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Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
1
Transmission Line Theory(Part 1)
Dr. José Ernesto Rayas Sánchez
2Dr. J.E. Rayas Sánchez
Outline
Common transmission media
Modeling uniform interconnects
Interconnect parasitics and their physical significance
From lumped circuits to distributed circuits
Fundamental transmission line equations
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
3Dr. J.E. Rayas Sánchez
Common Transmission Media
Uniform Interconnects
Microstrip
h
w
Coplanar
w1
w2
ε r
Waveguide
Twisted-pairCoaxial
b
a
h
w
(Hewlett-Packard's RF Design and Measurement Seminar, 2000)
4Dr. J.E. Rayas Sánchez
Common Transmission Media (cont)
Practical interconnects can be decomposed in segments of uniform interconnects (if necessary)
Components(Chip + Pkg)
PCB(Motherboard)
PCB(add-in card)
Connector
(H. Heck, 2005)
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
5Dr. J.E. Rayas Sánchez
Modeling Uniform Interconnects
(A. Weisshaar, Tutorial on High-Speed Interconnects, IMS June 2004, Fort Worth, TX)
6Dr. J.E. Rayas Sánchez
Modeling Uniform Interconnects (cont)
Parasitic effects associated to each transmission media
– Capacitance between conductors, C
– Resistance of conductors (conductor losses), R
– Inductance of conductor loops, L
– Dielectric conductivity (dielectric losses), G
R, C, L, and G must be determined per unit length
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
7Dr. J.E. Rayas Sánchez
Interconnect Shunt Capacitance
(A. Weisshaar, Tutorial on High-Speed Interconnects, IMS June 2004, Fort Worth, TX)
8Dr. J.E. Rayas Sánchez
Fringing Capacitance Effect
(A. Weisshaar, Tutorial on High-Speed Interconnects, IMS June 2004, Fort Worth, TX)
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
9Dr. J.E. Rayas Sánchez
Interconnect Series Inductance
(A. Weisshaar, Tutorial on High-Speed Interconnects, IMS June 2004, Fort Worth, TX)
10Dr. J.E. Rayas Sánchez
Interconnect Series DC Resistance
(A. Weisshaar, Tutorial on High-Speed Interconnects, IMS June 2004, Fort Worth, TX)
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
11Dr. J.E. Rayas Sánchez
Skin Effect
(A. Weisshaar, Tutorial on High-Speed Interconnects, IMS June 2004, Fort Worth, TX)
12Dr. J.E. Rayas Sánchez
EM-Simulation of Conductor Current Distribution
(A. Weisshaar, Tutorial on High-Speed Interconnects, IMS June 2004, Fort Worth, TX)
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
13Dr. J.E. Rayas Sánchez
Proximity Effect
(A. Weisshaar, Tutorial on High-Speed Interconnects, IMS June 2004, Fort Worth, TX)
14Dr. J.E. Rayas Sánchez
Edge and Indy Effects – Example
FR4
HW
L
W = 5 mm L = 25 mmH = 5 mm εr = 4.5dielectric loss tan = 0.025
0.6 GHz
1 GHz
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
15Dr. J.E. Rayas Sánchez
Interconnect Shunt Conductance
(A. Weisshaar, Tutorial on High-Speed Interconnects, IMS June 2004, Fort Worth, TX)
16Dr. J.E. Rayas Sánchez
Loss Tangent of Typical Materials
(A. Weisshaar, Tutorial on High-Speed Interconnects, IMS June 2004, Fort Worth, TX)
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
17Dr. J.E. Rayas Sánchez
Equivalent Circuit Models for Interconnects
On-chip Interconnects– lumped C if very short– lumped RC if very short and R significant– cascaded lumped RC if short– distributed RC if long– RLC distributed line (high performance VLSI circuits
and microwave ICs)
Off-chip Interconnects (→ usually distributed models)– LC line if losses can be ignored– RLC line on low dielectric loss PCBs– RLGC line (if dielectric loss is significant)
18Dr. J.E. Rayas Sánchez
Lumped Equivalent Circuit Models
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
19Dr. J.E. Rayas Sánchez
From Lumped Circuits to Distributed Circuits
(A. Weisshaar, Tutorial on High-Speed Interconnects, IMS June 2004, Fort Worth, TX)
20Dr. J.E. Rayas Sánchez
Transmission Line Model
The interconnect is modeled using an infinite number of RLCG sections
(R. Ludwig and P. Bretchko, RF Circuit Design, Prentice Hall, 2000)
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
21Dr. J.E. Rayas Sánchez
Transmission Line Model
The interconnect is modeled using an infinite number of RLCG sections
(R. Ludwig and P. Bretchko, RF Circuit Design, Prentice Hall, 2000)
22Dr. J.E. Rayas Sánchez
Transmission Line Model
Generic equivalent circuit for each section (R, L, C and G are per unit length)The interconnect is modeled using an infinite number of these sections, making
(R. Ludwig and P. Bretchko, RF Circuit Design, Prentice Hall, 2000)
0→z∆
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
23Dr. J.E. Rayas Sánchez
Transmission Line Equations
Time-Domain (Telegrapher Equations)
Telegrapher Equations in Frequency-Domain
ttziLtzRi
ztzv
∂∂−−=
∂∂ ),(),(),(
ttzvCtzGv
ztzi
∂∂−−=
∂∂ ),(),(),(
)()()( zILjRdz
zdV ω+−=
)()()( zVCjGdz
zdI ω+−=
24Dr. J.E. Rayas Sánchez
Transmission Line Equations (cont)
Wave Equation (frequency domain)
whereis the complex propagation constant
βαωωγ jCjGLjR +≡++= ))((
Solutions to the wave equation arez
oz
o eVeVzV γγ +−−+ +=)( zo
zo eIeIzI γγ +−−+ +=)(
0)()( 22
2
=− zVdz
zVd γ 0)()( 22
2
=− zIdz
zId γ
incident wavesreflected waves
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
25Dr. J.E. Rayas Sánchez
Transmission Line Equations (cont)
Characteristic Impedance of the TL
then
CjGLjRZo ω
ω++=
−
−
+
+
−=≡
o
o
o
oo I
VIVZ
Reflection Coefficient along the line, Γz
zo
zo eVeVzV γγ +−−+ +=)(
z
o
oz
o
zo
z eVV
eVeVz γ
γ
γ
Γ 2)( ++
−
−+
+−
==
26Dr. J.E. Rayas Sánchez
Transmission Line Equations (cont)
Solutions in the frequency domain
Solutions in the time domain
zo
zo eVeVzV γγ +−−+ +=)(
zo
zo eIeIzI γγ +−−+ +=)(
zo
zo eztVeztVtzv αα φβωφβω +−−−++ ++++−= )cos(||)cos(||),(
Phase velocity, wave velocity or propagation speed
βπλ 2==
fvp
βαωωγ jCjGLjR +≡++= ))((
Wavelength
βω==
dtdzvp
(speed at which a constant phase point travels down the line)
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
27Dr. J.E. Rayas Sánchez
Transmission Line Symbol
(Lossy) Transmission Line
Length along the line
Zo , γ
z
0l
Zo , γ
l
28Dr. J.E. Rayas Sánchez
Reflection Coefficient
Reflection coefficient along the line
Reflection coefficient at the load
l
o
ol
o
lo
l eVV
eVeVl γ
γ
γ
Γ 2)( −+
−
++
−−
==
oL
oL
o
ol ZZ
ZZVVl
+−==== +
−
)0(ΓΓ
Zo , γ
0l
ZL
Signal Integrity and High-Speed InterconnectsJanuary-May 2006
Dr. J. E. Rayas Sánchezhttp://iteso.mx/~erayas [email protected]
29Dr. J.E. Rayas Sánchez
Input Impedance
Input Impedance along the line
)tanh()tanh(
)()()(
lZZlZZZ
lIlVlZ
Lo
oLoin γ
γ++==
Zo , γ
0l
ZL