Design of crystal oscillators

Transcription

1 Design of crystal oscillators Willy Sansen KULeuven, ESAT-MICAS Leuven, Belgium Willy Sansen

2 Table of contents Oscillation principles Crystals Single-transistor oscillator MOST oscillator circuits Bipolar-transistor oscillator circuits Other oscillators Willy Sansen

3 The Barkhausen criterion F(jω) V f V in V ε A(jω) Σ V out V out = A(jω) V ε V f = F(jω) V out = F(jω) A(jω) V ε V f V ε = A(jω) F(jω) Oscillation if V in = 0 or if Ref. Barkhausen, Hirzel, Leipzig, 935 V f = A(jω) F(jω).0 V ε Positive FB! V f = Φ V A + Φ F = 0 o ε Willy Sansen

4 Split analysis Z resonator Z circuit Y res +Y circ Y res +Y circ = 0 Z res + Z cir = 0 Z circ +Z res Z res Z circ = 0 Oscillation if Re (Z circ +Z res ) = 0 sets the minimum gain! Im (Z circ +Z res ) = 0 sets the frequency! Willy Sansen

5 Table of contents Oscillation principles Crystals Single-transistor oscillator MOST oscillator circuits Bipolar-transistor oscillator circuits Other oscillators Willy Sansen

6 Crystal as resonator d f s =.66 d f s in MHz if d in mm quartz L s C s R s (series) C p = A ε 0 ε r d ω s 2 = Ls C s ε r 4.5 f s = 2π L s C s C p (package, parallel) L s ω s = Cs ω s L s Q ω s = Rs C s Q= Rs C s R s = Q Cs ωs Willy Sansen

7 Crystal parameters L s C s R s C p Xtal : f s = MHz Q = 0 5 C s = 0.03 pf C p 6 pf ( 200 C s ) L s ω s = Cs ω s L s 8.4 mh R s = = 5.3 Ω QC s ω s f s L s C s R s C p Q 00.0 khz 52 H 49 ff 400 Ω 8 pf MHz 2 H 6 ff 24 Ω 3.4 pf MHz 0 mh 26 ff 5 Ω 8.5 pf Willy Sansen

8 Series and parallel resonance L C R f r = 2π LC L C Z Cap. Ind. Z R R Ind. Cap. -90 o + 90 o + 90 o -90 o R f r f f r f Willy Sansen

9 Crystal impedance s 2 L s C s +sr s C s + Z s (s) = (s 2 L s C s C p R s C s C p s (C s +C p ) + s + ) C s +C p C s +C p Z s (s) R s f s f p C p s f Willy Sansen

10 Crystal impedance at resonance Z 00 kω f p f s =.998 MHz C s = 2.2 ff L s 0.52 H C p = 4.27 pf 00 Ω f s R s = 82 Ω Φ(Z) 00 o 0 o 90 o induct. Crystal operates in inductive region if circuit is capacitive! -00 o -90 o capac MHz Willy Sansen

11 Series and parallel resonance Z s (ω) = -j ωc p ω 2 - ω s 2 ω 2 - ω p 2 ω s 2 = Ls C s ω p 2 = ( + ) L s C p C s Z s (ω) = R s +jωl s + jωc s series parallel Z s (ω) = R s + ( - ) j ω s C s 2p ω ω s ω s ω Frequency pulling factor p = ω - ω s ω s Z s (ω) R s + j ωcs Ref. Vittoz, JSSC June 88, Willy Sansen

12 Series or parallel resonance? f s f p = khz p p = 0.25 % C p f m = khz p m = 0.25 % f s = khz p s = 0 f m - f s C s p m = = = 0.25 % 4C p khz f p f s = + + p p = C s 2C p f s C s C p C s f p - f s 2C p = 0.25 % Willy Sansen

13 Table of contents Oscillation principles Crystals Single-transistor oscillator MOST oscillator circuits Bipolar-transistor oscillator circuits Other oscillators Willy Sansen

14 Single-transistor X-tal oscillator C 3 C 2 Basic three-point oscillator g m C C 2 C 2 C 3 C 3 C 3 C 2 g m g m g m C C C Pierce Colpitts : -pin X=D Santos : -pin X=G Willy Sansen

15 Single-transistor X-tal oscillator analysis C 3 = C p + C DG C 3 C 2 L s C s C 3 C g m R s g m C 2 Z s Z c C Barkhausen : Z s +Z c = 0 Z s = R s + j Re (Z c ) = -R s 2p Im (Z c ) = - ωc s yields g m yields f or p 2p ωc s Ref. Vittoz, JSSC June 88, Willy Sansen

16 Complex plane for 3-pt oscillator : Design crit. g mmax g m A Im -R s 0 Re g m = 0 Im 0 - C C 2 ω(c 2p 3 + ) C Im A = - Im +C 2 0 ω s C s Ø = ωc3 + C C +C 2 3 C C 2 Small p : Large C,2 B g m = Im - ωc3 Large circle: Small C 3 Willy Sansen

17 Complex plane for 3-pt oscillator : Example -6 kω -80 Ω Im -R s 0 Re C = C 2 = 3 pf C 3 = 0.5 pf 20 MHz 80 Ω A g m = 0 Im 0-4 kω g mmax 3 ms 2p A Im A = - ωc s Ø = 2 kω p A = C s C 2(C 3 + C 2 ) C +C 2 g ma R s C C 2 ω s 2 g mb 450 ms B g m = Im - 6 kω µs Willy Sansen

18 Amplitude of oscillation i ds I ds I DSA t I ds V gs = = g ma 2 π I ds I DSA 2 I DSA g ma V GS -V T 2 kt V gs V GS -V T or 2n in wi q Large! I ds I DSA Nonlinear (Bessel) More spiked for higher C,2!!! Willy Sansen

19 Start-up of oscillation τ min occurs at g m g mmax τ min = L s Re (Z s ) + R s Re (Z s ) is half circle Ø Re (Z s ) = if C ω s C 3 <<C 2 3 R s << Re (Z s ) 2 C τ min since C C s ω s C s ωs or also τ min 2Q R s C 3 Willy Sansen

20 Power dissipation In MOST : g ma ω s 2 R s C C 2 R s (C ω s ) 2 I DSA g V GS -V T ma 2 µa 6 µw 2 V gs In X-tal : I c = = V gs C ω s V GS -V T C ω s Z C R s I 2 c R P c = = s V GS -V T 2 (C ω s ) = V GS -V T 2 g ma 0.2 µw 2 Willy Sansen

21 Design procedure for X-tal oscillators - X-tal : f s f p R s C p (or f s Q C s C p ) (Q = / ω s C s R s ). Take : C 3 > C p but as small as possible C s Pulling factor p = 2 C C 3 + C 2 2 C +C 2 C s C L C C L = = 2 C 2 2 C s If p < it is a series oscillator (best!) 4C p If p > it is a parallel oscillator (not stable!) Choose C L large (> C 3 ), subject to power dissipation! Willy Sansen

22 Design procedure for X-tal oscillators Calculate g ma R s C 2 ω L ω 2 s s ( C L C L ) C s Q and take g mstart 0 g ma 3. Choose V GS -V T, which gives the amplitude V gs g m (V GS -V T ) and current I DS = and W 2 L and power P = (V GS -V T ) 2 g m 2 4. Verify that biasing R B > / (R s C 3 2 ω s 2 ) Willy Sansen

23 Single-transistor X-tal oscillator C 3 C 2 Basic three-point oscillator g m C C 2 C 2 C 3 C 3 C 3 C 2 g m g m g m C C C Pierce Colpitts : -pin X=D Santos : -pin X=G Willy Sansen

24 Pierce X-tal oscillator I B V B R B C 3 C 2 g m C 32 khz.2 V 78 na Willy Sansen

25 Colpitts X-tal oscillator I B C 2 v OUT v OUT V B g m C 3 C 2 C 3 C C Crystal grounded : single-pin : X = D Willy Sansen

26 Santos X-tal oscillator i OUT I B (AGC) V B R B g m C v OUT C 3 C v OUT C 2 g m R B C 2 I B (AGC) C 3 Crystal grounded : single-pin : X = G Ref. Santos, JSSC April 84, Ref. Redman-White, JSSC Feb.90, Willy Sansen

27 Table of contents Oscillation principles Crystals Single-transistor oscillator MOST oscillator circuits Bipolar-transistor oscillator circuits Other oscillators Willy Sansen

28 Practical Pierce X-tal oscillator M5 M4 C C c M M6 00 MΩ C 2 C s = 0.5 ff C 3 = 0.6 pf C = C 2 = 2.8 pf 2 MHz M3 M2 g ma = 2 µs I DSA = 80 na I DS = 350 na V gs = 300 mv Ref. Vittoz, JSSC June 88, Willy Sansen

29 Full schematic Ref. Vittoz, JSSC June 88, Willy Sansen

30 Single-pin oscillator with crystal to Gate C C2 R B M OUT f s = MHz f p = 0.02 MHz C s = 24.3 ff C o = 7.4 pf L = 0.4 mh R = 7.2 Ω (?) p = C = C 2 = 50 pf g ma = 350 µs I DSA = 90 µa (V GS -V T = 0.5 V) Willy Sansen

31 Single-pin oscillator - g m + - g m g m C load C R B C 2 g m = R s (C s ω 0 ) 2 DC unstable! Positive FB dominant at crystal frequency! Ref. van den Homberg, JSSC July 99, Willy Sansen

32 Single-pin oscillator MHz, 3.3 V, 0.35 ma Ref. van den Homberg, JSSC July 99, Willy Sansen

33 X-tal oscillators with CMOS inverters = Large current peaks! Bad PSRR!! Willy Sansen

34 Table of contents Oscillation principles Crystals Single-transistor oscillator MOST oscillator circuits Bipolar-transistor oscillator circuits Other oscillators Willy Sansen

35 Pierce X-tal oscillator I B R 2 C 3 C C 2 R L vout C 3 C 2 V B R B g m R C Willy Sansen

36 Colpitts X-tal oscillator I B C 2 v OUT v OUT V B g m C 3 C 2 C 3 C C Crystal grounded : single-pin : X = D Willy Sansen

37 Santos X-tal oscillator V B R B g m C 3 C C 2 v OUT I B (AGC) Crystal grounded : single-pin : X = G Buffered output Ref. Santos, JSSC April 84, Ref. Redman-White, JSSC Feb.90, Willy Sansen

38 98 GHz VCO in SiGe Bipolar technology Colpitts 0.55 x 0.45 mm 2 ma at - 5 V -97 dbc/hz at MHz Ref. Prendl BCTM Toulouse 03 Willy Sansen

39 Positive feedback circuits - R L Q Q 2 v OUT T=g m R L R L >R s Ref. Nordholt, CAS 90, Willy Sansen

40 Positive feedback circuits Ω 200 v OUT Buffered ouput! Ω 500 µa 250 Ref. Nordholt, CAS 90, Willy Sansen

41 Positive feedback circuits - 3 g ma = 8 ms 00 MHz Ref. Nordholt, CAS 90, Willy Sansen

42 Table of contents Oscillation principles Crystals Single-transistor oscillator MOST oscillator circuits Bipolar-transistor oscillator circuits Other oscillators Willy Sansen

43 Voltage Controlled Oscillator I B R L L L R L ω s = LC D C D V c C D g ma R L (C D ω s )2 v OUT v OUT dv 2 out { ω}= 4 ω s 4kTR L ( + ) ( ) 2 df 3 ω Ref. Craninckx, ACD Kluwer 96, ; JSSC May 97, Willy Sansen

44 Differential crystal Oscillator R R v OUT v OUT C I B I B Willy Sansen

45 Relaxation Oscillator R R v OUT v OUT C I B I B Ref. Grebene, JSSC, Aug.69, 0-22; Gray, Meyer, Wiley, 984. Willy Sansen

46 RC Oscillators : 3 x 60 o = 80 o C R C R C R f c = φ 0-45 o -90 o -60 o at.73 f c 2π RC f c f - + V out Willy Sansen

47 Wien Oscillator : 3 x Gain required C R V ε + 2τ s + τ = 2 s 2 V out 3 + 3τ s + τ 2 s 2 C R V ε + - 2R V out φ τ = RC f osc = 2π τ R 0 f Willy Sansen

48 Voltage-controlled X-tal oscillator ± C Res. Resonator 457 khz Tuning ± 5 khz Wien bridge : R 2 = 2 R Ref. Huang, JSSC June 88, Willy Sansen

49 Variable capacitance ± C G m block ± C I 2 Y in = sc d G m R d 25 R d C d block ± G m with I 2 Ref. Huang JSSC June 88, Willy Sansen

50 G m block to generate ± G m I = 90 µa I 2 = 0 80 µa G m = B [(2βI ) /2 -(2βI 2 ) /2 ] Willy Sansen

51 R d C d block as differentiator C d = 4 pf R d = 40 kω Ref. Huang JSSC June 88, Willy Sansen

52 Table of contents Oscillation principles Crystals Single-transistor oscillator MOST oscillator circuits Bipolar-transistor oscillator circuits Other oscillators Willy Sansen

53 References X-tal oscillators - A.Abidi, "Low-noise oscillators, PLL s and synthesizers", in R. van de Plassche, W.Sansen, H. Huijsing, "Analog Circuit Design", Kluwer Academic Publishers, 997. J. Craninckx, M. Steyaert, "Low-phase-noise gigahertz voltage-controlled oscillators in CMOS", in H. Huijsing, R. van de Plassche, W.Sansen, "Analog Circuit Design", Kluwer Academic Publishers, 996, pp Q.T. Huang, W. Sansen, M. Steyaert, P.Van Peteghem, "Design and implementation of a CMOS VCXO for FM stereo decoders", IEEE Journal Solid-State Circuits Vol. 23, No.3, June 988, pp E. Nordholt, C. Boon, "Single-pin crystal oscillators" IEEE Trans. Circuits. Syst. Vol.37, No.2, Feb.990, pp D. Pederson, K.Mayaram, Analog integrated circuits for communications, Kluwer Academic Publishers, 99. Willy Sansen

54 References X-tal oscillators - 2 W. Redman-White, R. Dunn, R. Lucas, P. Smithers, "A radiation hard AGC stabilised SOS crystal oscillator", IEEE Journal Solid-State Circuits Vol. 25, No., Feb. 990, pp J. Santos, R. Meyer, "A one pin crystal oscillator for VLSI circuits", IEEE Journal Solid-State Circuits Vol. 9, No.2, April 984, pp M. Soyer, "Design considerations for high-frequency crystal oscillators", IEEE Journal Solid-State Circuits Vol. 26, No.9, June 99, pp E. Vittoz, M. Degrauwe, S. Bitz, "High-performance crystal oscillator circuits: Theory and application", IEEE Journal Solid-State Circuits Vol. 23, No.3, June 988, pp V. von Kaenel, E. Vittoz, D. Aebischer, " Crystal oscillators", in H. Huijsing, R. van de Plassche, W.Sansen, "Analog Circuit Design", Kluwer Academic Publishers, 996, pp Willy Sansen

55 Appendix: Polar diagrams Willy Sansen Willy Sansen

56 Amplitude, phase, Real & Imaginary Im φ Re = Re 2 + Im 2 tg(φ) = Im Re Re = cos (φ) Im = sin (φ) Willy Sansen

57 Polar diagram of RC network - Z R Im Z Z C C R 0 Im 0 ω = ω = 0 Cω R Z = R + ω = Cjω Re Re ω = 0 ω = RC Willy Sansen

58 Polar diagram of RC network - 2 Z C Z = R + Cjω R Im 0 Im 0 R ω = 0 R = ω = ω = ω C RC R = Re Re R = 0 Willy Sansen

59 Polar diagram of RC network - 3 Z Im 0 R ω = ω = 0 Re R Z = R + RCjω C Im 0 R = 0 ω = R = RC ωc Re - ωc R = Willy Sansen

60 Polar diagram of RC network - 4 Z R C Im 0 R ω = ω = 0 Re Z r R Z = R + RCjω C 0 r ω = ω = 0 R+r Re Z = r + R + RCjω ω = RC Ref. Sansen, JSSC Dec.72, Willy Sansen

61 Polar diagram of RC network - 5 Z R C Im 0 R = 0 Re Im 0 Re Z C 2 Z = R + RCjω - ωc 2 R = 0 R = Z = + jωc 2 R C R + RC jω - ωc R = C +C 2 - ωc C 2 R = ωc Willy Sansen

62 Circuit input impedance Zc Z c g m + 2 jωc C jωc 3 (g m + jωc ) C 3 C 3 C 2 if C 3 << C = C 2 g m = C Z c C For g m 0 Z c0 2 /ωc For g m Z c /ωc 3 Willy Sansen

63 Complex plane for 3-point oscillator g mmax g m A Im -R s 0 Re g m = 0 Im 0 - C C 2 ω(c 2p 3 + ) C Im A = - Im +C 2 0 ω s C s C 3 C 2 C B Ø = ωc3 g m = + C 3 C +C 2 C C 2 Im - ωc3 - + C 3 Willy Sansen

64 Calculation of g ma Z c C 3 = R S Z c = g ma C 2 = C C 3 s g m + (C +C 2 )s C C 2 g m + (C +C 2 + )s C 3 C Re (Z c ) = R s For small g m : g ma R s (C eff ω s ) 2 2C 3 C eff = C ( + ) C C Maximum negative resistance is / 2ωC 3 at g mmax = ωc C C 3 Willy Sansen