Phase Noise in CMOS Differential LC Oscillators

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1 Phase Noise in CMOS Differenial LC Oscillaors Ali Hajimiri Thomas H. Lee Sanford Universiy, Sanford, CA 94305

2 Ouline Inroducion and Definiions Tank Volage Noise Sources Effec of Tail Curren Source Measuremen Resuls Conclusion

3 Oscillaors Are Time-Varian Sysems i() δ( τ) i() C L τ V ou V Impulse injeced a he peak of ampliude. τ V ou V τ Impulse injeced a zero crossing. Even for an ideal LC oscillaor, he phase response is Time Varian.

4 Ampliude Resoring Mechanism i() δ( τ) i() C L G -G(A) τ Acive Device Once Inroduced, phase error persiss indefiniely. Non-lineariy quenches ampliude changes over ime. Limi Cycle dv d b θ θ a V V

5 Phase Impulse Response The phase impulse response of an arbirary oscillaor is a ime varying sep. i() i () h φ ( τ, ) φ() 0 τ 0 τ The uni impulse response is: h φ (, τ) = Γω ( o τ) u( τ) q max Γ( x )is a dimensionless funcion periodic in π, describing how much phase change resuls from applying an impulse a ime: = T x π

6 Impulse Sensiiviy Funcion (ISF) The ISF quanifies he sensiiviy of every poin in he waveform o perurbaions. V ou ( ) V ou ( ) Waveform Γω ( 0 ) Γω ( 0 ) ISF

7 Phase Response o an Arbirary Source i( ) h φ (, τ) = Γω ( 0 τ) u( τ) q max φ( ) Superposiion Inegral: φ( ) = h φ (, τ)i( τ)dτ = Γω q ( 0 τ)i( τ)dτ max Equivalen represenaion: i( ) q max Γω ( 0 ) Ideal Inegraion Phase Modulaion ψ( ) φ ( ) V( ) cos[ ω 0 + φ( ) ]

8 Phase Noise Due o Whie Noise LTV sysem Nonlinear sysem i () φ () V() h φ ( τ, ) cos[ ω 0 + φ() ] i n For a whie inpu noise curren wih specral densiy of , f he phase noise sideband power below he carrier a an offse of ω is: L { ω} = Γ rms q max i n f ω where Γ rms is he rms value of he ISF.

9 Noise Conribuions from nω o i n ( ω ) f 1 -- Noise f φ( ) 1 = c q 0 i ( τ )dτ max + c n i( τ) cos( nωτ) dτ ω ω ω n = 1 S φ ( ω) c ω 0 0 ω 0 3ω ω 0 c 1 c c 3 S v ( ω) ω PM ω ω ω 0 ω 0 3ω 0 ω

10 1/f 3 Corner of Phase Noise Specrum The 1/f 3 corner of phase noise is NOT he same as he 1/f corner of device noise c 0 c 1 c 3 c L ( ω) ω 1 f 3 = f Γ dc ω 1 f Γ rms ω f 3 ω 1 f -- log(ω-ω o ) By designing for a symmeric waveform, he performance degradaion due o low frequency noise can be minimized.

11 A Symmeric LC Oscillaor Vdd W P /L W P /L Adjus raios o fine une symmery L/ C L/ W N /L W N /L Uses he same curren wice for high ransconducance. [Also appears in: J.Craninckx, e al, Proceedings of CICC 97.]

12 Ouline Inroducion and Definiions Tank Volage Noise Sources Effec of Tail Curren Source Measuremen Resuls Conclusion

13 Tank Volage Ampliude I ail V DD L C Assuming fas swiching of he differenial pair, he curren can be approximaed as: i() I ail I ail I ail -I ail

14 Tank Volage Ampliude I ail i() Assuming recangular waveform: 4 V max = -- I π ail R eq -I ail Effecively, he curren waveform is closer o sinusoidal, herefore: i() C L R eq V max I ail R eq Curren limied mode.

15 Modes of Ampliude Limiing Complemenary cross-coupled LC oscillaor 3.5 Tank volage swing (vol) Curren Limied V dd =3.0V V dd =.5V V dd =1.5V Volage Limied Tail curren (ma)

16 Ouline Inroducion and Definiions Tank Volage Noise Sources Effec of Tail Curren Source Measuremen Resuls Conclusion

17 Major Noise Sources V DD i i p1 p Differen noise sources affec phase noise differenly. v r rs s C L i n W = 4 ktγµc ---- f ox ( V L GS V T ) i n1 bias i ail i n Valid in boh long and shor channel regimes. Inducor Noise: v n = 4 ktr f s

18 Equivalen Circui for Differenial Sources r i 1 () L C i () r Differenial Equivalen L C r R i () i 1 () i n f diff pair 1 i n 1 i n i p 1 i p = = 4 f f f f 1 i n f i p f

19 Ouline Inroducion and Definiions Tank Volage Noise Sources Effec of Tail Curren Source Measuremen Resuls Conclusion

20 Waveform and ISF.5 Node Volage (V) V- Vail V NMOS ISF Tail ISF ISF PMOS ISF x (radians)

21 Effec of Tail Curren Source V DD L C For he ail curren source, only low frequency noise and noise in he viciniy of even harmonics of he ail curren source affec phase noise. i n ( ω ) f i ail 1 -- Noise f ω 0 ω 0 ω

22 Ouline Inroducion and Definiions Tank Volage Noise Sources Effec of Tail Curren Source Measuremen Resuls Conclusion

23 Die Phoo of he Complemenary Oscillaor 0.5µm process Acive 700µm x 800µm Pad limied L L Bypass C Driver Bypass

24 Phase Noise vs. Offse from Carrier -50 Complemenary cross coupled LC oscillaor f0=1.8ghz, Pdiss=6mWa -60 Phase noise below carrier (dbc/hz) Offse from carrier (Hz)

25 Complemenary Cross-Coupled LC Oscillaor f 0 =1.8GHz, 0.5µm Process (V DD =3V) Phase noise a 600KHz offse (dbc/hz) Measuremen Γ rms =0.5 Simulaed ISF bias Vdd L C Gnd I ail Tail Curren (ma)

26 Complemenary Cross-Coupled VCO Phase noise below carrier a 600kHz offse V dd f 0 =1.8GHz, 0.5µm Process Iail (ma) 4 x 10 3 bias Vdd f 0 =1.8GHz L C Gnd I ail P=6mW -11dBc/Hz@600kHz

27 Complemenary vs. NMOS-Only VCO f 0 =1.8GHz, 0.5µm Process Vdd Phase noise below carrier a 600kHz offse Complemenary x 10 3 I ail (ma) NMOS-Only V dd L/ L/ bias bias C Gnd Vdd L C Gnd I ail I ail

28 Conclusion Phase noise of differenial MOS oscillaors is analyzed. The effec of ail curren source on he ampliude is discussed. Major noise sources are idenified. The effec of ail curren source noise is shown. Good agreemen beween heory and measuremens is observed.

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