ECE 451 Coupled Lines - University Of Illinois Urbana .
ECE 451Coupled LinesJose E. Schutt-AineElectrical & Computer EngineeringUniversity of Illinoisjesa@illinois.eduECE 451 – Jose Schutt‐Aine1
Crosstalk NoiseSignal istortionLossDelta I NoiseGround BounceRadiationDrive LineSense LineDrive LineECE 451 – Jose Schutt‐Aine2
TEM PROPAGATIONLI VC zzZ1Zo Z2VsECE 451 – Jose Schutt‐Aine3
Telegrapher’s EquationsLI VC- z V I L z t I V C z tL: Inductance per unit length.C: Capacitance per unit length.ECE 451 – Jose Schutt‐Aine4
Crosstalk noise depends on termination50 50 line 1line 1line 250 line 2line 1line 1line 2line 2ECE 451 – Jose Schutt‐Aine5
Crosstalk depends on signal rise time50 line 1line 250 tr 1 nstr 7 nsline 1line 2ECE 451 – Jose Schutt‐Aineline 1line 26
Crosstalk depends on signal rise time50 line 1line 2tr 1 nstr 7 nsline 1line 1line 2line 2ECE 451 – Jose Schutt‐Aine7
Coupled Transmission Linesw rhV1I1CmI2sCsLmV2CsECE 451 – Jose Schutt‐Aine8
Telegraphers Equations for Coupled Transmission LinesMaxwellian Form V1 I1 I2 L11 L12 z t t V2 I1 I2 L21 L22 z t t I1 V1 V2 C11 C12 z t t I2 V V C21 1 C22 2 z t tECE 451 – Jose Schutt‐Aine9
Telegraphers Equations for Coupled Transmission LinesPhysical form V1 I1 I2 Ls Lm z t t V2 I I Lm 1 Ls 2 z t t I1 V1 V1 V2 Cs Cm Cm z t t t I2 V1 V2 V2 Cm Cm Cs z t t tECE 451 – Jose Schutt‐Aine10
Relations Between Physicaland Maxwellian Parameters(symmetric lines)L11 L22 LsL12 L21 LmC11 C22 Cs CmC12 C21 - CmECE 451 – Jose Schutt‐Aine11
Even Mode Ve I e L11 L12 z t I e I e C11 C12 z tAdd voltageand currentequations1Ve : Even mode voltage Ve (V1 V2 )21Ie : Even mode current Ie (I1 I2 )2Ze L11 L12 C11 C12Ls LmCsve 1 (L11 L12 )(C11 C12 )Impedance1(Ls Lm )CsECE 451 – Jose Schutt‐Ainevelocity12
Odd Mode Vd I d L11 L12 z t I d I d C11 C12 z tSubtract voltageand currentequationsVd : Odd mode voltageId : Odd mode currentZd vd L11 L12Ls Lm C11 C12Cs 2Cm1 ( L11 L12 )(C11 C12 )1Vd V1 V2 21Id I1 I 2 2Impedance1( Ls Lm )(Cs 2Cm )ECE 451 – Jose Schutt‐Ainevelocity13
Mode Excitation 1 1EVEN-1 1ODDECE 451 – Jose Schutt‐Aine14
PHYSICAL SIGNIFICANCE OF EVEN- ANDODD-MODE IMPEDANCES* Ze and Zd are the wave resistance seen by the evenand odd mode travelling signals respectively.* The impedance of each line is no longer describedby a single characteristic impedance; instead, we haveV1 Z11 I1 Z12 I 2V2 Z21 I1 Z22 I2ECE 451 – Jose Schutt‐Aine15
DefinitionsEven-Mode Impedance: ZeImpedance seen by wave propagating through the coupledline system when excitation is symmetric (1, 1).Odd-Mode Impedance: ZdImpedance seen by wave propagating through the coupledline system when excitation is anti-symmetric (1, -1).Common-Mode Impedance: Zc 0.5ZeImpedance seen by a pair of line and a common return by acommon signal.Differential Impedance: Zdiff 2ZdImpedance seen across a pair of lines by differential modesignal.ECE 451 – Jose Schutt‐Aine16
EVEN AND ODD-MODE IMPEDANCESZ11, Z22 : Self ImpedancesZ12, Z21 : Mutual ImpedancesFor symmetrical lines,Z11 Z22 and Z12 Z21ECE 451 – Jose Schutt‐Aine17
Coupled LinesModal SpaceLine SpaceV1 Z11 I1 Z12 I 2Ve Z e I eV2 Z 21 I1 Z 22 I 2Vd Z d I d V1 Z11 V Z 2 21Z12 I1 Z 22 I 2 Ve Z e V 0 d ECE 451 – Jose Schutt‐Aine0 Ie Z d I d 18
EXAMPLE(Microstrip) r 4.3Zs 56.4 Single LineDielectric height 6 milsWidth 8 milsCoupled LinesHeight 6 milsWidth 8 milsSpacing 12 mils r 4.3Ze 68.1 Zd 40.8 Z11 54.4 Z12 13.6 ECE 451 – Jose Schutt‐Aine19
Even ModeZgVfITI1Zg Vb VTstep- I2generatorcoaxial lineI tdrline 1line 2reference plane tied to ground ae (t ,0) ad (t ,0) ae (t ,0) ad (t ,0) ZZZZeded Vtdr ae (t ,0) ad (t ,0)Vtdr Z e I tdr21 eZe 2() Zg1 eECE 451 – Jose Schutt‐Ainea d (t ,0) 0ve 2l e20
Odd ModeZgVfZgstepgeneratorVbIT V-TI1line 1line 2I2reference plane floatingcoaxial lineVtdr a e (t,0) a d (t,0)- a e (t,0)-a d (t,0) V f VbI tdr ae (t ,0) ad (t ,0) ZZed ae (t,0) 0,1 1 dZd 2 1 dI tdr ae (t ,0) ad (t ,0) - ZZed Vtdr 2ZdItdr Zg , vd ECE 451 – Jose Schutt‐Aine2l d21
EXTRACT INDUCTANCE ANDCAPACITANCE COEFFICIENTS1 Ze Zd Ls 2 vevd 1Cs Z e ve1 Ze Zd Lm 2 ve vd 1 11 Cm 2 Z e ve Z d vd Z d Zs Z eECE 451 – Jose Schutt‐Aine22
Measured even-mode impedanceEven-Mode Impedanceh 3 mils120h 5 milsh 7 mils100h 10 milsh 14 milsZ ( )e80h 21 mils6040204681012141618Spacing (mils)ECE 451 – Jose Schutt‐Aine23
Measured odd-mode impedanceh 3 milsOdd-Mode Impedanceh 5 mils50h 7 mils45h 10 milsh 14 milsZ ( )d40h 21 mils353025204681012141618Spacing (mils)ECE 451 – Jose Schutt‐Aine24
Measured even-mode velocityEven-Mode velocity0.17h 3 milsh 5 mils0.168h 7 milsh 10 mils0.166h 14 milsv e(m/ns)0.164h 21 mils0.1620.160.1584681012141618Spacing (mils)ECE 451 – Jose Schutt‐Aine25
Measured odd-mode velocityh 3 milsh 5 milsOdd-Mode Velocityh 7 mils0.21h 10 mils0.205h 14 mils0.2h 21 milsv (m/ns)d0.1950.190.1850.180.1754681012141618Spacing (mils)ECE 451 – Jose Schutt‐Aine26
Measured mutual inductanceMutual Inductanceh 3 milsh 5 mils250h 7 milsh 10 mils200h 14 milsh 21 mils100Lm(nH/m)1505004681012141618Spacing (mils)ECE 451 – Jose Schutt‐Aine27
Measured mutual capacitanceh 3 milsMutual Capacitanceh 5 mils40h 7 mils35h 10 milsh 14 milsmC (pF/m)30h 21 mils252015104681012141618Spacing (mils)ECE 451 – Jose Schutt‐Aine28
Even & Odd Mode ImpedancesTypical Even & Odd Mode Impedances110ZevenZoddZeven, Zodd (Ohms)1009080706050401020304050Distance (mils)ECE 451 – Jose Schutt‐Aine29
Modal Velocities in Stripline and MicrostripMicrostrip : Inhomogeneousstructure, odd and even-mode velocitiesmust have different values.ECE 451 – Jose Schutt‐AineStripline : Homogeneous configuration,odd and even-mode velocities haveapproximately the same values.30
Microstrip vs Stripline50 50 Microstrip (h 8 mils)w 8 mils r 4.32Ls 377 nH/mCs 82 pF/mLm 131 nH/mCm 23 pF/mve 0.155 m/nsvd 0.178 m/nsStripline (h 16 mils)w 8 mils r 4.32Ls 466 nH/mCs 86 pF/mLm 109 nH/mCm 26 pF/mve 0.142 m/nsvd 0.142 m/nsECE 451 – Jose Schutt‐Aine31
Microstrip vs Stripline50 50 ProbeSense line response at near tsVolts0.10-0.1-0.2-0.3-0.4-0.2-0.3ECE 451 – Jose Schutt‐Aine32
General Solution for VoltagesZL1Zs1line 1line 2Zs2ZL2 j zve j zve j zvd j zvd j zvdV1 ( z ) Ae e Be e Ad e Bd e even j zveodd j zve j zvdV2 ( z ) Ae e Be e Ad e Bd e evenECE 451 – Jose Schutt‐Aineodd33
General Solution for CurrentsZL1Zs1line 1line 2Zs2ZL2j zj zj zj z 11vevevdvdI1 ( z ) Ae e Be e Bd e Ad e Z e Z d evenoddj zj zj zj z 11vevevdvdI 2 ( z ) Ae e Be e Bd e Ad e Z e Z d evenoddECE 451 – Jose Schutt‐Aine34
Coupling of Modes(asymmetric load)ZL1Zs1line 1line oddoddFirst reflectionSecond reflectionECE 451 – Jose Schutt‐Aine35
Coupling of Modes(symmetric load)ZLZsline 1line 2ZsZLevenevenevenoddoddoddFirst reflectionSecond reflectionECE 451 – Jose Schutt‐Aine36
Capacitive TerminationsSense Line at Near EndDrive Line at Near 0-0.15-0.200510152025303551015202530354040Time (ns)Time (ns)ECE 451 – Jose Schutt‐Aine37
Odd-Mode Impedance: Z d Impedance seen by wave propagating through the coupled-line 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 .
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