Design of crystal oscillators


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1 Design of crystal oscillators Willy Sansen KULeuven, ESATMICAS Leuven, Belgium Willy Sansen
2 Table of contents Oscillation principles Crystals Singletransistor oscillator MOST oscillator circuits Bipolartransistor 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 Singletransistor oscillator MOST oscillator circuits Bipolartransistor 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 Singletransistor oscillator MOST oscillator circuits Bipolartransistor oscillator circuits Other oscillators Willy Sansen
14 Singletransistor Xtal oscillator C 3 C 2 Basic threepoint 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 Singletransistor Xtal 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 3pt 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 3pt 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 04 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 Startup 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 Xtal : 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 Xtal oscillators  Xtal : 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 Xtal 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 Singletransistor Xtal oscillator C 3 C 2 Basic threepoint 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 Xtal oscillator I B V B R B C 3 C 2 g m C 32 khz.2 V 78 na Willy Sansen
25 Colpitts Xtal oscillator I B C 2 v OUT v OUT V B g m C 3 C 2 C 3 C C Crystal grounded : singlepin : X = D Willy Sansen
26 Santos Xtal 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 : singlepin : X = G Ref. Santos, JSSC April 84, Ref. RedmanWhite, JSSC Feb.90, Willy Sansen
27 Table of contents Oscillation principles Crystals Singletransistor oscillator MOST oscillator circuits Bipolartransistor oscillator circuits Other oscillators Willy Sansen
28 Practical Pierce Xtal 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 Singlepin 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 Singlepin 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 Singlepin oscillator MHz, 3.3 V, 0.35 ma Ref. van den Homberg, JSSC July 99, Willy Sansen
33 Xtal oscillators with CMOS inverters = Large current peaks! Bad PSRR!! Willy Sansen
34 Table of contents Oscillation principles Crystals Singletransistor oscillator MOST oscillator circuits Bipolartransistor oscillator circuits Other oscillators Willy Sansen
35 Pierce Xtal 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 Xtal oscillator I B C 2 v OUT v OUT V B g m C 3 C 2 C 3 C C Crystal grounded : singlepin : X = D Willy Sansen
37 Santos Xtal oscillator V B R B g m C 3 C C 2 v OUT I B (AGC) Crystal grounded : singlepin : X = G Buffered output Ref. Santos, JSSC April 84, Ref. RedmanWhite, 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 Singletransistor oscillator MOST oscillator circuits Bipolartransistor 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, 022; Gray, Meyer, Wiley, 984. Willy Sansen
46 RC Oscillators : 3 x 60 o = 80 o C R C R C R f c = φ 045 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 Voltagecontrolled Xtal 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 Singletransistor oscillator MOST oscillator circuits Bipolartransistor oscillator circuits Other oscillators Willy Sansen
53 References Xtal oscillators  A.Abidi, "Lownoise 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, "Lowphasenoise gigahertz voltagecontrolled 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 SolidState Circuits Vol. 23, No.3, June 988, pp E. Nordholt, C. Boon, "Singlepin 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 Xtal oscillators  2 W. RedmanWhite, R. Dunn, R. Lucas, P. Smithers, "A radiation hard AGC stabilised SOS crystal oscillator", IEEE Journal SolidState Circuits Vol. 25, No., Feb. 990, pp J. Santos, R. Meyer, "A one pin crystal oscillator for VLSI circuits", IEEE Journal SolidState Circuits Vol. 9, No.2, April 984, pp M. Soyer, "Design considerations for highfrequency crystal oscillators", IEEE Journal SolidState Circuits Vol. 26, No.9, June 99, pp E. Vittoz, M. Degrauwe, S. Bitz, "Highperformance crystal oscillator circuits: Theory and application", IEEE Journal SolidState 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 3point 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
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