12/4/2002 interconnect i – class 16 prerequisite reading - chapter 4

12/4/2002

Interconnect I – class 16

Prerequisite reading - Chapter 4

12/4/2002Interconnect: Adv

2

Outline Transmission line losses

DC losses in the conductorFrequency dependent conductor lossesFrequency dependent dielectric lossesEffect of surface roughnessDifferential 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 designsOlder BKM assumptions break downBecome 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 comprehendedMany 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

Key Topics:

DC resistive losses in the conductorFrequency dependent resistive losses in the

conductorFrequency dependent dielectric resistive losses Effect of surface roughnessDifferential line resistive losses

Transmission Line Losses


5

Transmission Line Losses (cont’d) These losses can be separated into two categories

Metal losses Normal metals are not infinitely conductive

Dielectric lossesClassic model are derived from the alignment of Electric dipoles in the dielectric with the applied fieldDipoles 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 busesLosses degrade the signal edge rates, causing significant timing push-outsLosses will ultimately become a primary speed limiter of our current technology


6Incorporation 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

LR

C G


7

DC Resistive Losses

w

t

Reference Plane

Current flows throughentire cross section of signalconductor and ground plane

wt

L

A

LR

tioncrossDC

sec

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

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

Outer (Ground) conductor

Inner (signal) conductor

Areas of high current density

Coaxial Cable Cross Section at High Frequency


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

f

Skin Depth In Copper

0

1

2

3

4

5

6

7

8

9

10

0.E+00 1.E+09 2.E+09 3.E+09 4.E+09 5.E+09 6.E+09

Frequency, Hz

Sk

in D

ep

th, m

icro

ns

XAm

pli

tud

e

Penetration into conductor

Electromagnetic Wave


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

Skin Depths

0

0.1

0.20.3

0.4

0.5

0.6

0.70.8

0.9

1

0 1 2 3 4 5 6

Cu

rren

t

111

00

eedeArea

1 hwArea


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

fL

fw

L

w

L

A

LR

flowcurrentAC

_

wt E-fields


12

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

Example of frequency dependent resistance

0

5

10

15

20

25

30

35

40

0.E+00 1.E+09 2.E+09 3.E+09 4.E+09 5.E+09 6.E+09Frequency, Hz

Res

ista

nce

, Oh

ms

Microstrip Frequency Dependent Resistance Estimates

R tot R DC R AC Frequency

R R0 Rs fTline parameter terms

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

2)/(1

1)(

HDH

IDI O

wt

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

H

D

effectiveeffectiveground w

L

A

LR

(Current Density in plane)


14

Microstrip Return Path Resistance

oo

H

H

o II

dDHDH

I795.0)3(tan

2

)/(1

1 13

32

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

lengthH

F

HAR

groundgroundac /

66_


15

Total Microstrip AC Resistance

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

lengthHw

FH

F

w

FRtotal /

6

11

6

groundsignaltotalAC RRR _

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


16More exact Formula – Microstrip (From Collins)

This formula was derived using conformal mapping techniques The formula is not exact should only be used for estimates

101.0)(03.08.5

5.01

105.00062.0132.094.0

4ln

11

2

2

H

wfor

w

F

wHHw

HwR

H

wforLR

H

wfor

H

w

H

wLR

w

F

t

wLRR

ground

signal


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

1)(

HDDI

2)/(1

1)(

HDDI

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

)_2()_1(

)_2()_1(_

microHmicroH

microHmicroHstripac RR

RRR

wt

H1

H2


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

sHw

LR

fRFHw

LR

S

SAC

6

11

6

11

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 proportionsIncrease the effective path length and decreases the area

Skin-Depth

Plane

Trace

Tooth structure(4-7 microns)


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

do not equal

PCB PerformancePCB Performance

PCB ModelingPCB Modeling

2 right turns a right and a left.

PCB X-sectionPOOL Stackup

FiberglassBundles

Example of Surface Roughness

Tooth Structure

Measurements indicate that the surface roughness may cause the AC resistance to deviate from F0.5


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

'

'''''

Tanj

''21

F

dielectricdielectric

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

Resin Material

Glass Material

9 0 6 3

9 6 3

Er varation at 604 MHz of DDR sample #3

3.2

3.25

3.3

3.35

3.4

3.45

3.5

3.55

1 6 11 16 21 26 31 36 41 46 51 56 61

trace #

Er

Dielectric ConstantVariation – from different sample board

Data shows that Fiber Weave Effect cannot be ignored for High Speed signals

57

58

59

60

61

62

Impedance

5 10 15 20 25 30 35 40 45 50 55 60 65 70 Sample

Avg=58.92 LCL=58.34

UCL=59.51

Cut16

0

2

4

6

8

10

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61

TraceWea

ve A

lign

men

tT

race

Zo

Epoxy trough

Glass Weave


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

1 2 Zdiff

Zodd

4.5

Vary52

Zdiff Varies

10 GHz

5 GHz

Trace Separation (mils)

Lo

ss, 1

-|S

(2,1

)|

Differential Single LineTransitional


26

Microstrip losses as a function of frequency and loss tangent assuming smooth conductor(5/5/5; Circuit on page x)

Differential Microstrip Loss Trends - Tan

Differential Microstrip Loss Trends - Tan

• Model indicates linear behavior past 2.5 - 4 GHz

y = -1E-09x - 1.1925R2 = 0.9992

y = -5E-10x - 1.2079R2 = 0.9953

-25

-20

-15

-10

-5

0

0 5 10 15 20 25Frequency, GHz

Lo

ss,

dB

tand=0.01

tand=0.03


27

microstrip diffe loss, w=5, er=4.2, h=4.5, tand=0.03, Zodd over spacing = 50 +/- 5 ohms

-1.8

-1.6

-1.4

-1.2

-1

-0.8

-0.6

-0.4

1.00E+08 2.00E+08 3.00E+08 4.00E+08 5.00E+08 6.00E+08 7.00E+08

Frequency

loss

, dB

Low Freq. Differential Loss Trends - Spacing

Low Freq. Differential Loss Trends - Spacing

• 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

W/S/W=5/15/5

W/S/W=5/5/5

Curves Intersect


28

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

0

0 2 4 6 8 10 12 14 16 18 20Frequency, GHz

Los

s, d

B

5-5

5-10

5-15

5-20

High Freq. Microstrip Loss Trends - SpacingHigh Freq. Microstrip Loss Trends - Spacing

• 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)


29

Narrow Spacing Wide SpacingCurrent Distributions

E-Fields

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)


30Dielectric 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


31

Does Not Apply for Homogeneous Dielectric

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

0

0 2 4 6 8 10 12 14 16 18 20Frequency, 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


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.

T=1.5 mils

H1=10 mils

H2=10 mils W=1, 2, 5, 10, 20 mils

Er=4.0 Tand=.025

Metal sigma= 4.2e7

12/4/2002 interconnect i – class 16 prerequisite reading - chapter 4

Documents

losses variations

dc losses of fr4

possible dc losses

adv incorporation losses

adv ac resistive losses

long buses losses

high frequency slide

current technology slide