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Electronic Instrumentation and Measurement

Nondestructive Testing & Nano-Biomedical Integrated System Laboratory

(非破壞檢測暨奈米生醫整合系統實驗室) – Class Meeting Time: Tuesday 09:10~10:00am, Friday 10:10~12:00am

– Instructor: Cheng-Chi Tai (戴政祺，電機研究所儀器系統與晶片組)

– Office: 92605 EE Building

– Office Phone: 06-2757575 ext. 62388

– E-mail: [email protected]

– Handouts: http://140.116.164.38

註: NDT & NBMIS實驗室研究題目包括生物醫學電子整合系統(藍芽無線通訊系統及實驗板、居家監護與資訊家電系統、數位信號處理器在語音處理、噪音防制等之應用、電刺激治療器、電子聽診器、電子血壓計、針灸針深度計等) ；電磁控制(3D磁浮、膠囊型內視鏡)與癌細胞電磁熱療；非破壞檢測(渦電流、超音波、音射、電力設備局部放電)等。

Announcement

– 期末考暫訂：1/6 (五), am 10:10 – 11:50

– 考試地點在原本各自分班上課的教室

– 考試內容：合班上課部分

Time Domain Reflectometry: Measurement Theory and Techniques

時域反射儀

References

– 儀器總覽：電子測試儀器，行政院國家科學委員會，精密儀器發展中心，1998。

– “Time Domain Reflectometry Theory: Application Note 1304-2 ”, Agilent.

– “TDR Measurement Theory and Techniques”, Tek.

– “Evaluating Microstrip with TDR: Application Note 1304-1”, Agilent.

– IEEE Instrumentation and Measurement等相關期刊。

TDR-Introduction

TIME-DOMAIN REFLECTOMETRY (TDR) is a testing and

measurement technique that has found increasing usefulness

in testing transmission lines (both metallic and fiber-optic),

cables, strip lines, connectors, and other wideband systems

or components. Basically, time-domain reflectometry is an

extension of an earlier technique in which reflections from an

electrical pulse were monitored to locate faults and to

determine the characteristics of power transmission lines. You

can compare time-domain reflectometry to a closed-loop

radar system in which the transmitted signal, a very fast step

pulse, is fed into the system and the reflections resulting from

discontinuities or impedance deviations in the system are

monitored on a CRT .

TDR-Introduction

The technique used in time-domain reflectometry consists of feeding an impulse of energy into the system and then observing that energy as it is reflected by the system at the point of insertion. When the fast-rise input pulse meets with a discontinuity or impedance mismatch, the resultant reflections appearing at the feed point are compared in phase, time, and amplitude with the original pulse. By analyzing the magnitude, deviation, and shape of the reflected waveform, you can determine the nature of the impedance variation in the transmission system. Also, since distance is related to time and the amplitude of the reflected step is directly related to impedance, the comparison indicates the distance to the fault as well as the nature of the fault.

TDR-Introduction

Figure A, B, C, and D , illustrates typical transmission line

problems that can easily be identified by using a time-

domain reflectometer. In addition to showing both the

distance to and the nature (resistive, inductive, or

capacitive) of each line discontinuity, time-domain

reflectometry also reveals the characteristic impedance of

the line and indicates whether losses are shunt or series.

They are also used to locate and analyze connectors and

splices.

TDR-Introduction

Figure A & B. - Time-domain reflectometer display of

transmission line problems. (a) Crimped (起皺的) cable, (b)

Frayed (磨損的) cable.

TDR-Introduction

Figure C & D. - Time-domain reflectometer display of

transmission line problems. (C) Open cable, (D) Shorted cable.

TDR-Introduction

Time-domain reflectometry, basic equipment setup.

TDR-Introduction

Typical time-domain reflectometer.

TDR-Introduction

TDR-Introduction

– 時域反射量測(TDR)與時域穿透量測(TDT)經常用在測量電路中的不連續效應。時域反射儀的工作原理類似雷達探測目標物或超音波檢測物體，由步階訊號產生器送出類步階訊號至待測物中，經由待測物傳遞到達待測物另一端。時域反射儀使用示波器螢幕顥示反射訊號及入射訊號的時間關係。由這些時間關係上，吾人即可判斷某些不連續點的位置，對於了解個別元件所造成的結果十分有幫助。同時藉由時間軸的關係圖，亦可輕易判斷發生不連續波形的時間。這些資訊對數位工程師而言，比起頻域分析的結果格外顯得意義非凡。

– 對於簡單構造的不連續連接線，Diamond與Janko(1993)利用TDR的量測結果對時間軸積分，求得IC構裝接腳的等效PSPICE模型。這種方法可以求得總電感及電容，但對於整體電路結構無法描述，必須仰賴經驗法則的輔助。

TDR-Introduction

TDR Theory: Transmission Line

– The classical transmission line is assumed to

consist of a continuous structure of R’s, L’s and

C’s. By studying this equivalent circuit, several

characteristics of the transmission line can be

determined.


– If the line is infinitely long and R, L, G, and C are

defined per unit length, then

CjG

LjRZZ oin

– where Zo is the characteristic impedance of the

line. A voltage introduced at the generator will

require a finite time to travel down the line to a

point x.


– The phase of the voltage moving down the line will lag

behind the voltage introduced at the generator by an amount

b per unit length. Furthermore, the voltage will be attenuated

by an amount a per unit length by the series resistance and

shunt conductance of the line. The phase shift(b)and

attenuation(a) are defined by the propagation constant g,

where

CjGLjRj

and a = attenuation in nepers(奈, 8.686 dB) per unit length

b = phase shift in radians per unit length


– The propagation constant g can be used to define the

voltage and the current at any distance x down an

infinitely long line by the relations

and

Since the voltage and the current are related at any point

by the characteristic impedance of the line

xinx eEE x

inx eII

inin

inx

in

xin

o ZI

E

eI

eEZ

where = incident voltage

= incident current

inE

inI


If the load ( ) is different from Zo, these equations are not

satisfied unless a second wave is considered to originate at

the load and to propagate back up the line toward the source.

This reflected wave is energy that is not delivered to the load.

Therefore, the quality of the transmission system is indicated

by the ratio of this reflected wave to the incident wave

originating at the source. This ratio is called the voltage

reflection coefficient(電壓反射係數), r, and is related to the

transmission line impedance by the equation:

oL

oL

i

r

ZZ

ZZ

E

E

LZ


The magnitude of the steady-state sinusoidal voltage along a

line terminated in a load other than Zo varies periodically as a

function of distance between a maximum and minimum value.

This variation, called a standing wave, is caused by the phase

relationship between incident and reflected waves. The ratio of

the maximum and minimum values of this voltage is called the

voltage standing wave ratio (電壓駐波比), s, and is related

to the reflection coefficient (r) by the equation

1

1

TDR Theory: Step Reflection Testing

Functional block diagram for a time domain relectometer


– If the load impedance is equal to the characteristic impedance

of the line, no wave is reflected and all that will be seen on the

oscilloscope is the incident voltage step recorded as the wave

passes the point on the line monitored by the oscilloscope.

– If a mismatch exists at the load, part of the incident wave is

reflected. The reflected voltage wave will appear on the

oscilloscope display algebraically added to the incident wave.

Oscilloscope display when Er = 0

Oscilloscope display when Er 0


Locating Mismatches

– The reflected wave is readily identified since it is separated in

time from the incident wave. This time is also valuable in

determining the length of the transmission system from the

monitoring point to the mismatch. Letting D denote this length:

where =velocity of propagation

T= transit time from monitoring point to the mismatch and

back again, as measured on the oscilloscope

– Most TDR’s calculate this distance automatically for the user.

v2

TvD

TDR Theory: Step Reflection Testing TDR Theory: Step Reflection Testing

Analyzing Reflections (real load)

– The shape of the reflected wave is also valuable since it

reveals both the nature and magnitude of the mismatch. The

following figures show four typical oscilloscope displays and

the load impedance responsible for each.


Analyzing Reflections

Open circuit Short circuit

Er = - Ei


Analyzing Reflections


Also of interest are the reflections produced by complex load

impedances. These waveforms could be verified by writing

the expression for r (s) in terms of the specific ZL for each

example:

Analyzing Reflections (complex load impedances)

;oL

oL

i

r

ZZ

ZZ

E

Es

)( 性電感sLRZL

)(1

性電容sRC

RZL

multiplying r(s) by — the transform of a step function of Ei,

and then transforming this product back into the time

domain to find an expression for er(t).


A simpler analysis is possible without resorting to Laplace

transforms. The more direct analysis involves evaluating the

reflected voltage at t = 0 and at t = and assuming any

transition between these two values to be exponential. (For

simplicity, time is chosen to be zero when the reflected wave

arrives back at the monitoring point.) In the case of the

series R+L combination, for example, at t = 0 the reflected

voltage is +Ei. This is because the inductor will not accept a

sudden change in current; it initially looks like an infinite

impedance, and r = +1 at t = 0. Then current in L builds up

exponentially and its impedance drops toward zero. At t = ,

therefore er(t) is determined only by the value of R.

Analyzing Reflections (complex load impedances, R+L)


When

ZR

ZR

o

o

The exponential transition of er(t) has a time constant

determined by the effective resistance seen by the inductor.

Since the output impedance of the transmission line is Zo,

the inductor sees Zo in series with R, and

oZR

L


Analyzing Reflections (complex load impedances, R//C)

A similar analysis is possible for the case of the parallel R-C

termination. At time zero, the load appears as a short circuit

since the capacitor will not accept a sudden change in voltage.

Therefore, r = –1 when t = 0. After some time, however, voltage

builds up on C and its impedance rises. At t = , the capacitor is

effectively an open circuit:

o

oL

ZR

ZRandRZ

The resistance seen by the capacitor is Zo in parallel with R,

and therefore the time constant of the exponential transition of

er(t) is:


Analyzing Reflections (complex load impedances, R//C)

CRZ

RZ

o

o


Discontinuities on the Line

The junction of the two lines (both of characteristic impedance

Zo) employs a connector of some sort. Let us assume that the

connector adds a small inductor in series with the line.

Analyzing this discontinuity on the line is not much different

from analyzing a mismatched termination.



One can treat everything to the right of M in the figure as an

equivalent impedance in series with the small inductor and then

calls this series combination the effective load impedance for

the system at the point M. Since the input impedance to the

right of M is Zo, an equivalent representation is shown. The

pattern on the oscilloscope is merely a special case of R-L

circuit.


Evaluating Cable Loss

Time domain reflectometry is also useful for comparing

losses in transmission lines. Cables where series losses

predominate reflect a voltage wave with an exponentially

rising characteristic, while those in which shunt losses

predominate reflect a voltage wave with an exponentially-

decaying characteristic. This can be understood by looking at

the input impedance of the lossy line. Assuming that the lossy

line is infinitely long, the input impedance is given by:

CjG

LjRZZ oin


Evaluating Cable Loss: Series losses

Treating first the case where series losses predominate, G is

so small compared to wC that it can be neglected:

2/1

1

Lj

R

C

L

Cj

LjRZin

Recalling the approximation (1 + x)a ≈(I + ax) for x<1, Zin can

be approximated by:

LRWhenLj

R

C

L

Cj

LjRZin

21



Since the leading edge of the incident step is made up almost

entirely of high frequency components, R is certainly less than

wL for t = 0+. Therefore the above approximation for the lossy

line, which looks like a simple series R-C network, is valid for

a short time after t = 0. It turns out that this model is all that

is necessary to determine the transmission line’s loss. In terms

of an equivalent circuit valid at t = 0+, the transmission line

with series losses is shown as in the following page


Evaluating Cable Loss: Shunt losses

A similar analysis is possible for a conductor where shunt

losses predominate. Here the input admittance of the lossy

cable is given by:

2/1

11

Cj

G

L

C

Lj

CjG

LjR

CjG

ZY

inin

Since R is assumed small, re-writing this expression for Yin:

CGWhenCj

G

L

CYin

21


Evaluating Cable Loss: Shunt losses


Multiple Discontinuities

One of the advantages of TDR is its ability to handle cases

involving more than one discontinuity. An example of this is

shown below

Cables with multiple discontinuities



Accuracy decreases as you look further down a line with multiple

discontinuities

It is seen that the two mismatches produce reflections that can

be analyzed separately. The mismatch at the junction of the two

transmission lines generates a reflected wave, Er1 , where



ioo

ooir E

ZZ

ZZEE

1

1

Similarly, the mismatch at the load also creates a reflection due

to its reflection coefficient

oL

oL

ZZ

ZZ

2

Agenda

– TDR Overview

– TDR Accuracy Issues

– TDR Comparative Reflection Techniques

– TDR Simple Component Characterization

– TDT and Crosstalk

– TDR of Coupled Transmission Lines

Interconnect Challenges

– Distributed interconnect (wire, board runs, vias,

package lead frames, wirebonds, IC metal, etc.)

is a given in today’s designs

– Signals encountering any change in impedance

reflect some energy back toward the source

– Interconnect can limit performance Impedance

Change

Transmitted Energy

Incident Energy

Reflected Energy

Discontinuity Properties

– The reflected signal magnitude is a function of

the incident signal magnitude and the nature of

the impedance change

– The time elapsed between the incident and the

reflected signal is a function of the overall

distance traveled and the velocity of

propagation

– Fast sampling systems with TDR capability can

be a very useful tool for interconnect

discontinuity studies

– Time Domain Reflectometry - a measure of

reflection in an unknown device, relative to the

reflection in a standard impedance

– Compares reflected energy to incident energy on

a single-line transmission system

– Known incident stimulus is applied to the standard

impedance and intentionally propagated toward the

unknown device

– Reflections from the unknown device propagate back to

the source

– Amplitude and time of reflected signal is compared to

incident stimulus

TDR Measurement Basics

TDR Overview - Typical System

Incident Step

50 W

Step Generator

Reflections

Sampler

t = 0

50 W

Incident Step

Incident

Reflection

Test device Test device

Probe

Impedance

reference

TDR System Key Elements

1. High speed step generator (usually switched current

source) running on internal clock

2. High speed sampler

3. Digitizing oscilloscope

4. Reference transmission line standard impedance

with back termination

5. Probe

6. Device under test

Using TDR Results

Although TDR testing is usually done without device

powered, note that:

– The reflected signal is a function only of the incident

signal magnitude and the nature of the impedance

change, so stimulus amplitude is arbitrary

– The time elapsed between the incident and the

reflected signal depends only on the device and

physics

– Therefore, with linear devices, TDR results may be

extrapolated to situations that employ other stimuli

TDR Waveform Characteristics

– TDR systems observe the superposition of

incident and reflected signals at source

– Time separation t1-t0 assures ability to

discern difference

Time t0 t1

incidentV

reflectedV

TDR Rho Units Definition

Time

+ 1

0

- 1

t0 t1

0at 0 and ZZV

V

incident

reflected

Characteristic (Z = Z0)

Amplitude

incidentV

reflectedV

KCL Applied at r Discontinuity

– Transmission lines support propagation with

specific characteristic impedance Z

– Reflected and forward propagating signals will be

such that Si = 0 is satisfied at discontinuity

– Can easily solve for Z knowing r, Z0, and KCL for

lumped circuits

Step

Source

Forward

(Z = Z0)

Incident

Reflected Discontinuity

Z0

Solution for Z Units

0

0

ZZ

ZZ

1

10ZZ

– Where – Z0 is the known reference impedance

– the sampling oscilloscope directly measures r

– Z is the calculated test device impedance

– Note textbooks usually show reversed expression:

TDR Waveforms - Simple Cases

Waveforms with Open, Short and 50 terminations

Amplitude

Open (Z = )

(Z = 50 )

Short (Z = 0)

Time

rreflected =+1

+ 1

0

- 1

t0 t1

rincident=+1 rreflected =-1

Measuring Impedance

1

10ZZ

0

20

40

60

80

100

120

140

160

180

200

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

500 Z

Z

-1 0

-0.6 12.5

-0.5 16.67

-0.282 28

-0.2 33.33

0 50

0.2 75

0.4 116.67

0.5 150

0.6 200

1 ®

Z

Nonlinear Impedance / r Mapping

– Everything else equal, lower impedance line

measurements can tolerate more r error for a

given impedance tolerance

– Assumed conditions

– 250 mV step

– 50 Reference Line

– 1 mV or 4 mr error equates to:

– 0.40 for a 50 W test line

– 0.24 for a 28 test line



Measuring Impedance - Sensitivity to r

2

0

21

2

ZZ

0

20

40

60

80

100

120

140

160

180

200

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

500 Z

Z dZ/d

-1 0 25

-0.6 12.5 39.06

-0.5 16.67 44.44

-0.282 28 60.84

-0.2 33.33 69.44

0 50 100

0.2 75 156.25

0.4 116.67 277.78

0.5 150 400

0.6 200 625

1 ® ®

Z

More Complex Test Devices

– Not all devices measured are constant impedance

– The r waveform is a record of continuous reflection

along a transmission line, not just one location

– All reflection results are superpositioned

– Additional care is needed after first discontinuity, as

subsequent reflections are displayed relative to

earlier discontinuities

Step

Source

Forward

Z = Z0 Z1 > Z0

Incident

Reflected

Z1 > Z2 > Z0

Agenda

– TDR Overview






TDR Interconnect Issues

The following interconnect-related issues can affect

TDR accuracy:

– Aberrations (異常, 變異)

– Skin loss

– Attenuation

– Incorrect reference impedance level (Z Z0)

– Loss of horizontal resolution (TDR解析度不足，無法區別太接近的discontinuities )

TDR System Aberrations

– Aberrations are always present on incident edge

– TDR system

– Interconnect

– Test device preceding area of interest

– Reflections always contain some fraction of the

incident edge aberrations

– It’s important to index where the reference

impedance measurement point or zone is located

relative to incident edge

– Tektronix 80E04 example -> 70 ps - 550 ps round-trip

travel (35 ps - 275 ps one-way) beyond front

connector

TDR System Aberrations


– TDR displays reflections from lumped or short

discontinuities relative to the nearby impedance -

such as interconnect between TDR system and

unknown device

– Absolute r scale can mislead.

Time

0

- 1

t0 t1


Interconnect present (Z>Z0)


– If interconnect is lossy, TDR displays reflections

relative to the nearby lossy impedance level

– Lossy lines cause ramps on TDR response.

– Again, absolute r scale can mislead.

Time

0

- 1

t0 t1


Lossy interconnect present

TDR Interconnect Analogy

– Voltage measurements sometimes needed when

ground problems are present on the test device

– Without a differential voltage probe, the volts

measured are referenced to scope ground, not the

test device

TDR Resolution

– Insufficient TDR resolution

– Results from closely spaced discontinuities being

smoothed together

– Can miss details of device under test

– May lead to inaccurate impedance readings

Z1, tD Z0 Z0

Time

t1 t2

tr(system)

2tD

TDR Resolution

– First discontinuity reflection is witnessed at t1

– Twice the one way propagation delay tD between

discontinuities elapses

– Second discontinuity reflection is witnessed at t2

– System risetime is barely adequate when

– Resolution is defined as the one-way transit time tD

that puts the TDR system at this threshold:

)(Resolution 21

systemRTT

DR tttT 212(system)

TDR Resolution

– Sometimes quoted in distance as well as time

– 17.5 ps resolution TDR instrument equates to

discontinuity spacing of

– 3.5 mm on surface etched board traces

– 4 mm in most plastics

– 5.5 mm in air

TDR Resolution

Why is it important to know about resolution?

– Even with slower signals, systems built with

mixed components and technologies add

uncertainties to signal path - some quite short

– Analytical tools must exceed system performance

in order to debug

– Interconnect may matter - System rise time is

characterized by fall time of reflected edge from

ideal short at test point - thus resolution can be

greater than the TDR system resolution alone

2

ect)(interconn

2

(sampler)

2

(stepgen)(system) RRRR TTTT

Agenda

– TDR Overview






Comparative Reflection TDR Measurement

– Inserts a check against known standard impedance

at the location of the test device

– Standard impedance is transferred to interconnect

segment immediately preceding device under test

– Linearity guarantees that TDR signal experiences

identical source, interconnect, and sampler

imperfections with both standard and DUT present

– Greatly improves r and Z absolute accuracy

– Documented in IPC-TM-650

Comparative Reflection - Concept:

T DR

DUT

INTERCONNECT

STD IMPEDANCE

– Assume that you have a standard impedance and

you wish to use TDR to characterize a device

against this standard

Comparative Reflection Technique

1. Characterize the interconnect immediately adjacent

to the disconnect point, as a secondary standard:

– Open circuit end of interconnect and measure size of step

reflected from standard impedance rR-OPEN as seen by

TDR system over specified time zone

– Connect standard impedance and measure size of step

reflected from standard impedance rR-STD as seen by TDR

system over specified time zone

rR-OPEN

intercon

Open

rR-STD intercon standard

Comparative Reflection Technique

2. Measure the DUT impedance against this

interconnect impedance

– Connect DUT and measure size of step reflected rR-DUT

as seen by TDR system

rR-DUT

intercon device

STDROPENR

STDROPENRSTDINT ZZ

DUTROPENR

DUTROPENRINTDUT ZZ

Agenda

– TDR Overview






TDR Response of Simple Components

– Observe high frequency behavior (高頻行為)

– Discern lumped versus distributed

– Derive equivalent C, L, Z0, t values to put into

simulation

– Verify physical location of discontinuity

Limits:

– First or most significant discontinuity only

Shunt C and Series L Discontinuities

Shunt Capacitance Discontinuity

Series Inductance Discontinuity

Z

0

Z

0

Z

0

Z

0

L

thru

thru

seconds)-in (Area

2

0

Z

AreaC

C

AreaZL 02

Shunt C and L Terminations

Capacitor Load Termination

Inductor Load Termination

Z0

Z0

open

short

C

L

02 Z

AreaC

2

0 AreaZL

Distributed Discontinuities

Capacitive Discontinuity

Inductive Discontinuity

Z

Time

100

50

0

incident

Z0 Z0 Z0

1

1

2Z

tCeq

2

22tZLeq

Z1 Z2

t1 t2

Z1

Z2

Agenda

– TDR Overview






– Time Domain Transmission - a measure of signal

transmission through an unknown device,

relative to the incident signal.

– Compares transmitted energy to incident energy

on a single-line transmission system

– Known stimulus applied to the standard impedance is

propagated toward the unknown device

– Second channel measures transmitted signal

– Gives a second (but alternate) look at TDR

information

TDT Overview

TDR Reflected Units Definition

Time

+ 1

0

- 1

t0 t1

incident

reflected

V

V

Amplitude

reflectedV

incidentV

TDT Transmitted Units Definition

Time

+ 1

0

- 1

t0 t1

1incident

dtransmitte

V

V

Amplitude - r

reflectedV

incidentV dtransmitteV

reflectedincidentdtransmitte VVV

+ 1 t

0 t

Amplitude - t

r - t - Z Relationship

0

0

ZZ

ZZ

1

10ZZ

0

2

ZZ

Z

20ZZ

Z0 is the known reference impedance

the sampling oscilloscope directly measures r or t Z is the calculated test device impedance

TDT Example

Crosstalk

– The coupling of energy from one line to another

– Three Elements Contribute to Crosstalk:

– Port terminations (端點)

– Stimulus

– Moding on transmission system

– Generalities:

– If saturated, crosstalk energy is proportional to line length

– If unsaturated, crosstalk energy is proportional to rise time

of driving signal

– Can be positive or negative (inductive or capacitive)

– Occurs in both forward (near-end) and backward (far-end)

directions

– Non-characteristic port terminations make it worse

Crosstalk Measurement Techniques

– Set up TDR on aggressor line (干擾線)

– Observe victim lines (受干擾線) with TDT

– Take care to terminate all other lines

T DR 1

2

+ DUT

50 W

50 W

Agenda

– TDR Overview






Symmetric Coupled Lines - Odd and Even Mode Definitions

– Zodd is the single-ended driving impedance of a

transmission line, given the boundary condition that

the other line is driven with an equal amplitude but

opposite polarity signal (anti-phase sourcing)

– Zeven is the single-ended driving impedance of a

transmission line, given the boundary condition that

the other line is driven with an equal signal (in-phase

sourcing)

+ + + -

Od d M o d e E v e n M o d e

Symmetric Model Values

P i

T e e

2

oddeven ZZ

oddeven

oddeven

ZZ

ZZ

2

evenZ

oddZ oddZ

evenZ

oddeven

oddeven

ZZ

ZZ

edunterminatcrosstalk reverse

Odd Mode Characterization

R a / 2 R 1 R 1 R a / 2

Z o d d = ( R a / 2 ) | | R b

+ -

+ -

P i T e e

R b R b R 2

Z o d d = R 1

Even Mode Characterization

2 R 2

R 1

Z e v e n = R 1 + 2 R 2

2 R 2

R 1 R a

+ -

+ -

P i T e e

R b

Z e v e n = R b

R b

Symmetric Line Example

Symmetric

coupled

lines on

FR-4

w = 2.5 mm

s = 2 mm

h = 1.5 mm

Zeven = 56.0

Zodd = 47.85

Example Model Values

P i

T e e

56.0

658.6

47.85

56.0

47.85

4.08

Zeven = 56.0

Zodd = 47.85

TDR Measurement setup for EBGA

Step

Generator

Sampling

Circuit

TDR

Cable+Probe

Ground plane

Substrate

Solder ball

Trace Wire

Die

Incident

Reflection

IUA

What’s Enhanced Ball Grid Array (EBGA)?

Substrate

Anchor holes

Solder ball Bond wire Chip

Adhesive Heat-spreader Compound

Die pad Bond wire

Solder ball Substrate

Heat-spreader Compound

Chip Adhesive

Cavity up

Cavity down

The Problems for NDA of EBGA

With heat-spreader Without heat-spreader

•The difficulty on nondestructive analysis in EBGA package of multilayer substrates,

multi-layer bond-wires, solder ball and heatspreader using X-ray method has been

increased extremely.

•Some of these defective packages can not be detected because the limitation of the

X-ray inspections technique for under solder ball, heat-spreader or multi-layer bond

wire.

Failures on the Signal Interconnection of EBGA

Substrate Bond wire Die

Die pad

Ball

Gold wire Copper trace Solder ball

Measurement Setup

Solder ball

Ground

Semi-rigid probe

Pogo-pin array

Center conductor

Copper film

(a)

(b)

User-Made OEF

Copper film

EBGA

Cable+Probe

Center conductor

Copper film

TDR Technique and Equivalent Circuit Diagram of the Transmission Lines

L

C

R

G

L

C

R

G

Ground plane

Substrate

Solder ball

Trace Wire

Die

IUA

TDR Technique and Equivalent Circuit Diagram of the Transmission Lines

0Z

5Z

2Z

3Z

4Z

1Z

1

0

2

3

4

0t

1t

2t

3t

4t

0t

1t

2t

3t

4t Time

Tim

e

Voltage

Direction of propagation

1Z

2Z

3Z

nZ

1nZ

1t

2t

3t

1nt

nt

Measu

remen

t wav

eform

incidentTL

TLmeasured V

ZZ

ZV

0

2

0

Pro

be-tip

wire

CM

OS

I/O p

ad

Op

en-en

d

Sold

er ball

Time (ps)

Return transit time

Return of the signal

after final reflection

Su

bstrate

Voltag

e (mV

)

200 400 600 800 1000

500

450

400

350

300

250

200

150

100

TDR Response of an EBGA Interconnection

Open Circuits

open failure curve of substrate Open in the solder ball

0 Time (ps)

Voltag

e (mV

)

200 400 600 800 1000

500

450

400

350

300

250

200

150

100

(c) Fault-free

(a) Open in the solder ball

(b) open failure curve of substrate

TDR Responses of the Open Circuits

Short between two solder balls Short failure curve of bridged wire

Short Circuits

0

(a)

Time (ps)

Voltag

e (mV

)

200 400 600 800 1000

500

400

300

0

200

100

(b)

(c)

(d)

Fault-free

short failure curve of I/O pad of chip

Shorts between two solder ball short failure curve of bridged wire

TDR Responses of the Short Circuits

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