NKU, ainan ity, aiwan 6 郭泰豪, Electronics(), 6
27 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 positivefeedback loop having a loop gain greater than unity. I.e. βa> where β= /( + ) Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 7 郭泰豪, Electronics(), 6
28 Prof. aihaur 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
29 Prof. aihaur 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
30 Prof. aihaur 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
31 Prof. aihaur 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 
32 Prof. aihaur 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
33 Prof. aihaur 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)
34 Prof. aihaur 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
35 Prof. aihaur 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
36 Monostable Multivibrators Alternative name one shot Has one stable state (βl+ D) v E (t) an be triggered to a quasistate 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. aihaur Kuo, EE, NKU, ainan ity, aiwan 6 郭泰豪, Electronics(), 6
37 Prof. aihaur 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
38 Prof. aihaur 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
39 Prof. aihaur 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
40 Prof. aihaur 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
41 Prof. aihaur 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
42 Prof. aihaur 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 )
43 Prof. aihaur 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
44 Prof. aihaur 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
45 Prof. aihaur 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
46 Prof. aihaur 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 ( () )
47 Prof. aihaur 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
48 Sinewave shaper Precision rectifier circuits Precision fullwave rectifiers Peak rectifier rystal oscillators Appendix APP 48 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
49 SineWave Shaper Shape a triangular waveform into a sinusoid Extensively used in function generators Note: linear oscillators are not costeffective for low v O v f t frequency application not easy to time over wide frequency ranges t APP 49 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
50 SineWave Shaper (ont.) Nonlinearamplification 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. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
51 SineWave Shaper (ont.) Breakpoint method Piecewise linear transfer curve Lowvalued 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 APP45 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
52 SineWave Shaper (ont.) D in out D 5 5 in 4 D 5 4 out D 4 APP55 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
53 Precision ectifier ircuits Precision halfwave rectifier  superdiode "Superdiode" O i _ A O i An alternate circuit O D _ D O i i APP65 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
54 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 APP754 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
55 Precision ectifier ircuits (ont.) If ω 4 π P min 4 ;ω min is the lowest expected frequency of the input sine wave APP855 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
56 Precision FullWave ectifiers A D A A B D B B or L APP956 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
57 Precision FullWave ectifiers (ont.) i A _ A E D O O _ A D P i F L APP 57 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
58 With load Peak ectifier Super diode v i  _ L v O  Buffered D _ A D _ A v O  v i  APP 58 Prof. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
59 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. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
60 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. aihaur Kuo, EE, NKU, ainan ity, aiwan 郭泰豪, Electronics(), 6
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