ECE 546 – Jose Schutt-Aine 1 ECE 546 Lecture - 07 Nonideal Conductors and Dielectrics Spring 2014...
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Transcript of ECE 546 – Jose Schutt-Aine 1 ECE 546 Lecture - 07 Nonideal Conductors and Dielectrics Spring 2014...
ECE 546 – Jose Schutt-Aine 1
ECE 546Lecture - 07
Nonideal Conductors and Dielectrics
Spring 2014
Jose E. Schutt-AineElectrical & Computer Engineering
University of [email protected]
ECE 546 – Jose Schutt-Aine 2
s: conductivity of material medium (W-1m-1)
HE
t
EH J
t
J E
Material Medium
E j H
H J j E
1H E j E E j j Ej
2 2 1E Ej
1
j
or
since then
ECE 546 – Jose Schutt-Aine 3
Wave in Material Medium2 2 21E E E
j
g is complex propagation constant
2 2 1j
1j jj
: a associated with attenuation of wave
: b associated with propagation of wave
ECE 546 – Jose Schutt-Aine 4
Wave in Material Medium
ˆ ˆz z j zo oE xE e xE e e
1/22
1 12
decaying exponentialSolution:
1/22
1 12
ˆ z j zoEH y e e
j
j
Magnetic field
Complex intrinsic impedance
ECE 546 – Jose Schutt-Aine 5
Skin Depth
1
The decay of electromagnetic wave propagating into a conductor is measured in terms of the skin depth
2
For good conductors:
ˆ ˆz z j zo oE xE e xE e e
Wave decay
Definition: skin depth d is distance over which amplitude of wave drops by 1/e.
ECE 546 – Jose Schutt-Aine 6
Skin Depth
I VC
z t
d
e-1
Wave motion
For perfect conductor, d = 0 and current only flows on the surface
ECE 546 – Jose Schutt-Aine 8
AC Resistance
2 /ac
l l l fR
w ww
l: conductor lengths: conductivityf: frequency
ECE 546 – Jose Schutt-Aine 9
Frequency-Dependent Resistance
1J
0
z JJ e dz J
Approximation is to assume that all the current is flowing uniformly within a skin depth
ECE 546 – Jose Schutt-Aine 10
2 2
2 2
I ICL
z t
1ac
fR
w
1dcR
wt
Resistance is ~ constant when d >t
Resistance changes withf
Frequency-Dependent Resistance
ECE 546 – Jose Schutt-Aine 12
r
H. A. Wheeler, "Formulas for the skin effect," Proc. IRE, vol. 30, pp. 412-424,1942
Skin Effect in Microstrip
ECE 546 – Jose Schutt-Aine 13
/ /y jyoJ J e e
/ /
0 1y jy o
o
J wI J we e dy
j
oo o o
JE J E
oo
J DV E D
Current density varies as
Note that the phase of the current density varies as a function of y
The voltage measured over a section of conductor of length D is:
Skin Effect in Microstrip
ECE 546 – Jose Schutt-Aine 14
11o
skino
jJ DV DZ j f
I J w w
1
skin skin
DR X f
w
The skin effect impedance is
where
Skin Effect in Microstrip
is the bulk resistivity of the conductor
skin skin skinZ R jX
with
Skin effect has reactive (inductive) component
ECE 546 – Jose Schutt-Aine 15
internalac skinR R
L
The internal inductance can be calculated directly from the ac resistance
Internal Inductance
Skin effect resistance goes up with frequency
Skin effect inductance goes down with frequency
ECE 546 – Jose Schutt-Aine 16
When the tooth height is comparable to the skin depth, roughness effects cannot be ignored
Surface Roughness
Copper surfaces are rough to facilitate adhesion to dielectric during PCB manufacturing
Surface roughness will increase ohmic losses
ECE 546 – Jose Schutt-Aine 17
Hammerstad Model
when
whenH s
H
dc
K R f tR f
R t
when2
when2
Hexternal
HH t
externalt
R fL t
fL f
R fL t
f
ECE 546 – Jose Schutt-Aine 18
Hammerstad Model
22
1 arctan 1.4 RMSH
hK
hRMS: root mean square value of surface roughness heightd: skin depthfd=t: frequency where the skin depth is equal to the thickness of the conductor
ECE 546 – Jose Schutt-Aine 19
Hemispherical Model
when
whenhemi s
hemi
dc
K R f tR f
R t
when2
when2
hemiexternal
hemihemi t
externalt
R fL t
fL f
R fL t
f
ECE 546 – Jose Schutt-Aine 20
Hemispherical Model
1 when 1
when 1s
hemis s
KK
K K
3 1 / 121
3 1 / 2 1
r jjkr
r j
2Re 3 / 4 1 1 / 4
/ 4o tile base
so tile
k A AK
A
23
2
1 4 / 1/ 121
3 1 2 / 1/ 1
j k r jjkr
j k r j
ECE 546 – Jose Schutt-Aine 21
Huray Model
when
whenHuray s
Huray
dc
K R f tR f
R t
when2
when2
Hurayexternal
Huray
Huray texternal
t
R fL t
fL f
R fL t
f
ECE 546 – Jose Schutt-Aine 22
Huray Model_flat N spheres
Hurayflat
P PK
P
3 1 / 121
3 1 / 2 1
r jjkr
r j
/ 4flat o tileP A
23
2
1 4 / 1/ 121
3 1 2 / 1/ 1
j k r jjkr
j k r j
2
_ 21
1 3Re 1 1
2
N
N spheres onn
P Hk
/ 'o o
Ho: magnitude of applied H field.
ECE 546 – Jose Schutt-Aine 23
Dielectrics and Polarization
Field causes the formation of dipoles polarization
No field
Applied field
Bound surface charge density –qsp on upper surface and +qsp on lower surface of the slab.
ECE 546 – Jose Schutt-Aine 24
1o a o a o e a o e a s aD E P E E E E
s
D
o
eaE: electric flux density : applied electric field: electric susceptibility: free-space permittivity: static permittivity
Dielectrics and Polarization
P
: polarization vector
ECE 546 – Jose Schutt-Aine 25
Material e r
AirStyrofoamParaffinTeflonPlywoodRT/duroid 5880PolyethyleneRT/duroid 5870Glass-reinforced teflon (microfiber)Teflon quartz (woven)Glass-reinforced teflon (woven)Cross-linked polystyrene (unreinforced)Polyphenelene oxide (PPO)Glass-reinf orced polystyreneAmberRubberPlexiglas
1.00061.032.12.12.12.202.262.352.32-2.402.472.4-2.622.562.552.62333.4
Dielectric Constant
ECE 546 – Jose Schutt-Aine 26
Material e r
LuciteFused silicaNylon (solid)QuartzBakeliteFormicaLead glassMicaBeryllium oxide (BeO)MarbleFlint glassFerrite (FqO,)Silicon (Si)Gallium arsenide (GaAs)Ammonia (liquid)GlycerinWater
3.63.783.83.84.85666.8-7.081012-161213225081
Dielectric Constants
ECE 546 – Jose Schutt-Aine 27
When a material is subjected to an applied electric field, the centroids of the positive and negative charges are displaced relative to each other forming a linear dipole.
When the applied fields begin to alternate in polarity, the permittivities are affected and become functions of the frequency of the alternating fields.
AC Variations
ECE 546 – Jose Schutt-Aine 28
Reverses in polarity cause incremental changes in the static conductivity ssheating of materials using microwaves (e.g. food cooking)
When an electric field is applied, it is assumed that the positive charge remains stationary and the negative charge moves relative to the positive along a platform that exhibits a friction (damping) coefficient d.
AC Variations
ECE 546 – Jose Schutt-Aine 29
22 2
'2
22 2
1
eo
or
o
N Q
m
dm
2"
222 2
er
oo
dN Q m
m dm
Complex Permittivity
eN
o
Q
o
m
d : damping coefficient
: mass
: free space permittivity
: dipole charge
: dipole density
: natural frequency: applied frequency
o
s
m
s : spring (tension) factor
ECE 546 – Jose Schutt-Aine 30
' "i c i sH J J j E J E j j E
Complex Permittivity
" ' 'i s i eH J E j E J E j E
equivalent conductivity "e s s a
alternating field conductivity "a
static field conductivitys
se: total conductivity composed of the static portion ss and the alternative part sa caused by the rotation of the dipoles
ECE 546 – Jose Schutt-Aine 31
't i ce de i eJ J J J J E j E Complex Permittivity
iJ
tJ
ceJ
deJ
: total electric current density: impressed (source) electric current density: effective electric conduction current density: effective displacement electric current density
' ' 1 ' 1 tan'
et i e i i eJ J E j E J j j E J j j E
tan effective electric loss tangent' ' ' '
e s a s ae
ECE 546 – Jose Schutt-Aine 32
Complex Permittivity"
'
"tan tan tan
' 's e
e s ae
tan static electric loss tangent'
ss
"
'tan alternating electric loss tangent
'a
a
' ' 1 ' 1 tan'
ecd ce de e eJ J J E j E j j E j j E
ECE 546 – Jose Schutt-Aine 33
Dielectric Properties
' 1 ''
ecdJ j j E j E
1'
e
' 1'
ecd eJ j j E E
1'
e
Good Dielectrics:
Good Conductors:
ECE 546 – Jose Schutt-Aine 34
Dielectric Properties
' 1 ''
ecdJ j j E j E
1'
e
' 1'
ecd eJ j j E E
1'
e
Good Dielectrics:
Good Conductors:
ECE 546 – Jose Schutt-Aine 35
Kramers-Kronig Relations
"'
2 20
' '21 '
'
rr d
There is a relation between the real and imaginary parts of the complex permittivity:
Debye Equation
'"
2 20
1 '2'
'
rr d
' '' " '( ) ( ) ( )
1rs r
r r r re
jj
ECE 546 – Jose Schutt-Aine 36
Kramers-Kronig Relations
'
'
2
2rs
er
te is a relaxation time constant:
' '' '
21
rs rr r
e
' '
"2
1
rs r e
r
e
ECE 546 – Jose Schutt-Aine 37
Material er’ tandAirAlcohol (ethyl)Aluminum oxideBakeliteCarbon dioxideGermaniumGlassIceMicaNylonPaperPlexiglasPolystyrenePorcelain
1.0006258.84.741.001164*74.25.43.533.452.566
0.16 x 10-4
22x10-3
1 x 10-3
0.16x10-4
2x10-2
8 x 10-3
4 x 10-2
5x10-5
14x10-3
Dielectric Materials
ECE 546 – Jose Schutt-Aine 38
Material er’ tandPyrex glassQuartz (fused)RubberSilica (fused)SiliconSnowSodium chlorideSoil (dry)StyrofoamTeflonTitanium dioxideWater (distilled)Water (sea)Water (dehydrated)Wood (dry)
43.82.5-33.811.83.35.92.81.032.1100808111.5-4
6x10-4
7.5x10-4
2 x 10-3
7.5 x 10-4
0.51x10-4
7 x 10-2
1x10-4
3x10-4
15 x 10-4
4x10-2
4.6401x10-2
Dielectric Materials
ECE 546 – Jose Schutt-Aine 39
Source: H. Barnes et al, "ATE Interconnect Performance to 43 Gps Using Advanced PCB Materials", DesignCon 2008
PCB Stackup
ECE 546 – Jose Schutt-Aine 40
The skew (time delay) between the two traces of the differential pair should be zero. Any skew between the two traces causes the differential signal to convert into a common signal.
Differential signaling is widely used in the industry today. High-speed serial interfaces such as PCI-E, XAUI, OC768, and CEI use differential signaling for transmitting and receiving data in point-to-point topology between a driver (TX) and receiver (RX) connected by a differential pair.
Differential Signaling
ECE 546 – Jose Schutt-Aine 41
Fiber Weave Effect
Source: S. McMorrow, C. Heard, "The Impact of PCB Laminate Weave on the Electrical Performance of Differential Signaling at Multi-Gigabit Data Rates", DesignCon 2005.
Fiberglass weave pattern causes signals to propagate at different speeds in differential pairs
ECE 546 – Jose Schutt-Aine 42
Source: Lambert Simonovich, "Practical Fiber Weave Effect Modeling",White Paper-Issue 3, March 2, 2012.
Fiber Weave Effect
ECE 546 – Jose Schutt-Aine 43
Source: S. Hall and H. Heck , Advanced Signal Integrity for High-Speed Digital Designs, J. Wiley, IEEE , 2009.
Fiber Weave Effect
ECE 546 – Jose Schutt-Aine 44
Source: S. McMorrow, C. Heard, "The Impact of PCB Laminate Weave on the Electrical Performance of Differential Signaling at Multi-Gigabit Data Rates", DesignCon 2005.
Fiber Weave EffectGroup delay variation
ECE 546 – Jose Schutt-Aine 45
Source: S. McMorrow, C. Heard, "The Impact of PCB Laminate Weave on the Electrical Performance of Differential Signaling at Multi-Gigabit Data Rates", DesignCon 2005.
Fiber Weave EffectGroup delay variation: effect of angle
ECE 546 – Jose Schutt-Aine 46
Source: S. Hall and H. Heck , Advanced Signal Integrity for High-Speed Digital Designs, J. Wiley, IEEE , 2009.
Fiber Weave EffectStraight traces
ECE 546 – Jose Schutt-Aine 47
Source: S. Hall and H. Heck , Advanced Signal Integrity for High-Speed Digital Designs, J. Wiley, IEEE , 2009.
Fiber Weave Effect
45o traces
ECE 546 – Jose Schutt-Aine 48
Source: PCB Dielectric Material Selection and Fiber Weave Effect on High-Speed Channel Routing, Altera Application Note AN-528-1.1, January 2011.
Fiber Weave Effect
straight traces
zig-zag traces
ECE 546 – Jose Schutt-Aine 49
Source: PCB Dielectric Material Selection and Fiber Weave Effect on High-Speed Channel Routing, Altera Application Note AN-528-1.1, January 2011.
Fiber Weave Effect
Skew on straight traces
ECE 546 – Jose Schutt-Aine 50
Source: PCB Dielectric Material Selection and Fiber Weave Effect on High-Speed Channel Routing, Altera Application Note AN-528-1.1, January 2011.
Fiber Weave Effect
Skew on zig-zag traces
ECE 546 – Jose Schutt-Aine 51
• Mitigation TechniquesUse wider widths to achieve impedance targets. Specify a denser weave (2116, 2113, 7268, 1652)
compared to a sparse weave (106, 1080). Move to a better substrate such as Nelco 4000-13 Perform floor planning such that routing is at an angle
rather than orthogonal. Make use of zig-zag routing
Fiber Weave Effect