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.

1. RFIC Design
Lecture 5:
Passive devices

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.