using transmission lines iii – class 7 purpose – consider finite transition time edges and gtl....

Using Transmission Lines III – class 7

Purpose – Consider finite transition time edges and GTL.

Acknowledgements: Intel Bus Boot Camp: Michael Leddige

Using Transmission Lines

2

Agenda Source Matched transmission of signals

with finite slew rate Real Edges Open and short transmission line analysis

for source matched finite slew rates GTL Analyzing GTL on a transmission line Transmission line impedances DC measurements High Frequency measurements


3

Introduction to Advanced Transmission Line Analysis

Propagation of pulses with non-zero rise/fall times

Introduction to GTL current mode analysis

Propagation of pulses with non-zero rise/fall times

Introduction to GTL current mode analysis

Now the effect of rise time will be discussed with the use of ramp functions to add more realism to our analysis. Finally, we will wrap up this class with an example from Intel’s main processor bus and signaling technology.

Now the effect of rise time will be discussed with the use of ramp functions to add more realism to our analysis. Finally, we will wrap up this class with an example from Intel’s main processor bus and signaling technology.


4

Ramp into Source Matched T- line Ramp function is step

function with finite rise time as shown in the graph.

The amplitude is 0 before time t0

At time t0 , it rises with straight-line with slopeAt time t1 , it reaches final amplitude VA

Thus, the rise time (TR) is equal to t1 - t0 .The edge rate (or slew rate) is

VA /(t1 - t0 )

t0 t1

VA

Z0 ,T0

V1 V2

l

I2I1

VS

RS

T = T0l


5

Ramp into Source Matched T- line

t0 t1

VA

Z0 ,T0

V1 V2

l

I2I1

VS

RS

T = T0l


6

Ramp FunctionRamp function is step function

with finite rise time as shown in the graph.

The amplitude is 0 before time t0

At time t0 , it rises with straight-line with slopeAt time t1 , it reaches final amplitude VA

Thus, the rise time (TR) is equal to t1 - t0 .

The edge rate (or slew rate) is VA /(t1 - t0 )


7

Ramp Cases

When dealing with ramps in transmission line networks, there are three general cases:

Long line (T >> TR)

Short line (T << TR)

Intermediate (T ~ TR)


8

Real Edges

risetime

ns0.5risetime t

i_thresholds1 i_thresholds0 ti_thresholds0 i_thresholds hist threshold a( )

define 10 and 90% thresholdsthreshold2

.9 Athreshold1

.1 A

Neat trick to find rise time

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

time in nanoseconds

Am

plitu

de

bi

A ai

ai

A 1 e

sajf

rti

n

Define Wave signal vs. time array

sajf .849n 3A 1r .5 nsSpec Slew Adj FctrSpec WaveshapeSpec amplitudeSpecify Rise Time

ns 109

secti

tmintmax

imaxii 0 imaximax 1000tmax 1.5 nstmin 0 ns ps 10

12sec

Set up time array

Assignment: Find sajf for a Gaussian and capacitive edge


9

Short Circuit Case

Next stepReplace the step function response with one modified with a finite rise timeThe voltage settles before the reflected wave is encountered.

Volt

age (V

)

2T Time (ns)3TT 4T0

0.5VA

0.25VA

VA

0.75VA

V1

V2

Current (A

)

2T Time (ns)3TT 4T0

0.5IA

0.25IA

IA

0.75IA

I1

I2

Current

Voltage


10

Open Circuit with Finite Slew RateC

urr

en

t (A

)

2T Time (ns)3TT 4T0

0.5IA

0.25IA

IA

0.75IA

I1

I2

TR

TR

TR

Volt

ag

e (

V)

2T Time (ns)3TT 4T0

0.5VA

0.25VA

VA

0.75VA

V1

V2

TR

TR

Current

Voltage


11

Consider the Short Circuit CaseVoltage and current waveforms are

shown for the step function as a refresher

Below that the ramp case is shownBoth the voltages and currents

waveforms are shown with the rise time effect

For example I2 doubles at the load end

in step case, instantaneouslyin the ramp case, it takesTR


12

Ramp into Source Matched Short T-line

Very interesting caseInteraction between rising edge and reflectionsReflections arrive before the applied voltage reaches target amplitude

Again, let us consider the short circuit case

Let TR = 4TThe voltage at the source (V1) end is plotted

showing comparison between ramp and step

The result is a waveform with three distinct slopesThe peak value is 0.25VA

Solved with simple geometry

and algebra

Z0 ,T0

V1 V2

L, T

I2I1

VS Short

RS

VRamp

VStep

Volta

ge (V

)

4TTime (ns)

6T2T 8T0

0.25VA

0.125VA

0.5VA

0.375VA

TR


13Ramp into a Source Matched, Intermediate Length T-Line

For the intermediate length transmission line, let the TR = 2T

The reflected voltage arrives at the source end the instant the input voltage has reached target peak

The voltage at the source (V1) end is plotted for two cases

comparison between ramp and step Short circuit case

Negative reflected voltage arrives and reduces the amplitude until zeroThe result is a sharp peak of value 0.5VA

Open circuit casePositive reflected voltage arrives and increases the amplitude to VA

The result is a continuous, linear lineV

olta

ge (V

)

2TTime (ns)

3TT 4T0

0.25VA

0.125VA

0.5VA

0.375VA

VRamp

VStep

TR

Vol

tage

(V

)

2T Time (ns)3TT 4T0

0.5VA

0.25VA

VA

0.75VA

VRamp

VStep

TR

Short Circuit Case

Open Circuit Case


14

Gunning Transistor Logic (GTL)

Chip (IC)Chip (IC)V

Voltage source is outside of chip Reduces power pins and chip power dissipation “Open Drain” circuit Related to earlier open collector switching Can connect multiple device to same. Performs a “wire-or” function Can be used for “multi-drop bus”


15Basics of GTL signaling – current mode transitions

Zo

Vtt

R(n)

Rtt

Steady state low

)(nRRtt

VttIL

Zo

Vtt

R(n)

Rtt

Switch opens

ZoIV Lstep

Zo

Vtt

R(n)

Rtt

Steady state high

VttV

Zo

Vtt

R(n)

Rtt

Switch closes

)(nRZo

ZoVttVstep

)(

)(

nRRtt

nRVttVL

Low to High High to Low

Lstep VZoRtt

ZoRttVV

1

ZoRtt

ZoRttVVttV step 1


16

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

0 2 4 6 8 10 12

Time, ns

Vo

lts

V(b)V(a)

50 ohms

1.5 V

12 Ohms

70 ohmsV(a)

V(b)

VVL 219.01270

125.1

VmA

ZoIVVVV LLstepLriseaV

13.1)5029.18()219.0(

_)(

VV fallbV 088.05070

50701

1250

505.15.1_)(

29.01250

505.15.1_)(

fallaVV

VmAV risebV 29.1219.05070

507015029.18_)(

Basics of current mode transitions - Example

mAIL 29.181270

5.1


17

GTL, GTL+ BUS LOW to HIGH TRANSITIONEND AGENT DRIVING - First reflection

IL = Low steady state currentVL = Low steady state voltageVdelta = The initial voltage step launched onto the lineVinitial = Initial voltage at the driverT = The transmission coefficient at the stub

Ldelta

Ldelta

Ldeltainitial

stub

stub

LLdelta

L

L

VZoRtt

ZoRttVTBV

VVTAV

VVV

T

ZoZsZo

ZoZsZoRttZo

RttZoIRttZoIV

nRRtt

nRVttV

nRRtt

VttI

1)(

2)(

1

||

||

||

)(21

)(

)(21

@

@

Vtt Vtt

R(n)

Rtt Rtt

Zo

ZsV(A)

V(B)

Notice termination was added at the source

Why?


18GTL, GTL+ BUS HIGH to LOW TRANSITIONEND AGENT DRIVING - First reflection

IL = Low steady state currentVL = Low steady state voltageVdelta = Initial voltage launched onto the lineVinitial = Initial voltage at the driverT = The transmission coefficient at the stub

ZoRtt

ZoRttVTVttBV

VTVttAV

VVttV

T

ZoZsZo

ZoZsZo

nRZoRtt

ZoRttVttV

nRRtt

nRVttV

delta

delta

deltainitial

stub

stub

delta

L

1)(

2)(

1

||

||

)(||

||

)(21

)(

@

@

R(n)

Vtt Vtt

Rtt Rtt

Zo

ZsV(A)

V(B)


19Transmission Line Modeling Assumptions

All physical transmission have non-TEM characteristic at some sufficiently high frequency.

Transmission line theory is only accurate for TEM and Quasi-TEM channels

Transmission line assumption breaks down at certain physical junctions

Transmission line to loadTransmission line to transmission lineTransmission line to connector.

AssignmentElectrically what is a connector (or package)?Electrically what is a via? I.e. via modeling

PWB through viasPackage blind and buried vias


20Driving point impedance – freq. domain

Telegraphers formulaDriving point impedanceMathCAD and investigation

R, L, C, G per unit length

Rdie CdieZin


21

Driving Point Impedance Example

Set up Frequency Range For Plotting

Zin Zl Zo l ZoZl cos l j Zo sin l

Zo cos l j Zl sin l nl 100 nf 0 nl 1 fmin 1MHz fmax 1GHz freq

nffmin

fmax fmin( ) nfnl

Linear Lossy Transmission Line Parameters L 11nH

in C 4.4

pF

in R .2

in

G 1014 mho

in Characteristic Impedance

Z0 f( )L j 2 f R

C j 2 f GLoad ImpedanceCdie 1pF Rdie 40ohm Z1 f( ) par ZC Cdie f( ) Rdie( )

Expand and impedances to define driving point Impecnace

Zin er len f( ) Z0 f( )

Z1 f( ) cos 2 f

Vc er

1

2

len

i Z0 f( ) sin 2 f

Vc er

1

2

len

Z0 f( ) cos 2 f

Vc er

1

2

len

i Z1 f( ) sin 2 f

Vc er

1

2

len

0 2 108

4 108

6 108

8 108

1 109

20

40

60

80

Zin r 10in freqnf

freqnf

Physical Constants

ps 1012

sec ns 109

sec nH 109

henry h 106

henry 5.967107

mho

m o 4.0 10

7

henry

m r 1 o r r 4.3

Propagation Constant Speed of light Vc 3 108

m

sec

Function for parallel circuit:par a b( )a b

a b Cap function ZC Cx f( )

1

j 2 f Cx

Tpd1

Vcr f( ) 2 f Tpd Tpd 2.107

ns

ft

Input Impedance of a Transmission Line


22

Measurement – DC (low frequency)

UNKI

OhmMeter

Measure V

I*r=ERROR

UNKI

OhmMeter

Measure V4 Wire or

Kelvin measurement eliminates error

Calibration Method

Z=(V_measure-V_short)/I

2 Wire Method


23

High Frequency Measurement

At high frequencies 4 wires are impractical. The 2 wire reduces to a transmission line The Vshort calibration migrates to

calibration with sweep of frequencies for selection of impedance loads.

Because of the nature of transmission lines illustrated in earlier slides

Vector Network Analyzers (VNAs) used this basic method but utilized s-parameters

More later on s parameters.


24

Assignment

Find driving point impedance vs. frequency of a short and open line

(a) Derive the equation(b) given L=10inch, Er=4, L=11 nH/in, C=4.4 pF/in, R=0.2 Ohm/in, G=10^(-14) Mho/in, plot the driving point impedance vs freq for short & open line. (Mathcad or Matlab)(c) Use Pspice to do the simulation and validate the result in (b)

using transmission lines iii – class 7 purpose – consider finite transition time edges and gtl....

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