ECE 546 Lecture 06 Coupled Lines Spring 2018

ECE 546 Lecture - 06 Coupled Lines Spring 2018 Jose E. Schutt-Aine Electrical & Computer Engineering University of Illinois jesa@illinois. edu ECE 546 – Jose Schutt-Aine 1

Crosstalk Noise Signal Integrity Crosstalk Dispersion Attenuation Reflection Distortion Loss Delta I Noise Ground Bounce Radiation ECE 546 – Jose Schutt-Aine 2

TEM PROPAGATION ECE 546 – Jose Schutt-Aine 3

Telegrapher’s Equations L: Inductance per unit length. C: Capacitance per unit length. ECE 546 – Jose Schutt-Aine 4

Crosstalk noise depends on termination ECE 546 – Jose Schutt-Aine 5

Crosstalk depends on signal rise time tr = 1 ns tr = 7 ns ECE 546 – Jose Schutt-Aine 6

Crosstalk depends on signal rise time tr = 1 ns tr = 7 ns ECE 546 – Jose Schutt-Aine 7

Coupled Transmission Lines ECE 546 – Jose Schutt-Aine 8

Telegraphers Equations for Coupled Transmission Lines Maxwellian Form ECE 546 – Jose Schutt-Aine 9

Telegraphers Equations for Coupled Transmission Lines Physical form ECE 546 – Jose Schutt-Aine 10

Relations Between Physical and Maxwellian Parameters (symmetric lines) L 11 = L 22 = Ls L 12 = L 21 = Lm C 11 = C 22 = Cs+Cm C 12 = C 21 = - Cm ECE 546 – Jose Schutt-Aine 11

Even Mode Add voltage and current equations Ve : Even mode voltage Ie : Even mode current Impedance velocity ECE 546 – Jose Schutt-Aine 12

Odd Mode Subtract voltage and current equations Vd : Odd mode voltage Id : Odd mode current Impedance velocity ECE 546 – Jose Schutt-Aine 13

Mode Excitation ECE 546 – Jose Schutt-Aine 14

PHYSICAL SIGNIFICANCE OF EVEN- AND ODD-MODE IMPEDANCES * Ze and Zd 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 ECE 546 – Jose Schutt-Aine 15

Definitions Even-Mode Impedance: Ze Impedance seen by wave propagating through the coupledline system when excitation is symmetric (1, 1). Odd-Mode Impedance: Zd Impedance seen by wave propagating through the coupledline system when excitation is anti-symmetric (1, -1). Common-Mode Impedance: Zc = 0. 5 Ze Impedance seen by a pair of line and a common return by a common signal. Differential Impedance: Zdiff = 2 Zd Impedance seen across a pair of lines by differential mode signal. ECE 546 – Jose Schutt-Aine 16

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 ECE 546 – Jose Schutt-Aine 17

Coupled Lines Modal Space Line Space ECE 546 – Jose Schutt-Aine 18

EXAMPLE (Microstrip) er = 4. 3 Zs = 56. 4 W Single Line Dielectric height = 6 mils Width = 8 mils Coupled Lines Height = 6 mils Width = 8 mils Spacing = 12 mils er = 4. 3 Ze = 68. 1 W Zd = 40. 8 W Z 11 = 54. 4 W Z 12 = 13. 6 W ECE 546 – Jose Schutt-Aine 19

Even Mode ECE 546 – Jose Schutt-Aine 20

Odd Mode ECE 546 – Jose Schutt-Aine 21

EXTRACT INDUCTANCE AND CAPACITANCE COEFFICIENTS ECE 546 – Jose Schutt-Aine 22

Measured even-mode impedance ECE 546 – Jose Schutt-Aine 23

Measured odd-mode impedance ECE 546 – Jose Schutt-Aine 24

Measured even-mode velocity ECE 546 – Jose Schutt-Aine 25

Measured odd-mode velocity ECE 546 – Jose Schutt-Aine 26

Measured mutual inductance ECE 546 – Jose Schutt-Aine 27

Measured mutual capacitance ECE 546 – Jose Schutt-Aine 28

Even & Odd Mode Impedances ECE 546 – Jose Schutt-Aine 29

Modal Velocities in Stripline and Microstrip : Inhomogeneous structure, odd and even-mode velocities must have different values. ECE 546 – Jose Schutt-Aine Stripline : Homogeneous configuration, odd and even-mode velocities have approximately the same values. 30

Microstrip vs Stripline Microstrip (h =8 mils) w = 8 mils er = 4. 32 Ls = 377 n. H/m Cs = 82 p. F/m Lm = 131 n. H/m Cm = 23 p. F/m ve = 0. 155 m/ns vd = 0. 178 m/ns Stripline (h =16 mils) w = 8 mils er = 4. 32 Ls = 466 n. H/m Cs = 86 p. F/m Lm = 109 n. H/m Cm = 26 p. F/m ve = 0. 142 m/ns vd = 0. 142 m/ns ECE 546 – Jose Schutt-Aine 31

Microstrip vs Stripline Probe Sense line response at near end ECE 546 – Jose Schutt-Aine 32

General Solution for Voltages ECE 546 – Jose Schutt-Aine 33

General Solution for Currents ECE 546 – Jose Schutt-Aine 34

Coupling of Modes (asymmetric load) ECE 546 – Jose Schutt-Aine 35

Coupling of Modes (symmetric load) ECE 546 – Jose Schutt-Aine 36

Capacitive Terminations ECE 546 – Jose Schutt-Aine 37