RFIC Inductor Introduction

Transcription

1 FIC Inductor Introduction Dror egev Dror egev July 008

2 Layout of a Siral Inductor Mot lanar inductor are iral. Shae can be: Octagonal, Square or ectangle. Goal i to obtain the needed inductance within a minimal area while otimizing quality factor. L IND L elf M M Total inductance of the iral, include um of all line elf and mutual inductance. The Siral ha alo erial reitance of the metal line that limit the quality factor at every frequency. We will firt examine the inductor without Si ubtrate effect and later on add thoe effect. Dror egev July 008

3 Self and Mutual Inductance of a Micro tri Self inductance of a egment l (cm) with a rectangular cro ection w t (cm cm): l w t L l (ln 0.5 ) [ nh] w t 3l Self inductance require hyical length and indeendent of Eilon. w t l d Mutual inductance between filament at ditance d: M μ 4π *0 L 0 μ0 l (ln ( π 7 [ H Mutual inductance of adjacent egment can be oitive or negative deending on egment current direction Dror egev July 008 / m] l d IND Lelf M M Edge effect imact i tronger the horter the line i. Longer line have higher inductance er unit length!. Hence, corner in the trace reduce inductance. l d d d ) )[ H ] l l Dimenion in m L, M [H] 00 Inductance v. line length W0um, Tum. d w Trace length [um] 35 dl/dl

4 Micro tri Metal eitance AC current flowing in a Micro tri at F frequencie crowd cloer to F Ground in a henomena called kin effect. Hence, effective current cro ection may be maller than the hyical dimenion. Skin Deth: δ ω * μ * σ ρ π * μ * f δ t Skin Deth [um] Al kin deth Frequency [GHz] F reitance: er. kin ( w, l, t, ω, σ ) dc e t δ t δ F reitance increae with frequency due to kin effect erie of a00um line length with w0um and tum Frequency [GHz] Dror egev July 008 4

5 Micro tri Serie Quality Factor Serial Quality Factor: Q Serie, elf ωl L w l Quality factor for 00um line length, tum, Al t Q w 4um Q w 0um Frequency L& both deend on line length. determine erie Q factor and deend on w and t the thickne of the metal. Skin effect further increae. Increaing W eem to imrove erial Q, but alo reduce mutual inductance contribution from adjacent line and increae caacitance to ground which ha negative contribution to Q factor (a will be hown later). Dror egev July 008 5

6 Inductor Serial Caacitance C L C Equivalent caacitance from inductor inut to outut originate in two major mechanim: Metal Under ath caacitance In Caacitance deend on ize and number of under ath. Out L C_overla n L ut C_overla Dror egev July Mutual caacitance Out Caacitance deend on ditance between line center. 5 In

7 Inductor Serie Quality Factor Im( ) y I Q y I V 0 e( ) V y Q y j ( jωl ) ωc Im( Z e( Z ) ) ω ωl [ L ( L C ) C ] ω ( ω L C ) Serie quality factor: Q at low frequency follow ωl / value, but when aroaching reonance it reache a maximum and than tart to decreae and zeroe at reonance. After reonance it behave like a caacitor. Dror egev July Z L ωl C ω 0 ω I Q Q _ trace ( kin_ effect_ neglected) Q max Q max ω max low ω ω 0 max high

8 Siral Inductor with Si Subtrate - Simlified Pi Model C Lumed Pi Model: L ort Cox Cox ort ub Cub Cub ub L Inductance of Siral Inductor Metallization Serie eitance of Inductor C Inut to Outut Caacitance Cox Caacitance of metal trace to ubtrate (through ILD) ub Subtrate eitance C ub Subtrate Caacitance Dror egev July 008 8

9 Performance Effect of the Si Subtrate Z C Z C I ub Cox L Z Cub Im( y Z Z S y Z Z ) ωl I S equivalent I ( ω LC) ωl ( ω L C) L Z C C C Q e( ) ω L ω L y Inductor quality factor: with Z the arallel C imedance ha two imact:. eonance frequency decreae a total caacitance increae: C totalc C. There i a arallel diiation ath to ubtrate that further reduce Q 3., the equivalent arallel reitance to ground reduce with frequency. Dror egev July Serie quality factor with lower reonance frequency. I ( ω ) ( ω ) Subtrate loe at high frequencie

10 Siral Inductor Model with Higher Accuracy C Port L er K L er Port Cox L Cox L Cox Cub ub ub Cub ub Cub L 3 L 3 Skin Effect Higher order model with increaed comlexity and accuracy including modeling for kin effect Dror egev July 008 0

11 Model v. Tet Data Comarion S Parameter Z /Y Q Factor Inductor.5/60um Model v. Tet Performance Dror egev July 008

12 Symmetrical Inductor and Differential Mode Differential mode Common mode Virtual Ground Virtual Oen Differential excitation of the inductor create a virtual ground at the inductor center. Dror egev July 008

13 Differential Inductor Q v. Single Ended Q I L C I ωl [ ω L ( C C P Q ω L P )] C eonance frequency factor For ymmetric excitation we can ue the ame aroximation: C C Subtrate loe at high frequencie I L/ / / L/ I C Virtual Ground Q ωl[ ω L (C C )] P P ω L Dror egev July 008 3

14 Differential Inductor Q v. Single Ended Q Q So we found that ymmetrical excitation both decreae ubtrate loe and increae reonance frequency!. Symmetric: diff ωl[ ω L (C C )] P P ω L Single ended: ωl [ ω L ( C C P Qe ω L P )] Q ωl / Q max e Q max diff ω e max ω diff max ω 0 e ω 0 diff ω Dror egev July 008 4

15 Symmetrical Inductor Caacitance. Single Ended In Out Symmetrical Inductor Single ended Inductor SE Inductor Couling caacitor i horted by low inductance. Symmetric Inductor Couling caacitor i horted by a larger inductance. Hence caacitance between turn i increaed. The larger the number of turn, the bigger the caacitance difference between ymmetric and nonymmetrical inductor. Dror egev July 008 5

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