Interconnect I – class 21
Prerequisite reading - Chapter 4
2
Outline
 Transmission line losses
DC losses in the conductor
Frequency dependent conductor losses
Frequency dependent dielectric losses
Effect of surface roughness
Differential line losses
 Incorporating frequency domain
parameters into time domain waveforms
 Measuring Losses
 Variations in the dielectric constant
Interconnect: Adv
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Focus
 This chapter focuses on subtle high speed transmission
characteristics that have been ignored in most designs
in the past
These effects become critical in modern designs
Older BKM assumptions break down
Become more critical as speeds increase
 As speeds increase, new effects that did not matter
become significant
This increases the number of variables that must be
comprehended
Many of these new effects are very difficult to understand
 This chapter will outline several of the most prominent
non-ideal transmission lines issues critical to modern
design
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Transmission Line Losses
Key Topics:
 DC resistive losses in the conductor
 Frequency dependent resistive losses in the
conductor
 Frequency dependent dielectric resistive losses
 Effect of surface roughness
 Differential line resistive losses
Interconnect: Adv
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Transmission Line Losses (cont’d)
 These losses can be separated into two
categories
Metal losses
Normal metals are not infinitely conductive
Dielectric losses
Classic model are derived from the alignment of Electric
dipoles in the dielectric with the applied field
Dipoles will tend oscillate with the applied time varying
field – this takes energy
 Why do we care about losses?
Losses degrade the signal amplitude, causing severe
problems for long buses
Losses degrade the signal edge rates, causing
significant timing push-outs
Losses will ultimately become a primary speed
limiter of our current technology
Interconnect: Adv
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Incorporation Losses Into The Circuit Model
 A series resistor, R, is included to account
for conductor losses in both the power and
ground plane
 A shunt resistor, G, is included to account
for Dielectric Losses
R
L
C
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G
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6
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DC Resistive Losses
 At low frequencies, the current flowing in a conductor will spread
out as much as possible
 DC losses are dominated by the cross sectional area & the
resistively (inverse of conductivity) of the signal conductor
Current flows through
w
entire cross section of signal
conductor and ground plane
t
Reference Plane
RDC 
L
Across sec tion

L
wt
 The current in a typical ground plane will spread out so much that
the DC plane resistance is negligible
 The DC losses of FR4 are very negligible
Interconnect: Adv
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AC Resistive Losses
8
 As the frequency of a signal increases, the current will
tend to migrate towards the periphery or “skin” of the
conductor - This is known as the “skin effect”.
Coaxial Cable Cross Section at High Frequency
Outer (Ground) conductor
Inner (signal) conductor
Areas of high
current density
 This will cause the current to flow in a smaller area

than the DC case
Since the current will flow in a smaller area, the
resistance will increase over DC
Interconnect: Adv
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The Skin Effect
 Why? When a field impinges upon a conductor, the field will
penetrate the conductor and be attenuated
remember the signal travels between the conductors
 The field amplitude decreases exponentially into the thickness of
the conductor – skin depth is defined as the penetration depth at
a given frequency where the amplitude is attenuated 63% (e-1) of
initial value
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Skin Depth In Copper
Electromagnetic
Wave
Amplitude
Penetration into conductor
X
Skin Depth, microns
9
8
7
6
5
4
3


f
2
1
0
0.E+00
1.E+09
Interconnect: Adv
2.E+09
3.E+09
4.E+09
Frequency, Hz
5.E+09
6.E+09
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The Skin Effect – Spatial View
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 The fields will induce currents that flow in the metal
 Skin effect confines 63% (e-1) of the current to 1 skin depth –
Current
the current density will decease exponentially into the thickness
of the conductor
 The total area of current flow can be approximated to be in one
skin depth because the total area below the exponential curve can
be equated to the area of a square
Area  w  h  1
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
 
1 1
Area   e d  0    1
e e
 0
0
1
2
3
Skin Depths
4
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
5
6
10
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Microstrip Frequency Dependent Resistance
 Skin effect causes the current to flow in a smaller area
 Frequency dependent losses can be approximated by
modifying DC equations to comprehend current flow
Approximation assumes that the current is confined to on skin
depth, and it ignores the current return path
 The current will be concentrated in the lower portion
of the conductor due to local fields
w

t
RAC 
L
Acurrent _ flow
L


 w
E-fields
L f

w

w
f
Interconnect: Adv
L
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Microstrip Frequency Dependent Resistance Estimates
 The total resistance curve will stay at approximately the DC
value until the skin depth is less than the conductor
thickness, then it will vary with f
40
Example of frequency dependent resistance
Resistance, Ohms
35
30
25
R tot
20
15
10
Tline parameter terms
R R0  Rs f
5
0
0.E+00
R DC  R AC Frequency
1.E+09
2.E+09
3.E+09 4.E+09
Frequency, Hz
5.E+09
6.E+09
R0 ~ resistance/unit length Rs ~ resistance/sqrt(freq)/unit length
Interconnect: Adv
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Microstrip Return Path Resistance
13
 The return current in the reference plane also
contributes to the frequency dependent losses
w
t

H
IO
1
I ( D) 

H 1  ( D / H ) 2
(Current Density in plane)

D
The area that the return current will flow in will allow
an effective width to be estimated
Rground 
L
Aeffective

L
  weffective
Interconnect: Adv
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Microstrip Return Path Resistance
 The current density formulae can be integrated to get
the total current contained within chosen bounds
3H
Io
2I o
1
1

dD 
 tan (3)  0.795I o
2

H 1  ( D / H )

3 H
 This shows that 79.5% of the current is contained in a

distance +/- 3H (W of 6H) from the conductor center
Assuming a penetration of 1 skin depth, the ground
return resistance can be approximated as follows
Rac _ ground 

Aground


6 H

Interconnect: Adv
F
6H
 / length
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Total Microstrip AC Resistance
 The total resistance is approximately the sum
of the signal and ground path resistance
RAC _ total  Rsignal  Rground
Rtotal 
F
w

F
6H
1 
1
 F  
  / length
 w 6H 
This is an excellent “back of the envelope”
formula for microstrip AC resistance
Interconnect: Adv
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More exact Formula – Microstrip (From Collins)
 This formula was derived using conformal mapping

techniques
The formula is not exact should only be used for
estimates
4w  F
1 1
Rsignal  LR  2 ln

t  w
 
w
 w
LR  0.94  0.132  0.0062 
H
H
w
LR  1 for 0.5 
H
Rground
2
w
for 0.5   10
H
F
wH

w H  5.8  0.03( H w)
w
Interconnect: Adv
w
for 0.1   10
H
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Stripline Losses
 In a stripline, the fields are referenced to two planes
 The total current will be distributed in both planes, and
in the upper and lower portion of the signal conductor


I ( D) 
1
1  (D / H )2
 For example: In a symmetrical stripline,the area in
which current will travel increases by a factor of 2 and
the resistance decreases by a factor of 2
This inspires the parallel microstrip model
Interconnect: Adv
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Calculating Stripline Losses
 The skin effect resistance of a stripline can be
approximated as follows: where the resistances
are calculated from the microstrip formulae at
the appropriate heights
Rac _ strip 
R( H 1_ micro )  R( H 2 _ micro )
R( H 1_ micro )  R( H 2 _ micro )
w
t
H2
H1
Interconnect: Adv
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Surface Resistance for Microstrip
 The surface resistance (Rs) is often used to evaluate

the resistive properties of a metal
Observation of AC loss equations show the resistance
is proportional to the square root of Frequency
1 
1
RAC  L    
 F  RS f 
 w 6H 
1 
1
 RS  L    
  s
 w 6H 
 Rs is a constant that scales the square root behavior
 Is caused by the skin loss phenomena
 Used in specialized T-line models (i.e.,W-Element)
Interconnect: Adv
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Surface Roughness alters Rs
 The formulae presented assumes a perfectly smooth


surface
The copper must be rough so it will adhere to the
laminate
Surface roughness can increase the calculated
resistance 10-50% as well as frequency dependence
proportions
Increase the effective path length and decreases the area
Trace
Skin-Depth
Tooth structure
(4-7 microns)
Plane
Interconnect: Adv
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Surface Roughness Effects
Frequency Dependence
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 Surface roughness is not a significant factor
until skin depth approaches the tooth size
(typically 100 MHz – 300 MHz)
 At high frequencies, the loss becomes
unpredictable from regular geometric object
because it is heavily dependent on a random
tooth structure.
No longer varies with the root of frequency –
something else
Interconnect: Adv
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Example of Surface Roughness
Measurements indicate that the surface roughness
may cause the AC resistance to deviate from F0.5
PCB X-section
POOL Stackup
PCB
PCB Performance
Performance
PCB Modeling
Tooth
Structure

2 right turns do not equal a right and a left.
Fiberglass
Bundles
Interconnect: Adv
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Dielectric Losses
 Classic model of dielectric losses derived from damped
oscillations of electric dipoles in the material aligning with the
applied fields
• Dipoles oscillate with the applied time varying field – this takes energy
 Dielectric constant becomes complex with losses
 PWB board manufacturers specify this was a parameter called
“Loss Tangent” or Tan 
 ''
   ' j ' '  Tan 
'
 The real portion is the typical dielectric constant, the imaginary
portion represents the losses, or the conductivity of the dielectric
 dielectric 
1
 dielectric
 2F ' '
Interconnect: Adv
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Glass Weave Effects High Speed Signals
Resin
Material
Glass
Material
6
3
3
9
6
0
9
Glass
Weave
Epoxy
trough
Er varation at 604 MHz of DDR sample #3
3.55
62
3.4
Trace Zo
3.5
3.45
Im
pe
da
nc
e
3.35
3.3
3.25
61
56
51
46
41
36
31
26
21
16
6
11
3.2
1
Er
Dielectric
Constant
Variation –
from
different
sample
board
Weave Alignment
Data shows that Fiber Weave
Effect cannot be ignored for
High Speed signals
61
60
UCL=59.51
Avg=58.92
LCL=58.34
59
58
trace #
57
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5 10 15 20 25 30 35 40 45 50 55 60 65 70
Sample
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Current Distribution and Differential Losses
5
Vary
2
Zodd
4.5
2
1
Zdiff
Zdiff Varies
Transitional
Differential
Single Line
Loss, 1-|S(2,1)|
0.4
0.35
0.3
10 GHz
0.25
0.2
5 GHz
0.15
2
4
6
8
16
25
45
75
100
500
Trace Separation (mils)
• Ports matched to diff. mode impedance
• Current distributions effect the loss
• Evidence of a “sweet spot” where the loss is smallest
Interconnect: Adv
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Differential Microstrip Loss Trends - Tan
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Microstrip losses as a function of frequency and loss tangent assuming smooth conductor
(5/5/5; Circuit on page x)
0
tand=0.01
-5
y = -5E-10x - 1.2079
R2 = 0.9953
Loss, dB
-10
tand=0.03
-15
y = -1E-09x - 1.1925
R 2= 0.9992
-20
-25
0
5
10
15
Frequency, GHz
20
25
• Model indicates linear behavior past 2.5 - 4 GHz
Interconnect: Adv
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Low Freq. Differential Loss Trends - Spacing
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microstrip diffe loss, w=5, er=4.2, h=4.5, tand=0.03, Zodd over spacing = 50 +/- 5 ohms
-0.4
W/S/W=5/15/5
loss, dB
-0.6
Curves
Intersect
-0.8
-1
-1.2
W/S/W=5/5/5
-1.4
-1.6
-1.8
1.00E+08
2.00E+08
3.00E+08
4.00E+08
5.00E+08
6.00E+08
7.00E+08
Frequency
• Losses at low frequency are greater for narrow spaced diff. microstrip
• Model predicts that loss curves for wide and narrow spaces intersect at:
 700MHz when Tand=0.03,
 3 GHz when Tand=0.01
Interconnect: Adv
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High Freq. Microstrip Loss Trends - Spacing
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microstrip differential loss, w=5, er=4.2, h=4.5, tand=0.03, Zodd over spacing = 50 +/- 5 ohms
0
Loss, dB
-5
-10
-15
5-5
-20
5-10
5-20
-25
-30
0
5-15
2
4
6
8
10
12
Frequency, GHz
14
16
18
20
• Model predicts losses at high frequencies are greater for wide spacing
• Phenomenon is exacerbated with high values of Tand
(Don’t ask why yet … wait a few slides)
Interconnect: Adv
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Conductor Loss Concepts – S vs Spacing
 Conductor losses increase due to skin effect &
proximity effect
In absence of dielectric losses, narrow spacing will produce
higher losses due to proximity effect – area of current
flow determines losses (approx. root F behavior)
Current Distributions
Narrow Spacing
Wide Spacing
E-Fields
Interconnect: Adv
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Dielectric Loss Concepts – S vs Spacing
 Dielectric losses increase due to damped response
of electric dipoles with frequency of applied
oscillating electric field
Tan losses increase linear w/ freq. (assuming homogeneous
media)
 Why does narrow spacing have the highest losses
at low frequencies but the lowest loss at high
frequencies?
 At low frequencies, Tan losses are small and
losses are dominated by skin and proximity
effects;
Narrow spacing = smaller area for current = high loss
 At high frequencies, Tan losses dominate;
Smaller spacing leads to more E-fields fringing through the
air and less through the lossy dielectric
Interconnect: Adv
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Does Not Apply for Homogeneous Dielectric
stripline differential loss, w=5, er=4.2, B=18, tand=0.03, Zodd over spacing = 51 +/- 5 ohms
0
-5
-10
-15
S=10 through 20
-20
-25
S=5
-30
-35
-40
0
2
4
6
8
10
12
Frequency, GHz
14
16
18
20
• Narrow spacing remains the highest loss configuration in a stripline over freq.
• Since the dielectric media is homogeneous, all the fields are contained
within the lossy material
• Since no fields fringe into a loss-free dielectric, the only conductor losses
are affected by spacing
Interconnect: Adv
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Assignment
 Use Ansoft 2 (or HSPICE) and create a
family of plots of for different line widths of
losses verses frequency for the following
case.
H2=10 mils
H1=10 mils
W=1, 2, 5, 10, 20 mils
T=1.5 mils
Er=4.0 Tand=.025
Metal sigma= 4.2e7
Interconnect: Adv
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