Interconnect I

1
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

3
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

4
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

5
Transmission Line Losses (contd)

• 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

6
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
G
C
7
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 entire cross section of
signal conductor and ground plane
w
t
Reference Plane

• 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

8
AC Resistive Losses

• 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.
• 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

Coaxial Cable Cross Section at High Frequency
Outer (Ground) conductor
Inner (signal) conductor
Areas of high current density
9
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

10
The Skin Effect Spatial View

• The fields will induce currents that flow in the
  metal
• Skin effect confines 63 (e-1) of the current to
  1 skin depth 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

1
0.9
0.8
0.7
0.6
0.5
Current
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
Skin Depths
11
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

E-fields
12
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

Example of frequency dependent resistance
40
35
30
25
20
Resistance, Ohms
15
Tline parameter terms
10
5
0
0.E00
1.E09
2.E09
3.E09
4.E09
5.E09
6.E09
Frequency, Hz
R0 resistance/unit length Rs
resistance/sqrt(freq)/unit length
13
Microstrip Return Path Resistance

• The return current in the reference plane also
  contributes to the frequency dependent losses

w
t
H
(Current Density in plane)
D

• The area that the return current will flow in
  will allow an effective width to be estimated

14
Microstrip Return Path Resistance

• The current density formulae can be integrated to
  get the total current contained within chosen
  bounds

• 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

15
Total Microstrip AC Resistance

• The total resistance is approximately the sum of
  the signal and ground path resistance

This is an excellent back of the envelope
formula for microstrip AC resistance
16
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

17
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

d
d
d
d

• 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

18
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

w
H2
t
H1
19
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

• 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)

20
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

21
Surface Roughness Effects Frequency Dependence

• 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

22
Example of Surface Roughness
Measurements indicate that the surface roughness
may cause the AC resistance to deviate from F0.5
Tooth Structure
23
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 d

• The real portion is the typical dielectric
  constant, the imaginary portion represents the
  losses, or the conductivity of the dielectric

24
Glass Weave Effects High Speed Signals
Data shows that Fiber Weave Effect cannot be
ignored for High Speed signals
Glass Weave
Epoxy trough
Weave Alignment
Dielectric Constant Variation from different
sample board
Trace Zo
25
Current Distribution and Differential Losses

• Ports matched to diff. mode impedance
• Current distributions effect the loss
• Evidence of a sweet spot where the loss is
  smallest

26
Differential Microstrip Loss Trends - Tand
Microstrip losses as a function of frequency and
loss tangent assuming smooth conductor (5/5/5
Circuit on page x)

• Model indicates linear behavior past 2.5 - 4 GHz

27
Low Freq. Differential Loss Trends - Spacing
W/S/W5/15/5
Curves Intersect
W/S/W5/5/5

• 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 Tand0.03,
• 3 GHz when Tand0.01

28
High Freq. Microstrip Loss Trends - Spacing

• Model predicts losses at high frequencies are
  greater for wide spacing
• Phenomenon is exacerbated with high values of
  Tand
• (Dont ask why yet
  wait a few slides)

29
Conductor Loss Concepts mS 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
30
Dielectric Loss Concepts mS vs Spacing

• Dielectric losses increase due to damped response
  of electric dipoles with frequency of applied
  oscillating electric field
• Tand 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, Tand losses are small and
  losses are dominated by skin and proximity
  effects
• Narrow spacing smaller area for current high
  loss
• At high frequencies, Tand losses dominate
• Smaller spacing leads to more E-fields fringing
  through the air and less through the lossy
  dielectric

31
Does Not Apply for Homogeneous Dielectric

• 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

32
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.

W1, 2, 5, 10, 20 mils
H210 mils
T1.5 mils
H110 mils
Er4.0 Tand.025
Metal sigma 4.2e7