1. Prerequisite reading - Chapter 4
Interconnect I – class 16
Prerequisite reading - Chapter 4
12/4/2002

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
12/4/2002

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
Interconnect: Adv
12/4/2002

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
Interconnect: Adv
12/4/2002

5. 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
12/4/2002

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
Interconnect: Adv
12/4/2002

7. DC Resistive Losses w t Reference Plane
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
Interconnect: Adv
12/4/2002

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
Interconnect: Adv
12/4/2002

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 X
Amplitude
Penetration into conductor
Electromagnetic
Wave
Interconnect: Adv
12/4/2002

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 1 2 3 4 5 6
Interconnect: Adv
Skin Depths
12/4/2002

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 w t
E-fields
Interconnect: Adv
12/4/2002

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
Resistance, Ohms 20 15
Tline parameter terms 10 5
0.E+00
1.E+09
2.E+09
3.E+09
4.E+09
5.E+09
6.E+09
Frequency, Hz
R0 ~ resistance/unit length Rs ~ resistance/sqrt(freq)/unit length
Interconnect: Adv
12/4/2002

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
Interconnect: Adv
12/4/2002

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
Interconnect: Adv
12/4/2002

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
Interconnect: Adv
12/4/2002

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
Interconnect: Adv
12/4/2002

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 2 ) / ( 1 H D I + 2 ) / ( 1 H D I + 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
Interconnect: Adv
12/4/2002

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
Interconnect: Adv
12/4/2002

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)
Interconnect: Adv
12/4/2002

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
Skin-Depth
Plane
Trace
Tooth structure
(4-7 microns)
Interconnect: Adv
12/4/2002

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
Interconnect: Adv
12/4/2002

22. Example of Surface Roughness
Measurements indicate that the surface roughness may cause the AC resistance to deviate from F0.5
Tooth
Structure
Interconnect: Adv
12/4/2002

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
Interconnect: Adv
12/4/2002

24. Glass Weave Effects High Speed Signals
Resin Material
Glass Material
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
Interconnect: Adv
12/4/2002

25. Current Distribution and Differential Losses
4.5
Vary 5 2
Zdiff Varies
10 GHz
5 GHz
Trace Separation (mils)
Loss, 1-|S(2,1)|
Differential
Single Line
Transitional 1 2
Zdiff
Zodd
Ports matched to diff. mode impedance
Current distributions effect the loss
Evidence of a “sweet spot” where the loss is smallest
Interconnect: Adv
12/4/2002

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)
y = -1E-09x R 2 =
y = -5E-10x =
-25
-20
-15
-10 -5 5 10 15 20 25
Frequency, GHz
Loss, dB
tand=0.01
tand=0.03
Model indicates linear behavior past GHz
Interconnect: Adv
12/4/2002

27. Low Freq. Differential Loss Trends - Spacing
W/S/W=5/15/5
Curves
Intersect
W/S/W=5/5/5
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 Tand=0.03,
3 GHz when Tand=0.01
Interconnect: Adv
12/4/2002

28. High Freq. Microstrip Loss Trends - Spacing
microstrip differential loss, w=5, er=4.2, h=4.5, tand=0.03, Zodd over spacing = 50 +/- 5 ohms
-30
-25
-20
-15
-10 -5 2 4 6 8 10 12 14 16 18 20
Frequency, GHz
Loss, dB
5-5
5-10
5-15
5-20
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
12/4/2002

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
Interconnect: Adv
12/4/2002

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
Interconnect: Adv
12/4/2002

31. 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
-40
-35
-30
-25
-20
-15
-10 -5 2 4 6 8 10 12 14 16 18 20
Frequency, GHz
S=10 through 20
S=5
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
12/4/2002

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.
W=1, 2, 5, 10, 20 mils
H2=10 mils
T=1.5 mils
H1=10 mils
Er=4.0 Tand=.025
Metal sigma= 4.2e7
Interconnect: Adv
12/4/2002