Basic Principles of Sinusoidal Oscillators

Transcription

1 Basic Principles of Sinusoidal Oscillaors Linear oscillaor Linear region of circui : linear oscillaion Nonlinear region of circui : ampliudes sabilizaion Barkhausen crierion X S Amplifier A X O X f Frequency-selecive nework loop gain L(s) = β (s)a(s) characerisic equaion -L(s) = oscillaion crierion L(j = A(j ) β(j ) = - Elecronics(),

2 Basic Principles of Sinusoidal Oscillaors (on.) a, he phase of he loop should be zero and he magniude of he loop gain should be uniy. Oscillaion frequency is deermined solely by φ φ ω dφ dω φ ω ω A seep phase response resuls in a small for a given change in phase - Elecronics(),

3 Nonlinear Ampliude onrol o susain oscillaion : βa> a.overdesign for βa variaions b.oscillaion will grow in ampliude poles are in he righ half of he s-plane c.nonlinear nework reduces βa o when he desired ampliude is reached poles will be pulled o j-axis - Elecronics(),

4 Nonlinear Ampliude onrol (on.) Limier circui for ampliude conrol linear region O A B ( f ) 4 i 4 5 O O I D f D A O 4 B Elecronics(),

5 - 5 Elecronics(), Nonlinear Ampliude onrol (on.) nonlinear region ) ( L similarly, ) ( ) ( L 5 4 D 5 4 D D - O D A f ) ( Slope L L 4 f ) ( Slope O I f Slope

6 OPAMP- Oscillaor ircuis Wien-bridge oscillaor L L s jω Z p Zp Z S For phase. ω L ω S jω ω s s d ω Z P _ Z S O - 6 Elecronics(),

7 OPAMP- Oscillaor ircuis (on.) Wien-bridge oscillaor wih a limier 5 D k a.k k _ 4 k O k 6nF 6nF k 5 k D b 6 k 5-7 Elecronics(),

8 OPAMP- Oscillaor ircuis (on.) v O 5k b k a p - 6nF k 6nF k - 8 Elecronics(),

9 Phase-Shif Oscillaor Wihou ampliude sabilizaion - K phase shif of he nework is 8 degrees. oal phase shif around he loop is or 6 degrees. - 9 Elecronics(),

10 Phase-Shif Oscillaor (on.) Wih ampliude sabilizaion k 5k P x 6nF 6nF 6nF k k _ D vo D 4 - Elecronics(),

11 Quadraure Oscillaor - 4 _ O X _ OP O OP f (Nominally ) - Elecronics(),

12 Quadraure Oscillaor (on.) Break he loop a X, loop gain oscillaion frequency L(s) = X = S o is he inegral of o 9 phase difference beween o and o quadraure oscillaor - Elecronics(),

13 Block diagram Acive-Filer uned Oscillaor f - - High-disorion v High-Q bandpass low-disorion v - Elecronics(),

14 Acive-Filer uned Oscillaor (on.) Pracical implemenaion Q Elecronics(),

15 A General Form of L-uned Oscillaor onfiguraion Many oscillaor circuis fall ino a general form shown below O ˆ - A I Z Z Z O O - A v ˆ Z Z Z O Z L Z L Z,Z,Z :capaciive or inducive - 5 Elecronics(),

16 - 6 Elecronics(), A General Form of L-uned Oscillaor onfiguraion (on.) ) ( ) ( ) ( ) ( ) ( ˆ ˆ X X A X X X A X X X X X A X X X X X X X X X j X X A X L X jx Z jx Z jx Z Z Z Z Z Z Z Z A Z Z Z Z Z Z A v v v O v O v O O L L v O oscillaion, for capaciance for inducance for,, if

17 A General Form of L-uned Oscillaor onfiguraion (on.) Wih oscillaion = and =, 6, 7, degree. i.e. = (X =ωl or X = - ) ω X & X mus have he same sign if A v is posiive X & X are L, X = -(X + X ) is or X & X are, X = -(X + X ) is L ransisor oscillaors.ollpis oscillaor -- X & X are s, X is L.Harley oscillaor -- X & X are Ls, X is - 7 Elecronics(),

18 L uned Oscillaors wo commonly used configuraions.ollpis (feedback is achieved by using a capaciive divider).harley (feedback is achieved by using an inducive divider) onfiguraion.ollpis.harley L L a.c. ground( DD ) a.c. ground( ) DD L - 8 Elecronics(),

19 ollpis oscillaor Equivalen circui L uned Oscillaors (on.) sπ L O π( s L ) sπ π Gm π = loss of inducor + load resisance of oscillaor + oupu resisance of ransisor - 9 Elecronics(),

20 L uned Oscillaors (on.) S+gmv+( +S )(+S L )= L S L +S ( )+S( + )+(g m+ )= w L (g m+ )+j W( + ) W L = S=jw For oscillaions o sar, boh he real and imaginary pars mus be zero Oscillaion frequency ω = cc L( ) c +c - Elecronics(),

21 L uned Oscillaors (on.) Gain g m c c (Acually, g m c c ) Oscillaion ampliude.l uned oscillaors are known as self limiing oscillaors. (As oscillaions grown in ampliude, ransisor gain is reduced below is small signal value).oupu volage signal will be a sinusoid of high puriy because of he filering acion of he L uned circui Harley oscillaor can be similariy analyzed - Elecronics(),

22 Symbol of crysal rysal oscillaors ircui model of crysal L S P r - Elecronics(),

23 - Elecronics(), rysal oscillaors (on.) eacance of a crysal assuming r = (rysal is high Q device) ω p S ω ω inducive capaciive reacance rysal S P S P P S P P S P S S P S S P S P S P ω hen ω, If ω ω ω ω ω j jω Z L ω L ω Le L s L s s s sl s Z(s)

24 rysal oscillaors (on.) he crysal reacance is inducive over he narrow frequency band beween w s and w p ollpis crysal oscillaor onfiguraion crysal a.c. ground( DD ) - 4 Elecronics(),

25 Equivalen circui <<,, S P ω =ω L rysal oscillaors (on.) S S L - π S P v - 5 Elecronics(),

26 rysal oscillaors (on.) - L =pf 6~ uh L gd + D sray N68 - S MHz M Bias circui XAL.kΩ.μF (For A,- and ground are he same=) - 6 Elecronics(),

27 rysal oscillaors (on.) AX v Since reurn raio = X hen X mus be large for he loop gain o be greaer han one. X is very large when ω closes o ω ωs ω ωp p and X +X +X = & X = X &X are inducive ω j Z =L//= = jω + ω + jω L ω L X = > ωl> ω> ω+ ω L ωl For MHz crysal, =pf L 84.4μH π L MHz - 7 Elecronics(),

28 Bisable Mulivibraors Mulivibraors bisable:wo sable saes ( ypes) monosable:one sable sae asable:no sable sae Bisable Has wo sable saes an be obained by connecing an amplifier in a amplifier in a posiive-feedback loop having a loop gain greaer han uniy. I.e. βa> where β= /( + ) - 8 Elecronics(),

29 Bisable Mulivibraors (on.) Bisable circui wih clockwise hyseresis v o L v + - v O L H v I v I - L - lockwise hyseresis (or invering hyseresis) L + :posiive sauraion volage of OPAMP L - :negaive sauraion volage of OPAMP - 9 Elecronics(),

30 Bisable Mulivibraors (on.) H L βl βl L L Hyseresis widh = H - L - Elecronics(),

31 Noninvering Bisable ircui ounerclockwise hyseresis onfiguraion v o v I - v + L - v O L H v I L - v=v +v + I + + For v =L +, v + =,v I=vL v L = L + ( ) For v =L -, v + =,v I=vH v H= L ( ) - Elecronics(),

32 Noninvering Bisable ircui (on.) omparaor characerisics wih hyseresis an rejec inerference Signal corruped wih inerference H L Muliple zero crossings - Elecronics(),

33 Generaion of Square and riangular Waveforms using Asable Mulivibraors an be done by connecing a bisable mulivibraor wih a circui in a feedback loop. v L v v L H v H βl L - L L βl L - - Elecronics(),

34 Generaion of Square and riangular Waveforms using Asable Mulivibraors (on.) v O L v + L - v v O - H L H v - βl βl v βl o L o L - ime consan = L βl - 4 Elecronics(),

35 - 5 Elecronics(), Generaion of Square and riangular Waveforms using Asable Mulivibraors (on.) During During β L L β a βl if,β where e βl L L ln τ τ τ is assumed L L ; β β β L L β a βl if e βl L L τ ln τ ln τ

36 Generaion of riangular Waveforms v _ L H L v L - Bisable Slope -L L H L L Slope L - 6 Elecronics(),

37 Generaion of riangular Waveforms (on.) During L L H L ; i d where i H L L During Similarily H L L o obain symmerical waveforms L L - 7 Elecronics(),

38 Monosable Mulivibraors Is alernaive name is one sho Has one sable sae an be riggered o a quasi-sae E D 4 (βl+ D) L - v E v L A () () B D _ A βl βl - v v B D () () o L βl - o L - 8 Elecronics(),

39 During B B () L () βl For D L Monosable Mulivibraors (on.) (L βl ln( βl D D )e L L L (L ) ( ) β D )e βl + is greaer hen D Sable sae is mainained - 9 Elecronics(),

40 Monosable Mulivibraors(on.) Monosable mulivibraor using NO gaes DD in NO o vx NO O v in v O DD DD X v O DD DD DD DD - 4 Elecronics(),

41 Mono-sable Mulivibraor (on.) - - c O DD v X - - O - c DD DD v X - v () v (e ) x DD v() x DD(e ) DD ln ln.69 DD DD where ; is NO gae hreshold volage v v x ( ) DD e - 4 Elecronics(),

42 Mono-sable Mulivibraor (on.) Monosable mulivibraor wih caching diode DD in o D O NO x NO X 5.6 forward resisance of diode 5 D ime consan f ime consan - 4 Elecronics(),

43 Asable Mulivibraor Using NO(or Inverer) Gaes v o D D X O O v _ v o D D ransien behavior ()<< (i) v o:dd w hen = (ii) v : w hen = o DD (iii)v =( + )e x D D - (iv)v =v - =- +( + )e c x O DD DD - v X DD D D v D D - 4 Elecronics(),

44 Asable Mulivibraor Using NO(or Inverer) Gaes (on.) ()<<(+) (i) v : w hen = o DD (ii) v : w hen = o DD (iii)v = -( + )e x D D D D (- ) (iv)v =v - =v = -( + )e c x O x D D D D (- ) - 44 Elecronics(),

45 Asable Mulivibraor Using NO(or Inverer) Gaes (on.) Oscillaion frequency v ( )= x DD ( + )e = DD+ =ln DD If =, hen =ln and =ln.455 oscillaion frequency f = ln - 45 Elecronics(),

46 Asable Mulivibraor Using NO(or Inverer) Gaes (on.) Wih caching diode a X X O O v _ f ln.7 ln DD Asymmerical square wave (i) (ii) DD X O D D v _ O - 46 Elecronics(),

47 he 555 I imer Widely used as boh a monosable and asable mulivibraor n Used as monosable mulivibraor hreshold rigger c H L omparaor S Q omparaor Q Q oem-pole oupu sage O v v v c O ( ) ( ) H ( ) S n Q n+ Q n N/A c cc cc cc n v L ( e ) Discharge ransisor v() - 47 Elecronics(),

48 For v x he 555 I imer (on.) () e (() ) E(sa) For =, v ( ) H () ln ln (() ) - 48 Elecronics(),

49 he 555 I imer (on.) Used as an asable mulivibraor cc H = cc L = ( ) A B cc c S, cc c S, cc cc c S ln, ( )ln B A B Oscillaion frequency f hreshold A B c rigger H L (A omparaor omparaor B )ln 555 imer chip S Q Q Q Discharge oem-pole oupu sage ransisor O - 49 Elecronics(),

50 Sine-Wave Shaper Shape a riangular waveform ino a sinusoid Exensively used in funcion generaors Noe:linear oscillaors are no cos-effecive for low v O frequency applicaion no easy o ime over wide frequency ranges vf - 5 Elecronics(),

51 Sine-Wave Shaper (on.) Nonlinear-amplificaion mehod For various inpu values, heir corresponding oupu values can be calculaed ransfer curve can be obained and is similar o _ vo v i (riangular wave) (Sine wave) Q Q I I - EE - 5 Elecronics(),

52 Sine-Wave Shaper (on.) Breakpoin mehod Piecewise linear ransfercurve Low-valued is assumed and are consan in in in D D D ou ( in in is on (volage drop D is on limi 5 ) 5 o 4 D ) D - 5 Elecronics(),

53 Sine-Wave Shaper (on.) D In ou In 4 D D D 4 ou - 5 Elecronics(),

54 Precision ecifier ircuis Precision half-wave recifier --- superdiode " Superdiode " O i _ A O i An alernae circui O D _ D O i i - 54 Elecronics(),

55 Precision ecifier ircuis (on.) Applicaion:Measure A volages D 4 i _ A D _ A O π P Average ;where p is he peak ampliude of an inpu sinusoid - 55 Elecronics(),

56 Precision ecifier ircuis (on.) If ωmin ;ω min is he lowes expeced 4 P π 4 frequency of he inpu sine wave - 56 Elecronics(),

57 Precision Full-Wave ecifiers A D A A B D B B or L - 57 Elecronics(),

58 Precision Full-Wave ecifiers (on.) i A _ A E D O O _ D P i A F L - 58 Elecronics(),

59 Wih load Peak ecifier Super diode v i - _ L v O - buffered D _ A D _ A v O - v i Elecronics(),