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This document discusses passive devices used in RFIC design, including inductors, capacitors, and resistors. It covers topics like: - Different types of inductors and their modeling approaches. Enhancing inductor Q factors by reducing metal and substrate losses. - Varactors/tunable capacitors using junctions and accumulation modes. Their Q factors and tuning ranges as a function of bias. - RC and RLC networks, including their impedance transformations between series and parallel configurations. Definitions of Q factor for different passive components and networks.

Engineering
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RFIC Design Lecture 5: Passive devices
RFIC Design 5: Passive devices Slide 2 Inductor and Capacitor
RFIC Design 5: Passive devices Slide 3 Inductors  Different geometry of the spiral inductors
RFIC Design 5: Passive devices Slide 4 Inductance  Inductance : – Foundry model – Simulated by EM – Empirical equation
RFIC Design 5: Passive devices Slide 5 Monolithic Inductor  General consideration for monolithic inductors – Q factor – Resonant frequency – In band loss – Inductance – Area – Modeling accuracy
RFIC Design 5: Passive devices Slide 6 Inductor Physical Model  Physical model – Metal loss – Substrate loss Cp Ls Rs Cox1 Cox2 Csub1 Rsub1 Rsub2 Csub2
RFIC Design 5: Passive devices Slide 7 Q factor enhancement  The power loss degrades Q  Reducing Metal loss increases Q – Bond wire – Thick metal – High conductivity metal (Cu)  However, reducing metal loss only help in low frequency ( ~ <2GHz) – Skin effect – Substrate loss dominates at high frequency 7 0 2 2 ln 0.75 2 10 ln 0.75 2 u l l l L r r                                     
RFIC Design 5: Passive devices Slide 8 Skin effect m = permeability (4 * 10-7 H/m),  = pi ds = skin depth (m) r = resistivity (W*m) w = radian frequency = 2*f (Hz) Copper at 10GHz
RFIC Design 5: Passive devices Slide 9 Q factor enhancement  Reducing substrate loss increases Q – Pattern ground shield – Silicon bulk micromachined inductor – Substrate thinning
RFIC Design 5: Passive devices Slide 10 High Q Inductor  Reduce substrate loss -> enhance Q at high frequency  Reduce metal loss -> enhance Q at low frequency  Overall Q enhancement -> combine two approaches •Electroplated thik copper •Micromaching
RFIC Design 5: Passive devices Slide 11 all-copper solenoid inductor  solenoid inductor by MEMS techniques
RFIC Design 5: Passive devices Slide 12 Stack inductor  High inductance approach – Increase N – Stacked inductor – 3D inductor
RFIC Design 5: Passive devices Slide 13 Varactor
RFIC Design 5: Passive devices Slide 14 Junction Varactor  Capacitance :  (i) When the junction is forward biased P-sub P N N+ P+ T D T diff V I C   junc diff total C C C   m R jD R junc V A C V C           1 ) ( D A D A o r jD N N N N q C     2   0.0 0.5 1.0 1.5 2.0 2.5 -0.5 3.0 4 5 6 7 8 3 9 Vdc (V) Cs (pH)
RFIC Design 5: Passive devices Slide 15 Accumulation-mode Varactor s s c cap s C R Q    w , , 1 Depletion mode accumulation mode
RFIC Design 5: Passive devices Slide 16 Q and tuning range vs bias -3 -2 -1 0 1 2 3 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 Capacitance ( pF ) Vgs 20 40 60 80 100 120 140 160 Gate length: 0.18mm capacitance Q factor Q factor
RFIC Design 5: Passive devices Slide 17 Q factor vs Gate Length 0 1 2 3 4 5 6 -50 0 50 100 150 200 250 300 350 400 450 Vgs=0 Gate Length: 0.18mm Gate Length: 0.5mm Gate Length: 1mm Q factor frequency ( GHz )
RFIC Design 5: Passive devices Slide 18 Capacitor
RFIC Design 5: Passive devices Slide 19 Structure  MiM Capacitor
RFIC Design 5: Passive devices Slide 20 Layout & Model  MiM Capacitor
RFIC Design Common Centroid 5: Passive devices Slide 21
RFIC Design Matching of passive devices 5: Passive devices Slide 22
RFIC Design 5: Passive devices Slide 23 Resistor
RFIC Design 5: Passive devices Slide 24 Resistor catalog  N+ diffused resistor w/o salicide  P+ diffused resistor w/o salicide  N+ diffused resistor w/i salicide  P+ diffused resistor w/i salicide  N-Well resistor  N+ Poly resistor w/salicide  P+ Poly resistor w/salicide  N+ Poly resistor w/o salicide  P+ Poly resistor w/o salicide  P- Poly HRI resistor w/o salicide  Metal 1 resistor  Metal 2 resistor  Metal 3 resistor  Metal 4 resistor  Metal 5 resistor  Top metal resistor
RFIC Design 5: Passive devices Slide 25 Resistance  r = resistivity (W*m)  R = sheet resistance (W/) –  is a dimensionless unit(!)  Count number of squares – R = R * (# of squares) l w t 1RectangularBlock R = R (L/W) W 4RectangularBlocks R =R (2L/2W) W = R (L/W) W t l w w l l l R R t w w r  
RFIC Design 5: Passive devices Slide 26 Well Resistor  Well Resistor • Well Resistor • Large Rsh without extra mask • Rsh : 450 or 900 • Positive TC • Large TC • Large variation
RFIC Design 5: Passive devices Slide 27 Diffusion Resistor  P+/N+ Diffused resistor w/o and w/i salicide • w/o and w/i salicide • Rsh : 2~10W/□ •Negative TC • Large variation • rarely used
RFIC Design 5: Passive devices Slide 28 Poly Resistor  P+/N+ Poly resistor w/o and w/i salicide • w/o & w/i salicide • Rsh : ~ 300 & ~ 8 • Positive TC • Smaller variation • Smaller parasitic -> RF
RFIC Design 5: Passive devices Slide 29 HRI Resistor  P- Poly HRI resistor w/o salicide • w/o salicide • Rsh : > 1000 • Positive TC • High resistance • Smaller parasitic -> RF
RFIC Design 5: Passive devices Slide 30 R L C network
RFIC Design 5: Passive devices Slide 31 Passive device  R-L and R-C network
RFIC Design 5: Passive devices Slide 32 Definition of Q For an inductor : Cycle n Oscillatio one in Loss Energy Energy Capacitive Stored Maxium - Energy Magnetic Stored Maximum Q   π 2 For a capacitor : Cycle n Oscillatio one in Loss Energy Energy Magnetic Stored Maxium - Energy Capactive Stored Maximum Q   π 2 For a LC Tank : Cycle n Oscillatio one in Loss Energy Energy Magnetic Stored average Energy Capactive Stored average Q    π 2
RFIC Design 5: Passive devices Slide 33 Series R & L  Series R & L  Physical inductor model Ls Rl,s Ip P P ind L I E 2 max , 2 1   f R I T R I E s l p s l p R dis 1 2 1 2 1 , 2 , 2 ,         s l s s l p s P R dis ind ind s R L f R I L I E E Q , , 2 2 , max , , 1 2 1 2 1 2 2           w  
RFIC Design 5: Passive devices Slide 34 Parallel R & L  Parallel R & L  Tank in the VCO LP Ip Rl,p Vp P P ind L I E 2 max , 2 1   f R L I T R V E p l P P p l p R dis 1 ) ( 2 1 2 1 , 2 , 2 ,         w P p l p l P P P P R dis ind ind p L R f R L I L I E E Q            w w   , , 2 2 , max , , 1 ) ( 2 1 2 1 2 2
RFIC Design 5: Passive devices Slide 35 Series and parallel transformation  Series LR to parallel transformation       2 2 0 0 0 0 2 2 0 ( ) || P P P S S P P P P L j L R j L R j L R R L w w w w w      Ls Rl,s Ip LP Ip Rl,p Vp 0 0 S P P S L R Q L R w w   2 ( 1) P S R R Q   2 2 1 P S Q L L Q        
RFIC Design 5: Passive devices Slide 36 Capacitor network  Parallel R & C  Series R & C CP Vp Rc,p Cs Rc,s Vp s s c cap s C R Q    w , , 1 P p c cap p C R Q    w , ,
RFIC Design 5: Passive devices Slide 37 Series and parallel transformation  Series RC to parallel transformation   2 2 2 1 1 P S P S R R Q Q C C Q           CP Vp Rc,p Vp CP Vp ,p Cs Rc,s Vp   2 2 2 1 1 P S P S R R Q Q X X Q          
RFIC Design 5: Passive devices Slide 38 Parallel RLC tank  Parallel RLC tank Impedance – Inductive admittance at low frequency – Capacitive admittance at high frequency i(t) R C L V + -
RFIC Design 5: Passive devices Slide 39 Parallel RLC tank  The Q factor or quality factor is a measure of the "quality" of a resonant system.  General Definition : For resonant system  Hence :   2 2 1 2 1 2 tot pk avg pk E C I R P I R   energy stored average power dissipated Q w    2 0 2 1 1 2 1 / 2 pk tot avg pk C I R E R Q P LC L C I R w   
RFIC Design 5: Passive devices Slide 40  The impedance looking into RLC resonator can be derived as follows: where  Normalize the impedance response to its peak value:  According to this equation, it can be obtained that Q=w0/Dw , where Dw means the 3dB bandwidth. It indicates that the higher Q is, the narrower bandwidth the filter has. Impedance response 2 0 0 2 / w w    Q s s C s Z LC 1 0  w RC L C R Q 0 w               w w w w w 0 0 1 1 ) ( Q j j H
RFIC Design Impedance response with various Q 5: Passive devices Slide 41 Q=3 Q=1.5 Q=1 Q=0.5 Q=3 Q=6 Q=12
RFIC Design 5: Passive devices Slide 42 Parallel Q  How to calculate the Q of the parallel devices? i(t) C L Rc,s RL,s i(t) C L Rc,p RL,p S C c P C R Q R , 2 ,   S L L p L R Q R , 2 ,   S L L S C C Tank R Q R Q R , 2 , 2 //  L C R Q R Q Q S L L S C C Tank   ) // ( , 2 , 2 L C L C L C Q Q Q Q Q Q //    
RFIC Design 5: Passive devices Slide 43 Series RLC tank  Series RLC tank  At resonance, the voltage across either the inductor or capacitor is Q times as great as that across the resistor.  Ex. If a series RLC with a Q of 1000 is driven with a 1V at resonance, then 1000V will appear across L & C. / L C Q R 
RFIC Design 5: Passive devices Slide 44 Impedance transformation  Why need to transform impedance?  RLC network can be used to perform impedance transformation.  To draw a maximum power form source Vs with Zs, ZL must to match Zs :  Prove it:     2 2 2 2 R L s L L S L S V R V R R R X X    
RFIC Design 5: Passive devices Slide 45 Impedance transformation  Upwards impedance transformer  Downwards impedance transformer 0 2 2 2 2 0 S S P S S S S L L R R Q R R R w w         
RFIC Design 5: Passive devices Slide 46 Capacitive Divider  Impedance transformation by means of capacitive divider.  Rtotal is boosted by the factor of 2
RFIC Design 5: Passive devices Slide 47 Inductive divider  Impedance transformation by means of Inductive divider.
RFIC Design 5: Passive devices Slide 48 S parameter
RFIC Design 5: Passive devices Slide 49 Reflection coefficient  RF engineering  Reflect coefficient  Real & Imaging parts  For High Z  Easy Γ & Z transformation
RFIC Design 5: Passive devices Slide 50 Smith Chart  Bilinear transformation : From Real & Imaginary to Magnitude & Phase .  Z & Y smith charts
RFIC Design 5: Passive devices Slide 51 Smith Chart
RFIC Design 5: Passive devices Slide 52 Smith Chart S-L S-C P-C P-L  Matching
RFIC Design 5: Passive devices Slide 53 Two ports network  Impedance network
RFIC Design 5: Passive devices Slide 54 S parameter network  S -> scattering  Generally, Z0 = 50W  Most popular for RF measurement system. 1 11 1 12 2 2 21 1 22 2 b s a s a b s a s a     1 1 11 1 1 1 2 2 21 1 1 r i r i b E s a E b E s a E      
RFIC Design 5: Passive devices Slide 55 RF measurement and device modeling
RFIC Design 5: Passive devices Slide 56 RF probes  RF probes
RFIC Design 5: Passive devices Slide 57 Probe station  RF measurement equipments
RFIC Design 5: Passive devices Slide 58 Agilent 8510  Agilent 8510 for s-parameter measurement
RFIC Design 5: Passive devices Slide 59 RF device measurement  The calibration setup is very important for RF measurement.
RFIC Design 5: Passive devices Slide 60 Deembed & Calibration  Calibration for testing and deembed pad effect.  Deemebedding and calibration procedure is very important for the RF measurement and modeling.  Four patterns for testing calibration procedures. – Open , short , thru1, thru2.
RFIC Design 5: Passive devices Slide 61 Inductor model Cp Ls Rs Cox1 Cox2 Csub1 Rsub1 Rsub2 Csub2 Port1 Port2 ZA ZB ZC  Step 0 : prepare S or Y parameter  Step 1 : Ignore Cp first
RFIC Design 5: Passive devices Slide 62 Inductance extraction  Step 2 : Calculate Y21 Ls Rs Cox1 Cox2 Csub1 Rsub1 Rsub2 Csub2 0 2 1 2 21   v v i Y ) 1 ( 21 Y real Rs   ) 2 1 ( 21 Y freq imag Ls      Ls Rs
RFIC Design 5: Passive devices Slide 63 Extracted Rs & Ls 0 5 10 15 20 0 5 10 15 20 25 R S ( W ) Frequency ( GHz ) 0.1 1 10 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Inductance ( nH ) Frequency ( GHz ) with Cp Cp-10f Skin effect Because of Cp  Step 2 : Extracted Rs & Ls
RFIC Design 5: Passive devices Slide 64 Inductor model  Extraction of the Substrate Network Cox Csub Rsub 1 1 11 v i Y  1 ) ( 1 21 1 1 1 11 v i Y v i i Y b b a      21 11 2 1 _ 1 1 Y Y v i v i Y b In sub      Ls Rs C1 R1 V1 i1 i1a i1b i2 Cox1 21 11 2 1 _ 1 1 Y Y v i v i Y b In sub     
RFIC Design 5: Passive devices Slide 65 Substrate network Cox Csub Rsub C1 R1 C1' R1' 2 2 2 2 2 2 1 2 ) 1 1 ( 2 1 1 Cox Rsub Csub Cox Rsub R      2 2 2 2 2 1 ) 1 1 ( 1 ) 1 1 ( 1 1 1 1 1 Rsub Csub Cox Csub Cox Csub Rsub Cox C          Substrate network transformation  When the frequency (w) approaches zero, C1 is equal to Cox1 approximately.  When the frequency (w) is high enough, C1 would be equal to the series combination of Cox1 and Csub1
RFIC Design 5: Passive devices Slide 66 Extracted Cox  Step 3 : Extracted Cox freq Y Y imag Cox     2 ) 12 11 ( 1 when freq  0 0 5 10 15 20 10 15 20 25 30 35 40 45 50 55 C1(fH) Frequency ( GHz ) Cox Csub Rsub
RFIC Design 5: Passive devices Slide 67 Extracted Csub & Rsub  Extracted Csub & Rsub 1 2 1 ) 1 ( 1 1 12 11 Cox freq j Y Y Ysub        ) ( 1 1 1 Sub Sub Y real R  when freq  High (4.31) ) 2 ( 1 1 1 Sub Sub Y freq imag C     when freq  High (4.32) 0 5 10 15 20 -40 -20 0 20 40 60 80 Csub'(fH) Frequency ( GHz ) 0 5 10 15 20 -2000 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Frequency ( GHz ) Rsub1' (ohms)
RFIC Design 5: Passive devices Slide 68 Comparison f req (100.0MHz to 20.00GHz) S(1,1) model..S(1,1) f req (100.0MHz to 20.00GHz) S(2,2) model..S(2,2) 2 4 6 8 10 12 14 16 18 0 20 -10 -8 -6 -4 -2 -12 0 f req, GHz dB(S(2,1)) dB(model..S(2,1)) 2 4 6 8 10 12 14 16 18 0 20 -10 -8 -6 -4 -2 -12 0 f req, GHz dB(S(1,2)) dB(model..S(1,2)) 2,1) 2)
RFIC Design 5: Passive devices Slide 69 Dimension Definition of Square Inductor D D+W+S s W M5 M4
RFIC Design 5: Passive devices Slide 70 Extracted Ls vs D,N,W 60 80 100 120 140 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Indutance (nH) 3.5 turns Metal W idth:15mm Metal W idth:10mm inner diameter (mm) Metal Width from 10mm to 15mm 1.5 2.0 2.5 3.0 3.5 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Inductance ( nH ) turn numbers D : 60mm D : 70mm D : 80mm D : 90mm D : 100mm D : 110mm D : 120mm D : 130mm L=(0.21074+0.00409*W)*0.608(N-1.5)+0.09+0.03*(W-10)/5  Inductor Library
RFIC Design 5: Passive devices Slide 71 Q factor vs turns & D 0 2 4 6 8 10 0 2 4 6 8 10 12 14 Q factor Frequency ( GHz ) 60mm 70mm 80mm 90mm 100mm 110mm 120mm 130mm 140mm 1.5 turns Increasing D 0 2 4 6 8 10 0 2 4 6 8 10 12 Q factor Frequency ( GHz ) 3.5 turns 120mm 130mm 140mm 60mm 70mm 80mm 100mm 110mm Increasing D  Inductor Library
RFIC Design 5: Passive devices Slide 72 References  B. Razavi, “RF Microelectronics,” Upper Saddle River: Prentice-Hall,1998.  T. H. Lee, “The Design of CMOS Radio-Frequency Integrated Circuits,” Cambridge: Cambridge University Press, 1998.

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lecture5.ppt

  • 2. RFIC Design 5: Passive devices Slide 2 Inductor and Capacitor
  • 3. RFIC Design 5: Passive devices Slide 3 Inductors  Different geometry of the spiral inductors
  • 4. RFIC Design 5: Passive devices Slide 4 Inductance  Inductance : – Foundry model – Simulated by EM – Empirical equation
  • 5. RFIC Design 5: Passive devices Slide 5 Monolithic Inductor  General consideration for monolithic inductors – Q factor – Resonant frequency – In band loss – Inductance – Area – Modeling accuracy
  • 6. RFIC Design 5: Passive devices Slide 6 Inductor Physical Model  Physical model – Metal loss – Substrate loss Cp Ls Rs Cox1 Cox2 Csub1 Rsub1 Rsub2 Csub2
  • 7. RFIC Design 5: Passive devices Slide 7 Q factor enhancement  The power loss degrades Q  Reducing Metal loss increases Q – Bond wire – Thick metal – High conductivity metal (Cu)  However, reducing metal loss only help in low frequency ( ~ <2GHz) – Skin effect – Substrate loss dominates at high frequency 7 0 2 2 ln 0.75 2 10 ln 0.75 2 u l l l L r r                                     
  • 8. RFIC Design 5: Passive devices Slide 8 Skin effect m = permeability (4 * 10-7 H/m),  = pi ds = skin depth (m) r = resistivity (W*m) w = radian frequency = 2*f (Hz) Copper at 10GHz
  • 9. RFIC Design 5: Passive devices Slide 9 Q factor enhancement  Reducing substrate loss increases Q – Pattern ground shield – Silicon bulk micromachined inductor – Substrate thinning
  • 10. RFIC Design 5: Passive devices Slide 10 High Q Inductor  Reduce substrate loss -> enhance Q at high frequency  Reduce metal loss -> enhance Q at low frequency  Overall Q enhancement -> combine two approaches •Electroplated thik copper •Micromaching
  • 11. RFIC Design 5: Passive devices Slide 11 all-copper solenoid inductor  solenoid inductor by MEMS techniques
  • 12. RFIC Design 5: Passive devices Slide 12 Stack inductor  High inductance approach – Increase N – Stacked inductor – 3D inductor
  • 13. RFIC Design 5: Passive devices Slide 13 Varactor
  • 14. RFIC Design 5: Passive devices Slide 14 Junction Varactor  Capacitance :  (i) When the junction is forward biased P-sub P N N+ P+ T D T diff V I C   junc diff total C C C   m R jD R junc V A C V C           1 ) ( D A D A o r jD N N N N q C     2   0.0 0.5 1.0 1.5 2.0 2.5 -0.5 3.0 4 5 6 7 8 3 9 Vdc (V) Cs (pH)
  • 15. RFIC Design 5: Passive devices Slide 15 Accumulation-mode Varactor s s c cap s C R Q    w , , 1 Depletion mode accumulation mode
  • 16. RFIC Design 5: Passive devices Slide 16 Q and tuning range vs bias -3 -2 -1 0 1 2 3 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 Capacitance ( pF ) Vgs 20 40 60 80 100 120 140 160 Gate length: 0.18mm capacitance Q factor Q factor
  • 17. RFIC Design 5: Passive devices Slide 17 Q factor vs Gate Length 0 1 2 3 4 5 6 -50 0 50 100 150 200 250 300 350 400 450 Vgs=0 Gate Length: 0.18mm Gate Length: 0.5mm Gate Length: 1mm Q factor frequency ( GHz )
  • 18. RFIC Design 5: Passive devices Slide 18 Capacitor
  • 19. RFIC Design 5: Passive devices Slide 19 Structure  MiM Capacitor
  • 20. RFIC Design 5: Passive devices Slide 20 Layout & Model  MiM Capacitor
  • 21. RFIC Design Common Centroid 5: Passive devices Slide 21
  • 22. RFIC Design Matching of passive devices 5: Passive devices Slide 22
  • 23. RFIC Design 5: Passive devices Slide 23 Resistor
  • 24. RFIC Design 5: Passive devices Slide 24 Resistor catalog  N+ diffused resistor w/o salicide  P+ diffused resistor w/o salicide  N+ diffused resistor w/i salicide  P+ diffused resistor w/i salicide  N-Well resistor  N+ Poly resistor w/salicide  P+ Poly resistor w/salicide  N+ Poly resistor w/o salicide  P+ Poly resistor w/o salicide  P- Poly HRI resistor w/o salicide  Metal 1 resistor  Metal 2 resistor  Metal 3 resistor  Metal 4 resistor  Metal 5 resistor  Top metal resistor
  • 25. RFIC Design 5: Passive devices Slide 25 Resistance  r = resistivity (W*m)  R = sheet resistance (W/) –  is a dimensionless unit(!)  Count number of squares – R = R * (# of squares) l w t 1RectangularBlock R = R (L/W) W 4RectangularBlocks R =R (2L/2W) W = R (L/W) W t l w w l l l R R t w w r  
  • 26. RFIC Design 5: Passive devices Slide 26 Well Resistor  Well Resistor • Well Resistor • Large Rsh without extra mask • Rsh : 450 or 900 • Positive TC • Large TC • Large variation
  • 27. RFIC Design 5: Passive devices Slide 27 Diffusion Resistor  P+/N+ Diffused resistor w/o and w/i salicide • w/o and w/i salicide • Rsh : 2~10W/□ •Negative TC • Large variation • rarely used
  • 28. RFIC Design 5: Passive devices Slide 28 Poly Resistor  P+/N+ Poly resistor w/o and w/i salicide • w/o & w/i salicide • Rsh : ~ 300 & ~ 8 • Positive TC • Smaller variation • Smaller parasitic -> RF
  • 29. RFIC Design 5: Passive devices Slide 29 HRI Resistor  P- Poly HRI resistor w/o salicide • w/o salicide • Rsh : > 1000 • Positive TC • High resistance • Smaller parasitic -> RF
  • 30. RFIC Design 5: Passive devices Slide 30 R L C network
  • 31. RFIC Design 5: Passive devices Slide 31 Passive device  R-L and R-C network
  • 32. RFIC Design 5: Passive devices Slide 32 Definition of Q For an inductor : Cycle n Oscillatio one in Loss Energy Energy Capacitive Stored Maxium - Energy Magnetic Stored Maximum Q   π 2 For a capacitor : Cycle n Oscillatio one in Loss Energy Energy Magnetic Stored Maxium - Energy Capactive Stored Maximum Q   π 2 For a LC Tank : Cycle n Oscillatio one in Loss Energy Energy Magnetic Stored average Energy Capactive Stored average Q    π 2
  • 33. RFIC Design 5: Passive devices Slide 33 Series R & L  Series R & L  Physical inductor model Ls Rl,s Ip P P ind L I E 2 max , 2 1   f R I T R I E s l p s l p R dis 1 2 1 2 1 , 2 , 2 ,         s l s s l p s P R dis ind ind s R L f R I L I E E Q , , 2 2 , max , , 1 2 1 2 1 2 2           w  
  • 34. RFIC Design 5: Passive devices Slide 34 Parallel R & L  Parallel R & L  Tank in the VCO LP Ip Rl,p Vp P P ind L I E 2 max , 2 1   f R L I T R V E p l P P p l p R dis 1 ) ( 2 1 2 1 , 2 , 2 ,         w P p l p l P P P P R dis ind ind p L R f R L I L I E E Q            w w   , , 2 2 , max , , 1 ) ( 2 1 2 1 2 2
  • 35. RFIC Design 5: Passive devices Slide 35 Series and parallel transformation  Series LR to parallel transformation       2 2 0 0 0 0 2 2 0 ( ) || P P P S S P P P P L j L R j L R j L R R L w w w w w      Ls Rl,s Ip LP Ip Rl,p Vp 0 0 S P P S L R Q L R w w   2 ( 1) P S R R Q   2 2 1 P S Q L L Q        
  • 36. RFIC Design 5: Passive devices Slide 36 Capacitor network  Parallel R & C  Series R & C CP Vp Rc,p Cs Rc,s Vp s s c cap s C R Q    w , , 1 P p c cap p C R Q    w , ,
  • 37. RFIC Design 5: Passive devices Slide 37 Series and parallel transformation  Series RC to parallel transformation   2 2 2 1 1 P S P S R R Q Q C C Q           CP Vp Rc,p Vp CP Vp ,p Cs Rc,s Vp   2 2 2 1 1 P S P S R R Q Q X X Q          
  • 38. RFIC Design 5: Passive devices Slide 38 Parallel RLC tank  Parallel RLC tank Impedance – Inductive admittance at low frequency – Capacitive admittance at high frequency i(t) R C L V + -
  • 39. RFIC Design 5: Passive devices Slide 39 Parallel RLC tank  The Q factor or quality factor is a measure of the "quality" of a resonant system.  General Definition : For resonant system  Hence :   2 2 1 2 1 2 tot pk avg pk E C I R P I R   energy stored average power dissipated Q w    2 0 2 1 1 2 1 / 2 pk tot avg pk C I R E R Q P LC L C I R w   
  • 40. RFIC Design 5: Passive devices Slide 40  The impedance looking into RLC resonator can be derived as follows: where  Normalize the impedance response to its peak value:  According to this equation, it can be obtained that Q=w0/Dw , where Dw means the 3dB bandwidth. It indicates that the higher Q is, the narrower bandwidth the filter has. Impedance response 2 0 0 2 / w w    Q s s C s Z LC 1 0  w RC L C R Q 0 w               w w w w w 0 0 1 1 ) ( Q j j H
  • 41. RFIC Design Impedance response with various Q 5: Passive devices Slide 41 Q=3 Q=1.5 Q=1 Q=0.5 Q=3 Q=6 Q=12
  • 42. RFIC Design 5: Passive devices Slide 42 Parallel Q  How to calculate the Q of the parallel devices? i(t) C L Rc,s RL,s i(t) C L Rc,p RL,p S C c P C R Q R , 2 ,   S L L p L R Q R , 2 ,   S L L S C C Tank R Q R Q R , 2 , 2 //  L C R Q R Q Q S L L S C C Tank   ) // ( , 2 , 2 L C L C L C Q Q Q Q Q Q //    
  • 43. RFIC Design 5: Passive devices Slide 43 Series RLC tank  Series RLC tank  At resonance, the voltage across either the inductor or capacitor is Q times as great as that across the resistor.  Ex. If a series RLC with a Q of 1000 is driven with a 1V at resonance, then 1000V will appear across L & C. / L C Q R 
  • 44. RFIC Design 5: Passive devices Slide 44 Impedance transformation  Why need to transform impedance?  RLC network can be used to perform impedance transformation.  To draw a maximum power form source Vs with Zs, ZL must to match Zs :  Prove it:     2 2 2 2 R L s L L S L S V R V R R R X X    
  • 45. RFIC Design 5: Passive devices Slide 45 Impedance transformation  Upwards impedance transformer  Downwards impedance transformer 0 2 2 2 2 0 S S P S S S S L L R R Q R R R w w         
  • 46. RFIC Design 5: Passive devices Slide 46 Capacitive Divider  Impedance transformation by means of capacitive divider.  Rtotal is boosted by the factor of 2
  • 47. RFIC Design 5: Passive devices Slide 47 Inductive divider  Impedance transformation by means of Inductive divider.
  • 48. RFIC Design 5: Passive devices Slide 48 S parameter
  • 49. RFIC Design 5: Passive devices Slide 49 Reflection coefficient  RF engineering  Reflect coefficient  Real & Imaging parts  For High Z  Easy Γ & Z transformation
  • 50. RFIC Design 5: Passive devices Slide 50 Smith Chart  Bilinear transformation : From Real & Imaginary to Magnitude & Phase .  Z & Y smith charts
  • 51. RFIC Design 5: Passive devices Slide 51 Smith Chart
  • 52. RFIC Design 5: Passive devices Slide 52 Smith Chart S-L S-C P-C P-L  Matching
  • 53. RFIC Design 5: Passive devices Slide 53 Two ports network  Impedance network
  • 54. RFIC Design 5: Passive devices Slide 54 S parameter network  S -> scattering  Generally, Z0 = 50W  Most popular for RF measurement system. 1 11 1 12 2 2 21 1 22 2 b s a s a b s a s a     1 1 11 1 1 1 2 2 21 1 1 r i r i b E s a E b E s a E      
  • 55. RFIC Design 5: Passive devices Slide 55 RF measurement and device modeling
  • 56. RFIC Design 5: Passive devices Slide 56 RF probes  RF probes
  • 57. RFIC Design 5: Passive devices Slide 57 Probe station  RF measurement equipments
  • 58. RFIC Design 5: Passive devices Slide 58 Agilent 8510  Agilent 8510 for s-parameter measurement
  • 59. RFIC Design 5: Passive devices Slide 59 RF device measurement  The calibration setup is very important for RF measurement.
  • 60. RFIC Design 5: Passive devices Slide 60 Deembed & Calibration  Calibration for testing and deembed pad effect.  Deemebedding and calibration procedure is very important for the RF measurement and modeling.  Four patterns for testing calibration procedures. – Open , short , thru1, thru2.
  • 61. RFIC Design 5: Passive devices Slide 61 Inductor model Cp Ls Rs Cox1 Cox2 Csub1 Rsub1 Rsub2 Csub2 Port1 Port2 ZA ZB ZC  Step 0 : prepare S or Y parameter  Step 1 : Ignore Cp first
  • 62. RFIC Design 5: Passive devices Slide 62 Inductance extraction  Step 2 : Calculate Y21 Ls Rs Cox1 Cox2 Csub1 Rsub1 Rsub2 Csub2 0 2 1 2 21   v v i Y ) 1 ( 21 Y real Rs   ) 2 1 ( 21 Y freq imag Ls      Ls Rs
  • 63. RFIC Design 5: Passive devices Slide 63 Extracted Rs & Ls 0 5 10 15 20 0 5 10 15 20 25 R S ( W ) Frequency ( GHz ) 0.1 1 10 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 Inductance ( nH ) Frequency ( GHz ) with Cp Cp-10f Skin effect Because of Cp  Step 2 : Extracted Rs & Ls
  • 64. RFIC Design 5: Passive devices Slide 64 Inductor model  Extraction of the Substrate Network Cox Csub Rsub 1 1 11 v i Y  1 ) ( 1 21 1 1 1 11 v i Y v i i Y b b a      21 11 2 1 _ 1 1 Y Y v i v i Y b In sub      Ls Rs C1 R1 V1 i1 i1a i1b i2 Cox1 21 11 2 1 _ 1 1 Y Y v i v i Y b In sub     
  • 65. RFIC Design 5: Passive devices Slide 65 Substrate network Cox Csub Rsub C1 R1 C1' R1' 2 2 2 2 2 2 1 2 ) 1 1 ( 2 1 1 Cox Rsub Csub Cox Rsub R      2 2 2 2 2 1 ) 1 1 ( 1 ) 1 1 ( 1 1 1 1 1 Rsub Csub Cox Csub Cox Csub Rsub Cox C          Substrate network transformation  When the frequency (w) approaches zero, C1 is equal to Cox1 approximately.  When the frequency (w) is high enough, C1 would be equal to the series combination of Cox1 and Csub1
  • 66. RFIC Design 5: Passive devices Slide 66 Extracted Cox  Step 3 : Extracted Cox freq Y Y imag Cox     2 ) 12 11 ( 1 when freq  0 0 5 10 15 20 10 15 20 25 30 35 40 45 50 55 C1(fH) Frequency ( GHz ) Cox Csub Rsub
  • 67. RFIC Design 5: Passive devices Slide 67 Extracted Csub & Rsub  Extracted Csub & Rsub 1 2 1 ) 1 ( 1 1 12 11 Cox freq j Y Y Ysub        ) ( 1 1 1 Sub Sub Y real R  when freq  High (4.31) ) 2 ( 1 1 1 Sub Sub Y freq imag C     when freq  High (4.32) 0 5 10 15 20 -40 -20 0 20 40 60 80 Csub'(fH) Frequency ( GHz ) 0 5 10 15 20 -2000 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 Frequency ( GHz ) Rsub1' (ohms)
  • 68. RFIC Design 5: Passive devices Slide 68 Comparison f req (100.0MHz to 20.00GHz) S(1,1) model..S(1,1) f req (100.0MHz to 20.00GHz) S(2,2) model..S(2,2) 2 4 6 8 10 12 14 16 18 0 20 -10 -8 -6 -4 -2 -12 0 f req, GHz dB(S(2,1)) dB(model..S(2,1)) 2 4 6 8 10 12 14 16 18 0 20 -10 -8 -6 -4 -2 -12 0 f req, GHz dB(S(1,2)) dB(model..S(1,2)) 2,1) 2)
  • 69. RFIC Design 5: Passive devices Slide 69 Dimension Definition of Square Inductor D D+W+S s W M5 M4
  • 70. RFIC Design 5: Passive devices Slide 70 Extracted Ls vs D,N,W 60 80 100 120 140 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Indutance (nH) 3.5 turns Metal W idth:15mm Metal W idth:10mm inner diameter (mm) Metal Width from 10mm to 15mm 1.5 2.0 2.5 3.0 3.5 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Inductance ( nH ) turn numbers D : 60mm D : 70mm D : 80mm D : 90mm D : 100mm D : 110mm D : 120mm D : 130mm L=(0.21074+0.00409*W)*0.608(N-1.5)+0.09+0.03*(W-10)/5  Inductor Library
  • 71. RFIC Design 5: Passive devices Slide 71 Q factor vs turns & D 0 2 4 6 8 10 0 2 4 6 8 10 12 14 Q factor Frequency ( GHz ) 60mm 70mm 80mm 90mm 100mm 110mm 120mm 130mm 140mm 1.5 turns Increasing D 0 2 4 6 8 10 0 2 4 6 8 10 12 Q factor Frequency ( GHz ) 3.5 turns 120mm 130mm 140mm 60mm 70mm 80mm 100mm 110mm Increasing D  Inductor Library
  • 72. RFIC Design 5: Passive devices Slide 72 References  B. Razavi, “RF Microelectronics,” Upper Saddle River: Prentice-Hall,1998.  T. H. Lee, “The Design of CMOS Radio-Frequency Integrated Circuits,” Cambridge: Cambridge University Press, 1998.