px tdr measurement theory and techniques john rettig [email protected] (503)-627-3232

PX

TDR Measurement Theory and Techniques

John [email protected]

(503)-627-3232

Agenda

– TDR Overview– TDR Accuracy Issues– Comparative Reflection Technique– Simple Component Characterization– Advanced Component Characterization

– TDT and Crosstalk

– Coupled Transmission Lines

– TDR and Scattering Parameters

Interconnect Design Issues

– Distributed interconnect (wire, board runs, package lead frames, wirebonds, IC metal, etc.) is a given in today’s designs

– At high-speeds, interconnect limits performance– It is desirable to characterize and model

interconnect to predict the performance early in the design phase. Impedance

Change

Transmitted Energy

Incident Energy

Reflected Energy

Measurement of Interconnect

– Whenever an incident signal encounters a change in impedance, some of the energy is reflected back toward the source; the remainder is transmitted forward in the system

– 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

– System must be fast enough to capture these events

– 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 stimulus applied to the standard impedance is

propagated toward the unknown device– Reflections from the unknown device are reflected back

to the source– Known standard impedance may or may not be present

simultaneously with the device or system under test

TDR Basics

TDR Overview - Typical System

Incident Step

50

Step Generator

Reflections

Sampler

t = 050

Incident Step

TDR System 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

TDR Results Applicability

– TDR testing is usually done without device powered– The reflected signal is a function only of the incident

signal magnitude and the nature of the device, so vertical scale 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 using other stimuli

TDR Rho Units Definition

Time

Vreflected

+ 1

0

- 1

t0 t1

Vincident

incident

reflected

V

V

Characteristic (Z = Z0)

Amplitude

Vreflected

KCL at Discontinuity

– Transmission lines support propagation with specific characteristic impedance Z

– Reflected and forward propagating signals will be such that i = 0 is satisfied at discontinuity

– Can easily solve for Z knowing , Z0

StepSource

Forward

Z = Z0Z > Z0

Incident

ReflectedDiscontinuity

- Z Relationship

Where is directly indicated by the oscilloscopeZ represents the test impedanceZ0 is the reference impedance

0

0

ZZ

ZZ

1

10ZZ

TDR Waveforms

– TDR systems observe the superposition of incident and reflected signals at source

– Time separation t1-t0 assures ability to discern difference

Time

reflected

+ 1

0

- 1

t0 t1

Amplitude

incident=+1

TDR Waveforms

TDR Waveforms - Open, Short and 50 terminations

AmplitudeOpen (Z =)

(Z = 50)

Short (Z = 0)

Time

reflected =+1

+ 1

0

- 1

t0 t1

incident=+1 reflected =-1

Measuring Impedance

1

10ZZ

020406080

100

120140160180200

-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

0 500.2 750.4 116.670.5 1500.6 2001 ®

Z

Nonlinear Impedance / Mapping

– Everything else equal, lower impedance line measurements can tolerate more error for a given impedance tolerance

– Assumed conditions– 250 mV step– 50 Reference Line

– 1 mV or 4 m error equates to:– 0.40 for a 50 test line– 0.24 for a 28 test line – 0.79 for a 90 test line– 1.23 for a 125 test line

Measuring Impedance - Sensitivity to

20

21

2

ZZ

020406080

100

120140160180200

-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 1000.2 75 156.250.4 116.67 277.780.5 150 4000.6 200 6251 ® ®

Z

Transmission Lines and TDR

– Not all devices measured are constant impedance– The 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 relative to immediate impedance and are altered by earlier discontinuities

StepSource

Forward

Z = Z0Z1 > Z0

Incident

Reflected

Z1 > Z2 > Z0

Agenda





TDR System Aberrations

TDR System Aberrations

– Aberrations always present on incident edge– Device under test acts as a filter: input = incident,

output = reflected– Therefore reflections contain some portion of

aberrations– Important to index where impedance point or zone is

relative to incident edge– Tektronix 80E04 example -> 70 ps - 550 ps round-trip

travel (35 ps - 275 ps one-way)

TDR Interconnect Issues

– TDR is a measurement of relative reflection in an unknown device, to the reflection in a standard impedance

– If interconnect is present between standard and unknown device, the perception of reflection is relative to the interconnect

– If standard is not immediately adjacent to the unknown device, care must be taken

– If standard and unknown device have uncontrolled elements between them, care must be taken

– Aberrations can be added by interconnect

TDR Interconnect Analogy

– Voltage measurements needed when ground issues are present on the device under test

– Don’t have a differential voltage probe– Volts measured are referenced to scope ground, not

device

TDR Interconnect Issues

The following interconnect-related issues can affect TDR accuracy:– Attenuation– High frequency skin loss in interconnect– Aberrations contributed by connector, interconnect, or

probe

– Incorrect reference impedance level (ZZ0)

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

TDR Resolution

SMA through F-F barrel(8.6 mm dielectric)

Each end individually loosened 0.5 turns(0.35 mm)

Both ends loosened 0.5 turns; risetime filters applied

TDR Resolution

– TDR system risetime is related to resolution– Reflections last as long as the incident step and

display as long as the system risetime

Z1, tDZ0 Z0

Displayed Time

t01 t12

tr(system) 2tD

TDR Resolution

– First discontinuity reflection is witnessed at t01

– Twice the one way propagation delay tD between discontinuities elapses

– Second discontinuity reflection is witnessed at t02

– Ideally, leading corner of reflection from second discontinuity arrives back at first discontinuity no earlier than lagging corner of reflection from first discontinuity, thus

)()( 21

systemRresolution TT

TDR Resolution

Why is it important?

– 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

– 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

– Note that– This rule assumes 0-100% ramp model; real world specifies

10-90% quadratic-type responses– System rise time is characterized by fall time of reflected

edge from ideal short at test point– Other second order factors enter picture– System rise time approximated by:

2ect)(interconn

2(sampler)

2(stepgen)(system) RRRR TTTT

Agenda





Comparative Reflection TDR Measurements

– Comparative reflection technique inserts check with known impedance at the exact location of the device under test

– Impedance standard 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 and Z accuracy– Documented in IPC-TM-650

TDR Accuracy Improvement - Concept:

TDR

DUT

INTERCONNECT

STD IMPEDANCE

– Assume that you have a primary standard impedance and you wish to use TDR to characterize a device against this standard

TDR Accuracy Improvement

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 R-OPEN as seen by

TDR system over specified time zone

R-OPEN

intercon

Open

R-STDinterconstandard

Open

– Connect standard impedance and measure size of step reflected from standard impedance R-STD as seen by TDR system over specified time zone

ZINT = ZSTD(R-OPEN - R-STD) / (R-OPEN + R-STD)

TDR Accuracy Improvement

2. Measure the DUT impedance against this interconnect impedance– Connect DUT and measure size of step reflected R-DUT

as seen by TDR systemR-DUT

intercon device

Open

ZDUT = ZINT(R-OPEN + R-DUT) / (R-OPEN - R-DUT)

What can comparative reflection do?

– Takes care of accuracy issues related to:– TDR system aberrations– Interconnect– Incident amplitude variance

– Must still be careful with:– Launch resistance– Launch inductance– Measurement zone movement

Launch Resistance

– Lumped and indiscernible from device impedance– Effect is additive, always positive, and similar to

an equal amount of reference level error

Incident Step

Step Generator

ReflectionsSampler

t = 050

Incident Step

Launch Resistance

– May not necessarily be repeatable– Is a problem with lower impedance levels, e.g.

28Rambus measurements– Most often is reasonable bounded (tens of m)

– Can be measured with 4-wire measurement - replicate several in series if necessary

– May be present in both signal and ground contacts

– Use of exchanged standard impedance will only cancel launch resistance if it is constant

Launch Inductance

– Caused by– Non-characteristic launches– Air gaps at launch– Contorted launch paths– Poor attention to ground attach

– Time constant is longer for smaller Z0

DUTZZ

L

0

0Z DUTZL

Launch Inductance

– May affect measurement zone– Lumped time constant decay usually lasts much longer

than propagation through inductance element– Multiple reflections carried into measurement zone– If C present, may have second order ring (though

usually only a larger ZDUT is more vulnerable)

– May be partially compensated– Must be absolutely repeatable attach geometry

– Standard impedance Z0 must be very close to ZDUT

Launch Inductance

Launch from 0.141” semi-rigid coax to microstrip through center and ground wires, with gap

L-R: gap = 0/1/2/3 mm

Agenda





Simple Component Analysis

– High frequency behavior observed– Both lumped and distributed nature observed

– Can derive equivalent C, L, Z0, t values to put into simulation

– Can verify physical location of discontinuity

Limits:– First or most significant discontinuity only

Shunt Capacitance and Series Inductance Discontinuities

Shunt Capacitance Discontinuity

Series Inductance Discontinuity

Z0 C

Z0

L

Z0

Z0

L

thru

thru

seconds)-in (Area

2

0

Z

AreaC

C

AreaZL 02

Capacitive and Inductive Terminations

Capacitor Load Termination

Inductor Load Termination

Z0 C

Z0 L

open

short

C

L

02 Z

AreaC

20 AreaZ

L

Distributed Discontinuities

– Over short distances (</10), distributed discontinuities may be treated as an equivalent lumped L or C

– Impedance looking in is given by Richard’s transform

j

ZZ

ZZZZ

L

Lin

)sinh()cosh(

)sinh()cosh(

0

00

Z0, ZLZin

Distributed Discontinuities

CapacitiveDiscontinuity

InductiveDiscontinuity

Z

Time

100

50

0

incident

Z0Z0 Z0

1

1

2Z

tCeq 2

22tZLeq

Z1Z2

t1 t2

Z1

Z2

Agenda





Problem of Backscatter

– At any given point in time, TDR trace is by nature a net reflection superposition tool, not a true impedance profile

– Multiple reflections occur between downstream discontinuities and confuse true reflection

– Always has the effect of smearing discontinuities out longer in time

– Resolution may be lost due to rise time degradation

Problem of Backscatter

– Caused by superposition of multiple reflections– Can be sorted out by pulse-bounce diagram

Time

Z1 Z2 Z3 Z4 Z0Z0

Advanced Component Analysis

– Solve backscatter problem first, then impedance profile matches 1:1 with circuit Z

– Not limited to first or most significant discontinuity– Has all advantages listed under simple component

analysis– Can window out and disregard portions of

impedance profile that is not of interest


– Impedance profile can be deconvolved with DSP– Upper-triangular system matrix is well-conditioned

for stable solution– Tektronix used to offer product that does this;

outside vendor now offers product– Also converts impedance profile to either short

transmission line sections, or equivalent shunt capacitance and series inductance discontinuities, for insertion into simulator


Z1 Z2 Z3 Z4 Z0Z0

Z100

50

0

Impedance profile

L1

Z0Z0

Agenda





– 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

reflected

+ 1

0

- 1

t0 t1

incident

incident

reflected

V

V

Characteristic (Z = Z0)

Amplitude

TDT Transmitted Units Definition

Time

transmitted

+ 1

0

- 1

t0 t1

1incident

reflectedincident

V

VV

Amplitude

Vtransmitted = Vincident + Vreflected

reflected

incident

TDT Example

- - Z Relationship

Where or is directly indicated by the oscilloscopeZ represents the test impedanceZ0 is the reference impedance

0

0

ZZ

ZZ

1

10ZZ

0

2

ZZ

Z

20ZZ

Crosstalk

– The coupling of energy from one line to another– Three Elements Contribute to Crosstalk:

– Port terminations– 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– Observe victim lines with TDT– Take care to terminate all other lines

TDR1

2

+DUT

50

50

Crosstalk Example

Crosstalk between adjacent 50 runs on FR4 withW=2.5 mmS=2 mmFar end 50 terminations

Aggressor: 200 m/divVictim: 4%/div

Crosstalk

– Adjacent microstrips and striplines will always crosstalk to a degree if fringing fields overlap

– Impedance measurements include loading of adjacent lines, whether intended or not

– Three key questions:– Is the geometry measured representative of the geometry

in the application?– Are the port terminations of adjacent lines representative?– Are the driving conditions of adjacent lines representative?

Agenda





Types of Coupled Lines

– Symmetric Coupled Lines - “Differential” or "Balanced"– Homogeneous– Inhomogeneous

– Non-Symmetric Coupled Lines - “Unbalanced”

R

R

Odd and Even Mode Propagation

+ + +-Odd Mode Even Mode

Definitions - Symmetric

– 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 and 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)

Models for Symmetric Coupled Lines

Pi Tee

Ra

RbRb R2

R1 R1

Odd Mode Characterization

Ra/2 R1 R1Ra/2

Zodd = (Ra/2)|| Rb

+-

+-

Pi Tee

RbRb R2

Zodd =R1

Even Mode Characterization

2R2

R1

Zeven = R1 + 2R2

2R2

R1Ra

+-

+-

Pi Tee

Rb

Zeven =Rb

Rb

Model Values

Pi

Tee

2oddeven ZZ

oddeven

oddeven

ZZ

ZZ

2

evenZ

oddZ oddZ

evenZ

oddeven

oddeven

ZZ

ZZ

edunterminatcrosstalk reverse

Measurement Environment

Pi

Tee

2oddeven ZZ

oddeven

oddeven

ZZ

ZZ

2

evenZ

oddZ oddZ

evenZ

0Z

0Z

0Z

0Z

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

Model Values

Pi

Tee

56.0

658.6

47.85

56.0

47.85

4.08

Zeven = 56.0Zodd = 47.85

Higher Order Systems of Lines

Z30Z20

Z34

Z10

Z12

Z40

Z23

– n coupled lines produce n orthogonal modes of propagation

– Requires n(n+1)/2 resistors to describe coupling network and for characteristic termination

– May have n velocities of propagation

Z13

Z24Z14

Agenda





TDR and VNA Derived s-parameters

– Vector Network Analyzer (VNA) measures scattering parameters using a swept CW sinusoidal stimulus and relative magnitude and phase measurements on incident and reflected signals that are picked off with directional couplers

– TDR and TDT measure reflection and transmission parameters using step stimulus and voltage-time measurements on superpositioned incident and reflected signals

TDR and VNA Derived s-parameters

– But they can be correlated:

dt

dffts

dt

dffts inc

21

11

Questions?

px tdr measurement theory and techniques john rettig [email protected] (503)-627-3232

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