http:∥10.12.240.202，Copyright©2001-2004，Zhangwen Tang Outline ▣ Introduction ■ Fundamentals of LC VCOs Oscillator views Mathematics of LC VCOs O Structures of different LC-VCOs ▣ On-chip inductors ▣ Varactors and F-V tuning curve 0 Optimization of LC VCOs ▣ Techniques of lowering phase noise ▣ Design examples ▣ Conclusion and prospect ASIC System State-Key Laboratory,Fudan University -6
-6- ASIC & System State-Key Laboratory, Fudan University http://10.12.240.202, Copyright © 2001-2004, Zhangwen Tang Outline Outline Introduction Fundamentals of LC VCOs Oscillator views Mathematics of LC VCOs Structures of different LC-VCOs On-chip inductors Varactors and F-V tuning curve Optimization of LC VCOs Techniques of lowering phase noise Design examples Conclusion and prospect
http://10.12.240.202,Copyright@2001-2004,Zhangwen Tang Oscillator Views Two-port view feedback system One-port view:Negative Resistance H(s) Active Circuit ●Transfer function ●Active circuit H(s) 1+H(S) 尺cne=-R。 Barkhausen criterion Inductance cancels capacitance 1 H(j@)≥1&∠H(jo)=180 jl=、 j@C ASIC System State-Key Laboratory,Fudan University -7
-7- ASIC & System State-Key Laboratory, Fudan University http://10.12.240.202, Copyright © 2001-2004, Zhangwen Tang Oscillator Views Oscillator Views ∑ H s( ) Vin Vout Two-port view : feedback system One-port view : Negative Resistance CP RP LP Active Circuit RP ( ) ( )( ) = 1+ out in V H s s V Hs z Transfer function R R active P = − z Active circuit z Barkhausen criterion Hj Hj ( ) ω ω 0 0 ≥ ∠ =° 1 & 180 ( ) ω ω = − 1 j L j C z Inductance cancels capacitance
http://10.12.240.202,Copyright 2001-2004,Zhangwen Tang Ring Oscillator and LC Oscillator Ring oscillator LC-Tank oscillator A2 0000 ∠ R 2 9m Transfer function H(S)= Mn2 jo @o 0oc=0·tan N A- tan .Advantage: Large tuning range .Advantage: Low phase noise .Disadvantage:High phase noise .Disadvantage:Small tuning range Inductors MOS Varactor designs ASIC System State-Key Laboratory,Fudan University -8
-8- ASIC & System State-Key Laboratory, Fudan University http://10.12.240.202, Copyright © 2001-2004, Zhangwen Tang Ring Oscillator and LC Oscillator Ring Oscillator and LC Oscillator + - - + + - - + + - - + A1 A2 An … Ring oscillator LC-Tank oscillator Transfer function ( ) ω ω = − ⎛ ⎞ ⎜ ⎟ + ⎝ ⎠ 0 0 1 n n A H s j ω ω ° ⎛ ⎞ = ⋅ ⎜ ⎟ ⎝ ⎠ 0 180 osc tan N ° ⎛ ⎞ ⎛ ⎞ = + ⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎝ ⎠ ⎝ ⎠ 2 0 180 A 1 tan N Mn1 Mn2 CP RP LP − 2 gm X Y •Advantage: Large tuning range •Disadvantage: High phase noise •Advantage: Low phase noise •Disadvantage: Small tuning range Inductors & MOS Varactor designs
http://10.12.240.202,Copyright 2001-2004,Zhangwen Tang Mathematics of LC VCOs F-V characteristic function @out =@o+Kv Ved 02 An ideal integrator in Phase-Locked Loop (s)-ko slope K 01 Performance parameters Center frequency 0 ● Tuning range Voltage-controlled gain Tuning linearity ●Phase noise ● Oscillating amplitude ●Power dissipation ASIC System State-Key Laboratory,Fudan University -9
-9- ASIC & System State-Key Laboratory, Fudan University http://10.12.240.202, Copyright © 2001-2004, Zhangwen Tang Mathematics of LC Mathematics of LC VCOs ωout Vctrl ω0 ω1 ω2 V1 V2 slope KV ωout V ctrl = ω0 + ⋅ K V ( ) ex V ctrl K s V s φ = F-V characteristic function An ideal integrator in Phase-Locked Loop Performance parameters z Center frequency z Tuning range z Voltage-controlled gain z Tuning linearity z Phase noise z Oscillating amplitude z Power dissipation
http://10.12.240.202,Copyright@2001-2004,Zhangwen Tang Narrowband LC VCOs NMOS-only -G LC VCO Complementary MOS-Gm LC VCO dd Mp1 Mp2 L 2L 0009 9 C C C C Mn1 Mn2 Mn1 Mn2 M n3 Mn3 tail ASIC System State-Key Laboratory,Fudan University [Ali Hajimiri,JSSC,May,1999] -10-
-10- ASIC & System State-Key Laboratory, Fudan University http://10.12.240.202, Copyright © 2001-2004, Zhangwen Tang Narrowband LC Narrowband LC VCOs 2L Vc Mn1 Mn2 Mp1 Mp2 Mn3 CV L L Cv Vc Mn1 Mn2 Itail Vdd Vdd Mn3 Itail Y Vdd Vdd X Y Vdd Vdd Vss Vss X Cfix Cfix Cfix Cfix Cv CV NMOS-only –Gm LC VCO Complementary MOS –Gm LC VCO [Ali Hajimiri, JSSC, May, 1999]