PX TDR Measurement Theory and Techniques John Rettig (503)

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 = 0 50  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 V reflected + 1  0  - 1  t0t0 t1t1 V incident Characteristic (Z = Z 0 ) Amplitude V reflected

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 , Z 0 Step Source Forward Z = Z 0 Z > Z 0 Incident Reflected Discontinuity

 - Z Relationship Where  is directly indicated by the oscilloscope Z represents the test impedance Z 0 is the reference impedance

TDR Waveforms –TDR systems observe the superposition of incident and reflected signals at source –Time separation t 1 -t 0 assures ability to discern difference Time  reflected + 1  0  - 1  t0t0 t1t1 Amplitude  incident =+1

TDR Waveforms TDR Waveforms - Open, Short and 50  terminations Amplitude Open (Z =  ) (Z = 50  ) Short (Z = 0) Time  reflected =  0  - 1  t0t0 t1t1  incident =+1  reflected =-1

Measuring Impedance

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 

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 Step Source Forward Z = Z 0 Z 1 > Z 0 Incident Reflected Z 1 > Z 2 > Z 0

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

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 ps round-trip travel (35 ps 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 (Z  Z 0 )

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 Z 1, t D Z0Z0 Z0Z0 Displayed Time  t 01 t 12 t r(system) 2t D

TDR Resolution –First discontinuity reflection is witnessed at t 01 –Twice the one way propagation delay t D between discontinuities elapses –Second discontinuity reflection is witnessed at t 02 –Ideally, leading corner of reflection from second discontinuity arrives back at first discontinuity no earlier than lagging corner of reflection from first discontinuity, thus

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:

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

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-STD intercon standard Open –Connect standard impedance and measure size of step reflected from standard impedance  R-STD as seen by TDR system over specified time zone Z INT = Z STD (  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 system  R-DUT intercon device Open Z DUT = Z INT (  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 Reflections Sampler t = 0 50  Incident Step

Launch Resistance –May not necessarily be repeatable –Is a problem with lower impedance levels, e.g. 28  Rambus 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 Z 0

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 Z DUT is more vulnerable) –May be partially compensated –Must be absolutely repeatable attach geometry –Standard impedance Z 0 must be very close to Z DUT

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 –TDR Overview –TDR Accuracy Issues –Comparative Reflection Technique –Simple Component Characterization –Advanced Component Characterization –TDT and Crosstalk –Coupled Transmission Lines –TDR and Scattering Parameters

Simple Component Analysis –High frequency behavior observed –Both lumped and distributed nature observed –Can derive equivalent C, L, Z 0, 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 Z0Z0 C Z0Z0 L Z0Z0 Z0Z0 L thru C

Capacitive and Inductive Terminations Capacitor Load Termination Inductor Load Termination Z0Z0 C Z0Z0 L open short C 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 Z 0,  ZLZL Z in

Distributed Discontinuities Capacitive Discontinuity Inductive Discontinuity Z Time incident Z0Z0 Z0Z0 Z0Z0 Z1Z1 Z2Z2 t1t1 t2t2 Z1Z1 Z2Z2

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

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 Z1Z1 Z2Z2 Z3Z3 Z4Z4 Z0Z0 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

Advanced Component Analysis –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

Advanced Component Analysis Z1Z1 Z2Z2 Z3Z3 Z4Z4 Z0Z0 Z0Z0 Z Impedance profile L1L1 Z0Z0 Z0Z0

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

–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  t0t0 t1t1  incident Characteristic (Z = Z 0 ) Amplitude

TDT Transmitted Units Definition Time  transmitted + 1  0  - 1  t0t0 t1t1 Amplitude V transmitted = V incident + V reflected  reflected  incident

TDT Example

 -  - Z Relationship Where  or  is directly indicated by the oscilloscope Z represents the test impedance Z 0 is the reference impedance

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 TDR DUT 50 

Crosstalk Example Crosstalk between adjacent 50  runs on FR4 with W=2.5 mm S=2 mm Far end 50  terminations Aggressor: 200 m  /div Victim: 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 –TDR Overview –TDR Accuracy Issues –Comparative Reflection Technique –Simple Component Characterization –Advanced Component Characterization –TDT and Crosstalk –Coupled Transmission Lines –TDR and Scattering Parameters

Types of Coupled Lines –Symmetric Coupled Lines - “Differential” or "Balanced" –Homogeneous –Inhomogeneous –Non-Symmetric Coupled Lines - “Unbalanced” RR RR

Odd and Even Mode Propagation Odd ModeEven Mode

Definitions - Symmetric –Z odd 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) –Z even 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 PiTee RaRa RbRb RbRb R2R2 R1R1 R1R1

Odd Mode Characterization R a /2 R1R1 R1R1 Z odd = (R a /2)|| R b Pi Tee RbRb RbRb R2R2 Z odd =R 1

Even Mode Characterization 2R 2 R1R1 Z even = R 1 + 2R 2 2R 2 R1R1 RaRa Pi Tee RbRb Z even =R b RbRb

Model Values Pi Tee

Measurement Environment Pi Tee

Symmetric Line Example Symmetric coupled lines on FR-4 w = 2.5 mm s = 2 mm h = 1.5 mm Z even = 56.0 Z odd = 47.85

Model Values Pi Tee Z even = 56.0 Z odd = 47.85

Higher Order Systems of Lines Z 30 Z 20 Z 34 Z 10 Z 12 Z 40 Z 23 –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 Z 13 Z 24 Z 14

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

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:

Questions?