Design of crystal oscillators 水晶振荡器电路设计课件

-90o capac.
1.98 1.99 2.00 2.01 2.02 MHz willy.sansen
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-100o
1.97
Series and parallel resonance - 2
Zs(ω) = -j ω 2 - ω s2 ωCp ω2 - ωp2 Zs(ω) = Rs + jωLs + j Zs(ω) = Rs + Zs(ω) = Rs + j ω sC s 2p ωCs 1 jωCs ω s2 = 1 Ls Cs
LEUVEN
Oscillation if Re (Zcirc+Zres) = 0 sets the minimum gain ! Im (Zcirc+Zres) = 0 sets the frequency !
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Amplitude, phase, Real & Imaginary
Series and parallel resonance
LEUVEN
L C R
Ind. + 90o
C
R
fr = 2π Ls Cs
1
L
|Z|
Cap. Ind. + 90o - 90o
|Z| R
Cap. - 90o
R fr f fr
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f
Crystal impedance
Amplitude of oscillation
ids Ids IDSA t Vgs = Ids gmA = Ids IDSA IDSA gmA V -V 2 … 2 GS T π 2 Vgs ≈ VGS - VT or 2n Ids IDSA
x Oscillation x Crystals x Single-transistor
LEUVEN
principles oscillator x MOST oscillator circuits x Bipolar-transistor oscillator circuits x Other oscillators
LEUVEN
d
fs = εr ≈ 4.5 1 Ls Cs 1 Csωs fs =
fs in MHz if d in mm
quartz
1.66 d ε0 εr Cp = A d
(series)
Ls
L s ωs =
Cs Rs
ωs =
2
1 2π Ls Cs Q ωs = 1 RsCs
Cp (package, parallel)
Polar diagram of RC network - 4
Z R C
Im 0
ω=∞
LEUVEN
R
ω=0
Re
1
Z
r R
R Z= 1 + RCjω
0
r C
ω=∞
R+r
ω=0
Re
R Z=r+ 1 + RCjω
ω=
1 RC
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Polar diagram of RC network - 5
LEUVEN
C3 = Cp + CDG
C3 C2 gm Zc Zs = Rs + j C1 2p ωCs
ωCs
Ref. Vittoz, JSSC June 88, 774-783
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Polar diagram of RC network - 1
LEUVEN
Z R
LEUVEN
|Z|
100 kΩ
fp Cs = 12.2 fF Ls ≈ 0.52 H Cp = 4.27 pF
fs = 1.998 MHz
100 Ω
fs
90o induct.
Rs = 82 Ω
Φ(Z) 100o
0o
Crystal operates in inductive region if circuit is capacitive !
C3 gm C1 Ls C2 Cs Rs Zs Barkhausen : Zs + Zc = 0 Re (Zc) = -Rs 2p Im (Zc) = yields f or p yields gm
LEUVEN
C3 = Cp + CDG
C3 C2 gm Zc Zs = Rs + j C1 2p ωCs
LEUVEN
Im | |= | | φ Re Re = | | cos (φ) Im = | | sin (φ)
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Re 2 + Im 2 Im Re
tg(φ) =
Table of contents
x Oscillation x Crystals x Single-transistor
willy.sansen
Re
1 ωC R=∞
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Polar diagram of RC network - 3
LEUVEN
Z
ω=∞
Im 0
R
ω=0
Re
R C
Im 0 R=0
ω=
1 RC
Re
Z=
R 1 + RCjω
R= 1 ωC
1 ωC R=∞
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Q=
1 Rs
Ls Cs
Rs =
1 Q Cs ω s
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Crystal parameters
Ls Cs Rs
Q = 105
LEUVEN
Xtal : fs = 10 MHz
Cs = 0.03 pF
Cp
L s ωs =
fs 100 kHz 1 MHz 10 MHz
Cp ≈ 6 pF (≈ 200 Cs) 1 Csωs
C3
C2 C1
1 Ø= ωC3 1 + C C1+C2 3 C1C2
+
willy.sansen
C3
B
1 Im ≈ gm = ∞ ∞ ωC3
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Design criteria
Im -Rs 0 A gm ImA = gmopt Ø= 1 gm = 0 Re Im0 ≈ ≈ Im0 ω sC s 1 ωC3 1 + C C1+C2 3 C1C2 B 1 Im ≈ gm = ∞ ∞ ωC3 2p 1 ω(C3 +
Zs (s) = s[s2 s2LsCs+ sRsCs+ 1 LsCsCp Cs+Cp |Zs (s)| 1 Cps Rs fs fp f +s RsCsCp Cs+Cp + 1](Cs+Cp)
LEUVEN
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Crystal impedance at resonance
Ls 52 H 2H 10 mH
Ls ≈ 8.4 mH
Cs 49 fF 6 fF 26 fF
Rs =
Rs 400 Ω 24 Ω 5Ω
1 Q Cs ω s
Cp 8 pF 3.4 pF 8.5 pF
= 5.3 Ω
Q 0.8 105 5.3 105 1.2 105
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0
ω=∞
Im
R
Re
Z C
ω=0
1 Cω Z=R+
ω=∞ ω= 1
Im
Z R
C来自百度文库
0
1 Cjω
Re
ω=0
RC
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Polar diagram of RC network - 2
Z C R
ω= ω=0
LEUVEN
Im 0
R
ω=∞ 1 RC
Re
Im
Z=R+
1 Cjω
0
R= R=0
series
LEUVEN
ωp =
2
1 Ls
(
+ ) Cp Cs
parallel
1
1
(ω s
ω
ωs ω
)
Frequency pulling factor p= ω
- ωs
ωs
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Series and parallel resonance - 2
LEUVEN
fp
-80 Ω -Rs 0
Im
C1 = C2 = 3 pF C3 = 0.5 pF 20 MHz 80 Ω
1 2 (C3 + C1C2 C1+C2 ) gmA ≈ ωs2RsC1C2
≈ 11 µS
gmB ≈ 450 mS B
gm = ∞ Im∞ ≈ - 16 kΩ
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LEUVEN
Design of crystal oscillators
Willy Sansen
KULeuven, ESAT-MICAS Leuven, Belgium
willy.sansen@esat.kuleuven.ac.be willy.sansen
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Table of contents
fm- fs = Cs
ps = 0
= 0.125 %
Table of contents
x Oscillation x Crystals x Single-transistor
LEUVEN
principles oscillator x MOST oscillator circuits x Bipolar-transistor oscillator circuits x Other oscillators
Vf = |A(jω)| |F(jω)| ≥ 1.0 Vε Positive FB ! Vf = ΦA + ΦF = 0o Vε
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Split analysis
Yres + Ycirc Zcircuit Zresonator Yres + Ycirc = 0 1 1 =0 + Zres Zcir Zcirc + Zres Zres Zcirc =0
LEUVEN
Z R C
0 R=0
-
Im Re 0
Im Re
R=0 1 ωC 2 R= 1 ωC 1 R=∞ C1+C2 ωC1C2 R = ∞
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Z R C1
1 ωC
R Z= 1 + RCjω C2
1 R Z= + jωC2 1 + RC1jω
Single-transistor X-tal osc. analysis
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The Barkhausen criterium
LEUVEN
F(jω)
Vout = A(jω) Vε Vf = F(jω) Vout = F(jω) A(jω) Vε Vf Vε = A(jω) F(jω)
Vf Vin
Σ A(jω)
Vε Vout
Oscillation if Vin = 0 or if
ωCs
Ref. Vittoz, JSSC June 88, 774-783
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Complex plane for 3-pt oscillator
LEUVEN
Im -Rs 0 Re Im0 ≈ 2p ω sC s ≈ Im0 ω(C3 + 1 C1C2 C1+C2 ) A gm = 0 ImA = gmopt 1 gm
LEUVEN
C1C2 C1+C2
)
Small p : Large C1,2 Large circle: Small C3
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Complex plane for 3-pt oscillator
LEUVEN
-6 kΩ Re Im0 ≈ - 4 kΩ 2pA ωCs pA = A gm = 0 ImA = gmopt ≈ 3 mS Ø = 12 kΩ
C3 gm C1
C2
Santos : 1-pin X=G
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Single-transistor X-tal osc. analysis
C3 gm C1 Ls C2 Cs Rs Zs Barkhausen : Zs + Zc = 0 Re (Zc) = -Rs 2p Im (Zc) = yields f or p yields gm
LEUVEN
principles oscillator x MOST oscillator circuits x Bipolar-transistor oscillator circuits x Other oscillators
willy.sansen
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Crystal as resonantor
fp = 89.000 kHz pp = 0.25 %
fs
=
1+
Cs Cp
Cp
fm = 88.850 kHz pm = 0.125 % fs = 88.700 kHz
kHz
≈ 1+
Cs 2Cp fp- fs pp = Cs 2Cp fs = 0.25 %
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pm = fs 4Cp
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Single-transistor X-tal oscillator
LEUVEN
C3 gm C1 C2 C3 gm C1
Colpitts Pierce : 1-pin X=D
C2
Basic three-point oscillator
C3 gm C1
C2