ECE 451 Transmission Lines & Packaging

Transcription

1 Transmission Lines & Packaging Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois 1

2 Radio Spectrum Bands The use of letters to designate bands has long ago been declared obsolete. Nevertheless, people seem to continue to use them and add more letters as users move up the microwave spectrum. The original definitions had very specific non-overlapping definitions (not counting subband definitions). Modern usage seems to associate the bands with waveguide ranges. P MHz L GHz S GHz C GHz X GHz Ku GHz K GHz Ka GHz Q GHz V GHz E GHz W GHz F GHz D GHz G GHz Y GHz J GHz 2

3 Coaxial Connectors Source: Allied Electronics, Inc. 3

4 Coaxial Connectors B A C C A B Type A B C SMA

5 Coaxial Transmission Line μ ε a b TEM Mode of Propagation L = μ ln b a C = 2πε ln(b/a) 5

6 Coaxial Air Lines μ ε a b Infinite Conductivity Zo = μ/ ε ln / 2π ( b a) Finite Conductivity ( 1/ a+ 1/ b) μ/ ε Zo = ln ( b/ a) j 2π 4 π fμσ ln( b/ a) ( ) 6

7 Coaxial Connector Standards μ ε a b Connector Frequency Range 14 mm DC GHz GPC-7 DC - 18 GHz Type N DC - 18 GHz 3.5 mm DC - 33 GHz 2.92 mm DC - 40 GHz 2.4 mm DC - 50 GHz 1.85 mm DC - 65 GHz 1.0 mm DC GHz 7

8 Microstrip ε Z o w/h < h h = ln ( εr + 1) w w Z o w/h > π w ln(4) ln( eπ /16) εr 1 = ε 2h π 2π ε r r εr + 1 πe w + ln ln πε + + r 2 2h 8

9 Dual-in-Line (DIP) Package -Mounted on PWB in pin-through-hole (PTH) configuration - Chip occupies less than 20% of total space - Lead frame with large inductance 9

10 Stacked Wire Bonds 10

11 Package Types DIP QFP CSP Flip Chip Top View (showing chip topackage connection) Plane View (showing package to board connection) Chip Size (mm mm) Chip Perimeter (mm) Number of I/Os Chip Pad Pitch (μm) Package Size (in in) Lead Pitch (mils) Chip Area (mm 2 ) Feature Size (μm) Gates/Chip 30K 300K 2M 10M Max Frequency (MHz) Power Dissipation (W) Chip Pow Dens (W/cm 2 ) Pack Pow Dens (W/cm 2 ) Supply Voltage (V) Supply Current (A)

12 Ball Bonding for Flip Chip 12

13 Flip Chip Pin Grid Array (FC-PGA) Bumped Die Package Body Pins 13

14 Crosstalk Noise Signal Integrity Crosstalk Dispersion Attenuation Reflection Distortion Loss Delta I Noise Ground Bounce Radiation Drive Line Sense Line Drive Line 14

15 TEM PROPAGATION I L + V C - Δz z Z 1 Z o β Z 2 V s 15

16 I Telegrapher s Equations L + V C - Δz V = L z I = C z I t V t L: Inductance per unit length. C: Capacitance per unit length. 16

17 Crosstalk noise depends on termination 50 Ω line 1 line 2 50 Ω 50 Ω line 1 line 2 line 1 line 2 line 1 line 2 17

18 Crosstalk depends on signal rise time 50 Ω line 1 line 2 50 Ω t r = 1 ns t r = 7 ns line 1 line 2 line 1 line 2 18

19 Crosstalk depends on signal rise time 50 Ω line 1 line 2 t r = 1 ns t r = 7 ns line 1 line 2 line 1 line 2 19

20 Coupled Transmission Lines w s h ε r V 1 V 2 I 1 C m I 2 C s C s L m 20

21 Telegraphers Equations for Coupled Transmission Lines Maxwellian Form V = L I + L I z t t V = L I + L I z t t I = C V + C V z t t I = C V + C V z t t

22 Telegraphers Equations for Coupled Transmission Lines Physical form V = L I + L I z t t s m V = L I + L I z t t m s I V V V = C + C C z t t t s m m I V V V = C + C + C z t t t m m s 22

23 Relations Between Physical and Maxwellian Parameters (symmetric lines) L 11 = L 22 = L s L 12 = L 21 = L m C 11 = C 22 = C s +C m C 12 = C 21 = - C m 23

24 V z ( L L ) e = I z ( C C ) e = Even Mode I t e I t V e : Even mode voltage e Add voltage and current equations V e = 1 ( 2 V 1 + V 2) I e : Even mode current I e = 1 ( 2 I 1 + I 2) Z e = v e = L 11 + L 12 C 11 + C 12 = L s + L m C s 1 (L 11 + L 12 )(C 11 + C 12 ) = 1 (L s + L m )C s Impedance velocity 24

25 Odd Mode V z Id = z C C ( L L ) d = ( ) I t I t V d : Odd mode voltage I d : Odd mode current d d Subtract voltage and current equations V = 1 V V 2 I ( ) d 1 2 = 1 2 I I ( ) d 1 2 L L L L s m Z d = = C11 C12 Cs + 2Cm 1 1 v d = = ( L L )( C C ) ( L L )( C 2 C ) s m s + m Impedance velocity 25

26 Mode Excitation EVEN +1-1 ODD 26

27 PHYSICAL SIGNIFICANCE OF EVEN- AND ODD-MODE IMPEDANCES *Z e and Z d are the wave resistance seen by the even and odd mode travelling signals respectively. * The impedance of each line is no longer described by a single characteristic impedance; instead, we have V 1 = Z 11 I 1 + Z 12 I 2 V 2 = Z 21 I 1 + Z 22 I 2 27

28 Definitions Even-Mode Impedance:Z e Impedance seen by wave propagating through the coupledline system when excitation is symmetric (1, 1). Odd-Mode Impedance:Z d Impedance seen by wave propagating through the coupledline system when excitation is anti-symmetric (1, -1). Common-Mode Impedance:Z c = 0.5Z e Impedance seen by a pair of line and a common return by a common signal. Differential Impedance:Z diff = 2Z d Impedance seen across a pair of lines by differential mode signal. 28

29 EVEN AND ODD-MODE IMPEDANCES Z 11, Z 22 : Self Impedances Z 12, Z 21 : Mutual Impedances For symmetrical lines, Z 11 = Z 22 and Z 12 = Z 21 29

30 EXAMPLE (Microstrip) ε r = 4.3 Z s = 56.4 Ω ε r = 4.3 Z e = 68.1 Ω Z 11 = 54.4 Ω Single Line Dielectric height = 6 mils Width = 8 mils Coupled Lines Height = 6 mils Width = 8 mils Spacing = 12 mils Z d = 40.8 Ω Z 12 = 13.6 Ω 30

31 Even Mode I Z g V 1 f IT line 1 Z g + line 2 step V b V T generator - I 2 reference plane tied to ground coaxial line I tdr ae(,0) t ad(,0) t ae(,0) t ad(,0) t = + Ze Z + d Ze Z d V = a (,0) t a (,0) t tdr e d a(,0) d t = 0 V I tdr tdr Z = 2 e Z = 2( e 1+ ρe ) Z 1 ρ e g v = e 2l τ e 31

32 Z g step generator Odd Mode I V 1 f I T line 1 Z g + V line 2 V T b - I2 reference plane floating coaxial line tdr e d [ e d ] V = a (t,0)+a (t,0)- a (t,0)-a (t,0) = Vf + Vb ae( t,0) ad( t,0) I tdr = + Ze Z d ae(,0) t ad(,0) t I tdr =- Ze Z d Z a e (t,0) =0, V tdr I tdr =2Z d d 1 1+ ρ d 2l = Zg, v d = 2 1 ρd τ d 32

33 EXTRACT INDUCTANCE AND CAPACITANCE COEFFICIENTS 1 Ze L s = + 2 ve C s = 1 Z v e e Z v d d 1 Ze L m = - 2 ve Z v d d C m = - Z v Z v 2 e e d d Z d < Z s < Ze 33

34 Measured even-mode impedance Z e ( Ω ) Even-Mode Impedance h=3 mils h=5 mils h=7 mils h=10 mils h=14 mils h=21 mils Spacing (mils) 34

35 Measured odd-mode impedance Odd-Mode Impedance h=3 mils h=5 mils h=7 mils h=10 mils h=14 mils h=21 mils Z d ( Ω ) Spacing (mils) 35

36 Measured even-mode velocity v e (m/ns) Even-Mode velocity h=3 mils h=5 mils h=7 mils h=10 mils h=14 mils h=21 mils Spacing (mils) 36

37 Measured odd-mode velocity Odd-Mode Velocity h=3 mils h=5 mils h=7 mils h=10 mils h=14 mils h=21 mils v d (m/ns) Spacing (mils) 37

38 Measured mutual inductance Mutual Inductance h=3 mils h=5 mils h=7 mils h=10 mils h=14 mils h=21 mils L m (nh/m) Spacing (mils) 38

39 Measured mutual capacitance Mutual Capacitance h=3 mils h=5 mils h=7 mils h=10 mils h=14 mils h=21 mils C m (pf/m) Spacing (mils) 39

40 Even & Odd Mode Impedances 110 Typical Even & Odd Mode Impedances 100 Zeven Zodd Zeven, Zodd (Ohms) Distance (mils) 40

41 Modal Velocities in Stripline and Microstrip Microstrip : Inhomogeneous structure, odd and even-mode velocities must have different values. Stripline : Homogeneous configuration, odd and even-mode velocities have approximately the same values. 41

42 Microstrip vs Stripline 50 Ω 50 Ω Microstrip (h =8 mils) w = 8 mils ε r = 4.32 L s = 377 nh/m C s = 82 pf/m L m = 131 nh/m C m = 23 pf/m v e = m/ns v d = m/ns Stripline (h =16 mils) w = 8 mils ε r = 4.32 L s = 466 nh/m C s = 86 pf/m L m = 109 nh/m C m = 26 pf/m v e = m/ns v d = m/ns 42

43 Microstrip vs Stripline 50 Ω 50 Ω Probe Sense line response at near end C C 0.4 microstrip 0.3 stripline Volts Volts

44 General Solution for Voltages Z s1 Z s2 line 1 line 2 Z L1 Z L2 jω z jωz jωz jωz + + ve ve vd vd V1( z) = Ae e + Be e + Ade + Bde even odd jω z jωz jωz jωz + + ve ve vd vd V2( z) = Ae e + Be e Ade Bde even odd 44

45 Z s1 Z s2 General Solution for Currents line 1 line 2 Z L1 Z L2 jωz jωz jωz jωz 1 + v 1 + e ve vd vd I1( z) = Ae e Be e + Ade Bde Ze Zd even odd jωz jωz jωz jωz 1 + v 1 + e ve vd vd I2( z) = Ae e Be e Ade Bde Ze Zd even odd 45

46 Coupling of Modes (asymmetric load) Z s1 Z L1 line 1 line 2 Z s2 ZL2 even even even odd odd even odd odd even even odd odd even odd First reflection Second reflection 46

47 Coupling of Modes (symmetric load) Z s Z s line 1 line 2 Z L ZL even even even odd odd odd First reflection Second reflection 47

48 1 Drive Line at Near End 0.2 Sense Line at Near End Volts Volts Time (ns) Time (ns) 48

49 Three Line Microstrip V1 I1 I2 I = L11 + L12 + L13 z t t t 3 I1 V1 V2 V = C11 + C12 + C13 z t t t 3 V2 I1 I2 I = L21 + L22 + L23 z t t t 3 I2 V1 V2 V = C21 + C22 + C23 z t t t 3 V I I I = L + L + L z t t t I V V V = C + C + C z t t t

50 Three Line Alpha Mode Subtract (1c) from (1a) and (2c) from (2a), we get Vα I = ( L11 L13) z t Iα V = ( C11 C13) z t This defines the Alpha mode with: α α and Vα = V1 V Iα = I1 I3 3 The wave impedance of that mode is: Z α = L C L C and the velocity is u α = 1 ( L L )( C C )

51 Three Line Modal Decomposition In order to determine the next mode, assume that V = V + βv + V β I = I + β I + I β Vβ I I I = z t t t ( L βl L ) ( L βl L ) ( L βl L ) I β V V V = z t t t ( C βc C ) ( C βc C ) ( C βc C ) By reciprocity L 32 = L 23, L 21 = L 12, L 13 = L 31 By symmetry, L 12 = L 23 Also by approximation, L 22 L 11, L 11 +L 13 L 11 51

52 Three Line Modal Decomposition Vβ I I3 I = ( L + βl + L ) + + ( 2L + βl ) z t t t In order to balance the right-hand side into I β, we need to have ( + β ) = β ( + β + ) β ( + β ) 2L L I L L L I L L I L = β L or β =± 2 Therefore the other two modes are defined as The Beta mode with 52

53 The Beta mode with Three Line Beta Mode Vβ = V + 2V + V I = I + β 2I + I The characteristic impedance of the Beta mode is: Z β = L + 2L + L C + 2C + C and propagation velocity of the Beta mode is 1 u = β ( L11 2L12 L13 )( C11 2C12 C13 ) 53

54 Three Line Delta Mode The Delta mode is defined such that V = V δ 2V + V I = I δ 2I + I The characteristic impedance of the Delta mode is Z δ = L 2L + L C 2C + C The propagation velocity of the Delta mode is: 1 u = δ + + ( L11 2L12 L13 )( C11 2C12 C13 ) 54

55 Symmetric 3 Line Microstrip In summary: we have 3 modes for the 3-line system E = Alpha mode Beta mode* Delta mode* *neglecting coupling between nonadjacent lines 55

56 Coplanar Waveguide ε r = LnH ( / m) = C( pf/ m) = E = H =

57 Coplanar Waveguide ε r = 4.3 Z m ( Ω ) = Z c ( Ω ) = vp ( m/ ns) =

58 Coplanar Waveguide S' W S W S' h ε r Kk ( ) : Complete Elliptic Integral of the first kind S k = 30 π K'( k) S + 2W Zocp = (ohm) ε ( ) r + 1 Kk K'( k) = K( k') 2 k' = (1 k ) 2 1/2 v cp 2 = εr + 1 1/2 c 58

59 Coplanar Strips W S W h ε r Z ocs = 120 π K'( k) (ohm) ε 1 Kk ( ) r

60 Qualitative Comparison Characteristic Microstrip Coplanar Wguide Coplanar strips ε eff * ~6.5 ~5 ~5 Power handling High Medium Medium Radiation loss Low Medium Medium Unloaded Q High Medium Low or High Dispersion Small Medium Medium Mounting (shunt) Hard Easy Easy Mounting (series) Easy Easy Easy * Assuming ε r =10 and h=0.025 inch 60

61 3-Line Matching Network Extend matching network synthesis to multiconductor transmission line (MTL) systems, specifically coupled microstrip Characterize MTL systems by their normal mode parameters Mode configurations Propagation constants Characteristic impedance matrices 61

62 Longitudinal Immittance Matrix Functions (LIMFs) Given terminations, the immittance matrices are expressed as input longitudinal functions looking toward the load S Y m,c m,c in,out, Γ,, Z m,c in,out m,c in,out 62

63 Calibration Methods 1st order calibration: 6 distinct TRL calibrations were required to deembed the fan-in and fan-out sections 2nd order calibration: 1 multimode TRL calibration required to deembed all fan-ins and fan-outs Multiconductor transmission line matching network device under test 63

64 Bias Networks and Multiline/Multimode TRL Self-biasing for DC power done using air bridges Regulator circuit may be built on board with surface mount/chip components Calibration must include all modes and allow for the 6- port discontinuity S- parameter measurement Proposed calibration fixture for transistor amplifier device discontinuity with self-biasing network 64

65 3-line Transistor Amplifier The general amplifier structure with generic matching networks Note that a transistor seating hole may be present for convenience, but is not necessary Photograph of a three-line transistor amplifier autobiased w/o matching networks 65

66 Transistor Amplifier Matching Matching pf chip cap pf chip cap. Gains GHz m=5.14 / um= GHz m=6.54 / um= 0.32 S-parameter comparison between unmatched and matched three-line amplifier. Dotted line - unmatched; dashed line - matched. Design frequency: 3.1 GHz. 66

67 V Transmission Line w signal strip h dielectric α ground 2p 67

68 V Line Characteristic Impedance 250 CHARACTERISTIC IMPEDANCE Zo (ohms) º 37.5º 45º 52.5º 60º Microstrip w/h Calculated values of the characteristic impedance for a single-line v-strip structure as a function of width-to-height ratio w/h. The relative dielectric constant is εr =

69 V Line Effective Permittivity º 37.5º EFFECTIVE PERMITTIVITY º 52.5º Effective Relative Dielectric Constant º Microstrip w/h Calculated values of the effective relative dielectric constant for a single-line v-strip structure as a function of width-to-height ratio w/h. The relative dielectric constant is εr =

70 Three Line V Transmission Line y signal strip w s 2p h ground surface dielectric x Region 1 Region 2 Region 3 Region 4 Region 5 Region 6 70

71 V Line and Microstrip Microstrip C (pf/m) = L (nh/m) = V-line C (pf/m) = L (nh/m) = y w s signal strip 2p h ground surface dielectric x Region 1 Region 2 Region 3 Region 4 Region 5 Region 6 Comparison of the inductance and capacitance matrices between a three-line v-line and microstrip structures. The parameters are p/h = 0.8 mils, w/h = 0.6 and ε r =

72 V Line: Coupling Coefficients 350 Mutual Inductance 40 Mutual Capacitance L m (nh/m) V-line microstrip C m (pf/m) V-line microstrip s/h s/h Plot of mutual inductance (top) and mutual capacitance (bottom) versus spacing-to-height ratio for v-line and microstrip configurations. The parameters are w/h = 0.24, εr =

73 V Line vs Microstrip: Coupling Coefficients Coupling Coefficient V-line microstrip K v s/h Plot of the coupling coefficient versus spacing-to-height ratio for v-line and microstrip configurations. The parameters are w/h = 0.24, εr =

74 Advantages of V Line ground reference signal strip w signal strip dielectric substrate h dielectric α ground ground reference 2p Propagation Function Advantages of V Line * Higher bandwidth microstrip V-60 V-30 * Lower crosstalk * Better transition Linear Attenuation Frequency (GHz) 74

75 V Line vs Microstrip: Insertion Loss 0 Insertion Loss 20*log10* S Vline Microstrip Frequency (GHz) 75