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Agilent Specifying Calibration Standards for the Agilent 8510
Network Analyzer
Application Note 8510-5B
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IntroductionMeasurement errors Measurement calibration
Calibration kit Standard definition Class assignment Modification
procedure Select standards Define standards Standard number
Standard type
Open circuit capacitance: C0, C1, C2 and C3Short circuit
inductance: L0, L1, L2 and L3Fixed or sliding Terminal impedance
Offset delay Offset Z0Offset loss Lower/minimum frequency
Upper/maximum frequency Coax or waveguide Standard labels
Assign classes Standard classes S
11A,B,C and S
22A,B,C
Forward transmission match/thru Reverse transmission match/thru
Isolation Frequency response TRL Thru TRL Reflect TRL Line Adapter
Standard class labels TRL options Calibration kit label
Enter standards/classes Verify performance User modified cal
kits and Agilent 8510 specifications Modification examples Modeling
a thru adapter Modeling an arbitrary impedance Appendix A
Calibration kit entry procedure Appendix B Dimensional
considerations in coaxial connectors Appendix CCal coefficients
model
Table of contents
Known devices called calibration standardsprovide the
measurement reference for net-work analyzer error-correction. This
notecovers methods for specifying these stan-dards and describes
the procedures for theiruse with the Agilent Technologies 8510
net-work analyzer.
The 8510 network analyzer system has thecapability to make
real-time error-correctedmeasurements of components and devicesin a
variety of transmission media.Fundamentally, all that is required
is a setof known devices (standards) that can bedefined physically
or electrically and usedto provide a reference for the physical
inter-face of the test devices.
Agilent Technologies supplies full calibrationkits in 1.0-mm,
1.85-mm, 2.4-mm, 3.5-mm, 7-mm, and Type-N coaxial interfaces.
The8510 system can be calibrated in other inter-faces such as other
coaxial types, waveguideand microstrip, given good quality
stan-dards that can be defined.
The 8510s built-in flexibility for calibrationkit definition
allows the user to derive aprecise set of definitions for a
particular setof calibration standards from precise physi-cal
measurements. For example, the charac-teristic impedance of a
matched impedanceairline can be defined from its actual physi-cal
dimensions (diameter of outer and innerconductors) and electrical
characteristics(skin depth). Although the airline isdesigned to
provide perfect signal transmis-sion at the connection interface,
the dimen-sions of individual airlines will varysomewhatresulting
in some reflection dueto the change in impedance between the
testport and the airline. By defining the actualimpedance of the
airline, the resultantreflection is characterized and can beremoved
through measurement calibration.
The scope of this product note includes ageneral description of
the capabilities of the8510 to accept new cal kit descriptions
viathe MODIFY CAL KIT function found in the8510 CAL menu. It does
not, however,describe how to design a set of physicalstandards. The
selection and fabrication ofappropriate calibration standards is as
var-ied as the transmission media of the partic-ular application
and is beyond the scope ofthis note.
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3IntroductionThis product note covers measurement
calibrationrequirements for the Agilent 8510B/C networkanalyzer.
All of the capabilities described in thisnote also apply to the
Agilent 8510A with the following exceptions: response &
isolation calibra-tion; short circuit inductance; class
assignmentsfor forward/reverse isolation, TRL thru, reflect,line
and options; and adapter removal.
Measurement errorsMeasurement errors in network analysis can
beseparated into two categories: random and system-atic errors.
Both random and systematic errors arevector quantities. Random
errors are non-repeat-able measurement variations and are
usuallyunpredictable. Systematic errors are repeatablemeasurement
variations in the test setup.
Systematic errors include mismatch and leakagesignals in the
test setup, isolation characteristicsbetween the reference and test
signal paths, andsystem frequency response. In most
microwavemeasurements, systematic errors are the most sig-nificant
source of measurement uncertainty. Thesource of these errors can be
attributed to the sig-nal separation scheme used.
The systematic errors present in an S-parametermeasurement can
be modeled with a signal flow-graph. The flowgraph model, which is
used for errorcorrection in the 8510 for the errors associated
withmeasuring the S-parameters of a two port device, isshown in the
figure below.
The six systematic errors in the forward directionare
directivity, source match, reflection tracking,load match,
transmission tracking, and isolation.The reverse error model is a
mirror image, giving atotal of 12 errors for two-port measurements.
Theprocess of removing these systematic errors fromthe network
analyzer S-parameter measurement iscalled measurement
calibration.
EDF, EDR-Directivity ELF, ELR-Load MatchESF, ESR-Source Match
ETF, ETR-Trans. TrackingERF, ERR-Refl. Tracking EXF,
EXR-Isolation
Measurement calibrationA more complete definition of measurement
cali-bration using the 8510, and a description of theerror models
is included in the 8510 operating andprogramming manual. The basic
ideas are summa-rized here.
A measurement calibration is a process whichmathematically
derives the error model for the8510. This error model is an array
of vector coeffi-cients used to establish a fixed reference plane
ofzero phase shift, zero magnitude and knownimpedance. The array
coefficients are computed bymeasuring a set of known devices
connected at afixed point and solving as the vector
differencebetween the modeled and measured response.
Figure 1. Agilent 8510 full 2-port error model
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4The array coefficients are computed by measuringa set of known
devices connected at a fixed pointand solving as the vector
difference between themodeled and measured response.
The full 2-port error model shown in Figure 1 is an example of
only one of the measurement calibra-tions available with the 8510.
The measurementcalibration process for the 8510 must be one ofseven
types: RESPONSE, RESPONSE & ISOLATION,Sll 1-PORT, S22 1-PORT,
ONE PATH 2-PORT, FULL2-PORT, and TRL 2-PORT. Each of these
calibrationtypes solves for a different set of the
systematicmeasurement errors. A RESPONSE calibrationsolves for the
systematic error term for reflec-tion or transmission tracking
depending on the S-parameter which is activated on the 8510 at
thetime. RESPONSE & ISOLATION adds correction for crosstalk to
a simple RESPONSE calibration.An S11 l-PORT calibration solves for
the forwarderror terms, directivity, source match and reflec-tion
tracking. Likewise, the S22 1-PORT calibrationsolves for the same
error terms in the reversedirection. A ONE PATH 2-PORT calibration
solvesfor all the forward error terms. FULL 2-PORT andTRL 2-PORT
calibrations include both forward andreverse error terms.
The type of measurement calibration selected bythe user depends
on the device to be measured(i.e., 1-port or 2-port device) and the
extent ofaccuracy enhancement desired. Further, a combi-nation of
calibrations can be used in the measure-ment of a particular
device.
The accuracy of subsequent test device measure-ments is
dependent on the accuracy of the testequipment, how well the known
devices are mod-eled and the exactness of the error
correctionmodel.
Calibration kitA calibration kit is a set of physical devices
calledstandards. Each standard has a precisely known orpredictable
magnitude and phase response as afunction of frequency. In order
for the 8510 to usethe standards of a calibration kit, the response
ofeach standard must be mathematically defined andthen organized
into standard classes which corre-spond to the error models used by
the 8510.Agilent currently supplies calibration kits with 1.0-mm
(85059A), 1.85-mm (85058D), 2.4-mm(85056A/D/K), 3.5-mm
(85052A/B/C/D/E), 7-mm(85050B/C/D) and Type-N (85054B) coaxial
con-nectors. To be able to use a particular calibrationkit, the
known characteristics from each standardin the kit must be entered
into the 8510 non-volatile memory. The operating and service
manu-als for each of the Agilent calibration kits containthe
physical characteristics for each standard inthe kit and
mathematical definitions in the formatrequired by the 8510.
Waveguide calibration using the 8510 is possible.Calibration in
microstrip and other non-coaxialmedia is described in Agilent
Product Note 8510-8A.
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5Standard definitionStandard definition is the process of
mathematical-ly modeling the electrical characteristics
(delay,attenuation and impedance) of each calibrationstandard.
These electrical characteristics can bemathematically derived from
the physical dimen-sions and material of each calibration standards
orfrom its actual measured response. A standard definition table
(see Table 1) lists the parametersthat are used by the 8510 to
specify the mathemati-cal model.
Class assignmentClass assignment is the process of organizing
cali-bration standards into a format which is compati-ble with the
error models used in measurementcalibration. A class or group of
classes correspondto the seven calibration types used in the
8510.The 17 available classes are identified later in thisnote (see
Assign classes).
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6Table 1. Standard definitions table
Table 2. Standard class assignments
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7Modification procedureCalibration kit modification provides the
capabilityto adapt to measurement calibrations in other con-nector
types or to generate more precise errormodels from existing kits.
Provided the appropri-ate standards are available, cal kit
modificationcan be used to establish a reference plane in thesame
transmission media as the test devices and ata specified point,
generally the point of device con-nection/insertion. After
calibration, the resultantmeasurement system, including any
adapterswhich would reduce system directivity, is fully cor-rected
and the systematic measurement errors aremathematically removed.
Additionally, the modifi-cation function allows the user to input
more pre-cise physical definitions for the standards in agiven cal
kit. The process to modify or create a calkit consists of the
following steps:
1. Select standards2. Define standards3. Assign classes4. Enter
standards/classes5. Verify performance
To further illustrate, an example waveguide cali-bration kit is
developed as the general descriptionsin MODIFY CAL KIT process are
presented.
Select standardsDetermine what standards are necessary for
cali-bration and are available in the transmissionmedia of the test
devices.
Calibration standards are chosen based on the fol-lowing
criteria:
A well defined response which is mechanicallyrepeatable and
stable over typical ambient tem-peratures and conditions. The most
commoncoaxial standards are zero-electrical-lengthshort, shielded
open and matched load termina-tions which ideally have fixed
magnitude andbroadband phase response. Since waveguideopen circuits
are generally not modelable, thetypes of standards typically used
for waveguidecalibration are a pair of offset shorts and a fixedor
sliding load.
A unique and distinct frequency response. Tofully calibrate each
test port (that is to providethe standards necessary for S11 or S22
1-PORTcalibration), three standards are required thatexhibit
distinct phase and/or magnitude at eachparticular frequency within
the calibrationband. For example, in coax, a zero-length shortand a
perfect shielded open exhibit 180 degreephase separation while a
matched load will pro-vide 40 to 50 dB magnitude separation
fromboth the short and the open. In waveguide, apair of offset
shorts of correct length providephase separation.
Broadband frequency coverage. In broadbandapplications, it is
often difficult to find stan-dards that exhibit a known, suitable
responseover the entire band. A set of frequency-bandedstandards of
the same type can be selected inorder to characterize the full
measurementband.
The TRL 2-PORT calibration requires only a sin-gle precision
impedance standarda transmis-sion line. An unknown high reflection
deviceand a thru connection are sufficient to completethis
technique.
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8Define standardsA glossary of standard definition parameters
usedwith the Agilent 8510 is included in this section.Each
parameter is described and appropriate con-versions are listed for
implementation with the8510. To illustrate, a calibration kit for
WR-62 rec-tangular waveguide (operating frequency range12.4 to 18
GHz) will be defined as shown in Table1. Subsequent sections will
continue to developthis waveguide example.
The mathematical models are developed for eachstandard in
accordance with the standard defini-tion parameters provided by the
8510. These stan-dard definition parameters are shown in Figure
2.
Figure 2. Standard definition models
Model for reflection standard(short, open, load or
arbitraryimpedance)
Model for transmission standard (Thru)
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9Each standard is described using the StandardDefinition Table
in accordance with the 1- or 2-port model. The Standard Definition
table for awaveguide calibration kit is shown in Table 1.
Eachstandard type (short, open, load, thru, and arbi-trary
impedance) may be defined by the parame-ters as specified
below.
Standard number and standard type Fringing capacitance of an
open, or inductance
of a short, specified by a third order polynomial Load/arbitrary
impedance, which is specified as
fixed or sliding Terminal resistance of an arbitrary impedance
Offsets which are specified by delay, Z0, Rloss Frequency range
Connector type: coaxial or waveguide Label (up to 10 alphanumeric
characters)
Standard numberA calibration kit may contain up to 21
standards(See Table 1). The required number of standardswill depend
on frequency coverage and whetherthru adapters are needed for sexed
connectors.
For the WR-62 waveguide example, four standardswill be
sufficient to perform the FULL 2-PORT cali-bration. Three
reflection standards are required,and one transmission standard (a
thru) will be suf-ficient to complete this calibration kit.
Standard typeA standard type must be classified as a shortopen,
load, thru, or arbitrary impedance.The associated models for
reflection standards(short, open, load, and arbitrary impedance)
andtransmission standards (thru) are shown in Figure 1.
For the WR-62 waveguide calibration kit, the fourstandards are a
1/8 and 3/8 offset short, a fixedmatched load, and a thru. Standard
types areentered into the Standard Definition table underSTANDARD
NUMBERS 1 through 4 as short, short,load, and thru
respectively.
Open circuit capacitance: C0 , C1 , C2 and C3If the standard
type selected is an open, the C0through C3 coefficients are
specified and then usedto mathematically model the phase shift
caused byfringing capacitance as a function of frequency.
As a reflection standard, an open offers theadvantage of
broadband frequency coverage, whileoffset shorts cannot be used
over more than anoctave. The reflection coefficient ( = pe-je) of
aperfect zero-length-open is 1 at 0 for all frequen-cies. At
microwave frequencies however, the magni-tude and phase of an open
are affected by theradiation loss and capacitive fringing
fields,respectively. In coaxial transmission media, shield-ing
techniques are effective in reducing the radia-tion loss. The
magnitude (p) of a zero-lengthopen is assigned to be 1 (zero
radiation loss) forall frequencies when using the Agilent
8510Standard Type open.
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10
It is not possible to remove fringing capacitance,but the
resultant phase shift can be modeled as afunction of frequency
using C0 through C3 (C0 +Clx f + C2 x f2 + C3 x f3,with units of
F(Hz), C0(fF),C1(10-27F/Hz), C2(10-36F/Hz2) and
C3(10-45F/Hz3),which are the coefficients for a cubic
polynomialthat best fits the actual capacitance of the open.
A number of methods can be used to determine thefringing
capacitance of an open. Three tech-niques, described here, involve
a calibrated reflec-tion coefficient measurement of an open
standardand subsequent calculation of the effective capaci-tance.
The value of fringing capacitance can be cal-culated from the
measured phase or reactance as afunction of frequency as
follows.
Ceff effective capacitance measured phase shiftf measurement
frequencyF faradZ0 characteristic impedanceX measured reactance
This equation assumes a zero-length open. Whenusing an offset
open the offset delay must bebacked-out of the measured phase shift
to obtaingood C0 through C3 coefficients.
This capacitance can then be modeled by choosingcoefficients to
best fit the measured responsewhen measured by either method 3 or 4
below.
1. Fully calibrated 1-PortEstablish a calibratedreference plane
using three independent standards(that is, 2 sets of banded offset
shorts and load).Measure the phase response of the open and
solvefor the capacitance function.
2. TRL 2-PORTWhen transmission lines standardsare available,
this method can be used for a com-plete 2-port calibration. With
error-correctionapplied the capacitance of the open can be
meas-ured directly.
3. GatingUse time domain gating to correct themeasured response
of the open by isolating thereflection due to the open from the
source matchreflection and signal path leakage (directivity).
Figure 3 shows the time domain response of theopen at the end of an
airline. Measure the gatedphase response of the open at the end of
an airlineand again solve for the capacitance function.
tan( )2
2fZ01
2fXCeff = =
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11
NoteIn some cases (when the phase response is linearwith respect
to frequency) the response of an opencan be modeled as an
equivalent incrementallength.
This method will serve as a first order approxima-tion only, but
can be useful when data or stan-dards for the above modeling
techniques are notavailable.
For the waveguide example, this parameter is notaddressed since
opens cannot be made valid stan-dards in waveguide, due to the
excessive radiationloss and indeterminant phase.
Short circuit inductance L0 , L1, L2 and L3If the standard type
selected is a short, the L0through L3 coefficients are specified to
model thephase shift caused by the standards residualinductance as
a function of frequency. The reflec-tion coefficient of an ideal
zero-length short is 1 at180 at all frequencies. At microwave
frequencies,however, the residual inductance can produceadditional
phase shift. When the inductance isknown and repeatable, this phase
shift can beaccounted for during the calibration.
Figure 3. Time domain response of open at the end of an
airline
2f (length)c
(radians) =
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The inductance as a function of frequency can bemodeled by
specifying the coefficients of a third-order polynomial (L0 + L1 x
f + L2 x f2 + L3 x f3),with units of L0(nH), L1(10-24H/Hz),
L2(10-33 H/Hz2) and L3(10-42H/Hz3).
For the waveguide example, the inductance of theoffset short
circuits is negligible. L0 through L3 areset equal to zero.
Fixed or slidingIf the standard type is specified to be a load
or anarbitrary impedance, then it must be specified asfixed or
sliding. Selection of sliding provides asub-menu in the calibration
sequence for multipleslide positions and measurement. This enables
cal-culation of the directivity vector by mathematicallyeliminating
the response due to a non-ideal termi-nal impedance. A further
explanation of this tech-nique is found in the Measurement
Calibration section in the Agilent 8510 Operating andProgramming
manual.
The load standard #4 in the WR-62 waveguide cali-bration kit is
defined as a fixed load. Enter FIXEDin the table.
Terminal impedanceTerminal impedance is only specified for
arbitraryimpedance standards. This allows definition ofonly the
real part of the terminating impedance inohms. Selection as the
standard type short,open, or load automatically assigns the
termi-nal impedance to be 0, or 50 ohms respectively.
The WR-62 waveguide calibration kit example doesnot contain an
arbitrary impedance standard.
Offset delayIf the standard has electrical length (relative to
thecalibration plane), a standard is specified to havean offset
delay. Offset delay is entered as the one-way travel time through
an offset that can beobtained from the physical length using
propaga-tion velocity of light in free space and the appro-priate
permittivity constant. The effectivepropagation velocity equals .
See Appendix Bfor a further description of physical offset
lengthsfor sexed connector types.
Delay (seconds) =
= precise measurement of offset length in metersr = relative
permittivity (= 1.000649 for coaxial
airline or air-filled waveguide in standard labconditions)
c = 2.997925 x 108 m/s
In coaxial transmission line, group delay is con-stant over
frequency. In waveguide however, groupvelocity does vary with
frequency due to disper-sion as a function of the cut-off
frequency.
r c
12
cr
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13
The convention for definition of offset delay inwaveguide
requires entry of the delay assuming nodispersion. For waveguide
transmission line, theAgilent 8510 calculates the effects of
dispersion asa function of frequency as follows:
fco = lower cutoff frequencyf = measurement frequency
NoteTo assure accurate definition of offset delay, aphysical
measurement of offset length is recom-mended.
The actual length of offset shorts will vary by man-ufacturer.
For example, the physical length of a 1/8 offset depends on the
center frequency chosen.In waveguide this may correspond to the
arith-metic or geometric mean frequency. The arithmeticmean
frequency is simply (F1 + F2)/2, where F1 andF2 are minimum and
maximum operating frequen-cies of the waveguide type. The geometric
meanfrequency is calculated as the square root of F1 xF2. The
corresponding (g) is then calculated fromthe mean frequency and the
cutoff frequency of thewaveguide type. Fractional wavelength
offsets arethen specified with respect to this wavelength.
For the WR-62 calibration kit, offset delay is zerofor the thru
(std #4) and the load (std #3). Tofind the offset delay of the 1/8
and 3/8 offsetshorts, precise offset length measurements are
nec-essary. For the 1/8 offset short, l = 3.24605 mm, r = 1.000649,
c = 2.997925 x 108m/s.
Delay =(3.24605 x 10 -3 m) (1.000649)
= 10.8309 pS2.997925 x 108 m/s
For the 3/8 offset short, I = 9.7377 mm, r = 1.000649, c =
2.997925 x 108 m/s.
Delay = (9.7377 x 10-3 m) (1.000649)
= 32.4925 pS2.997925 x 108 m/s
Offset Z0Offset Z0 is the characteristic impedance within
theoffset length. For coaxial type offset standards,specify the
real (resistive) part of the characteris-tic impedance in the
transmission media. The char-acteristic impedance in lossless
coaxialtransmission media can be calculated from itsphysical
geometry as follows.
Actual delay = Linear delay
1 - (fco/f)2
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r = relative permeability constant of the medium(equal to 1.0 in
air)r = relative permittivity constant of the medium(equal to
1.000649 in air)D = inside diameter of outer conductord = outside
diameter of inner conductor
The 8510 requires that the characteristic imped-ance of
waveguide transmission line is assigned tobe equal to the SET
Z0.
The characteristic impedance of other transmis-sion media is not
as easily determined throughmechanical dimensions. Waveguide
impedance, forexample, varies as a function of frequency. In
suchcases, normalized impedance measurements aretypically made.
When calibrating in waveguide, theimpedance of a matched load is
used as theimpedance reference. The impedance of this load
ismatched that of the waveguide across frequency.Normalized
impedance is achieved by entering SETZ0 and OFFSET Z0 to 1 ohm for
each standard.
Offset Z0 equal to system Z0 (SET Z0) is theassigned convention
in the 8510 for matched wave-guide impedance.
Offset lossOffset loss is used to model the magnitude loss dueto
skin effect of offset coaxial type standards only.The value of loss
is entered into the standard defi-nition table as gigohms/second or
ohms/nanosec-ond at 1 GHz.
The offset loss in gigohms/second can be calculat-ed from the
measured loss at 1 GHz and the physi-cal length of the particular
standard by thefollowing equation.
where:dBlOSS |1 GHz =measured insertion loss at 1 GHzZ0 = offset
Z0
= physical length of the offset
The 8510 calculates the skin loss as a function offrequency as
follows:
Note: For additional information refer to Appendix C.
For all offset standards, including shorts or opens,enter the
one way skin loss. The offset loss inwaveguide should always be
assigned zero ohms bythe 8510.
Z0 = = 59.9585 In
1
2
D
d
rr( ) In Dd( )
Offset loss = Gs 10 log
e(10) e
r1 GHz
dBloss 1 GHz C Z0( )
Offset loss X G
s 1GHzf(GHz) Offset loss
Gs
=( ) ( )
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15
Therefore, for the WR-62 waveguide standard defi-nition table,
offset loss of zero ohm/sec is enteredfor all four standards.
Lower/minimum frequencyLower frequency defines the minimum
frequency atwhich the standard is to be used for the purposesof
calibration.
NoteWhen defining coaxial offset standards, it may benecessary
to use banded offset shorts to specify asingle standard class. The
lower and upper fre-quency parameters should be used to indicate
thefrequency range of desired response. It should benoted that
lower and upper frequency serve a dualpurpose of separating banded
standards whichcomprise a single class as well as defining the
over-all applicable frequency range over which a cali-bration kit
may be used.
In waveguide, this must be its lower cut-off fre-quency of the
principal mode of propagation.Waveguide cutoff frequencies can be
found in mostwaveguide textbooks. The cutoff frequency of
thefundamental mode of propagation (TE10) in rectan-gular waveguide
is defined as follows.
f = c 2a
c = 2.997925 x 1010 cm/sec.a = inside width of waveguide, larger
dimension in cm
As referenced in offset delay, the minimum fre-quency is used to
compute the dispersion effects inwaveguide.
For the WR-62 waveguide example, the lower cutofffrequency is
calculated as follows.
f = c = 2.997925 x 1010 cm/s = 9.487 GHz
2a 2 x 1.58 cm
c = 2.997925 x 1010 cm/sa = 1.58 cm
The lower cut-off frequency of 9.487 GHz is enteredinto the
table for all four WR-62 waveguide standards.
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16
Upper/maximum frequencyThis specifies the maximum frequency at
whichthe standard is valid. In broadband applications, aset of
banded standards may be necessary to pro-vide constant response.
For example, coaxial offsetstandards (i.e., 1/4 offset short) are
generally spec-ified over bandwidths of an octave or less.Bandwidth
specification of standards, using mini-mum frequency and maximum
frequency, enablesthe 8510 to characterize only the specified
bandduring calibration. Further, a submenu for bandedstandards is
enabled which requires the user tocompletely characterize the
current measurementfrequency range. In waveguide, this is the
uppercutoff frequency for the waveguide class and modeof
propagation. For the fundamental mode of prop-agation in
rectangular waveguide the maximumupper cutoff frequency is twice
the lower cutofffrequency and can be calculated as follows.
F(upper) = 2 x F(lower)
The upper frequency of a waveguide standard mayalso be specified
as the maximum operating fre-quency as listed in a textbook.
The MAXIMUM FREQUENCY of the WR-62 wave-guide cal kit is 18.974
GHz and is entered into thestandard definition table for all four
standards.
Coax or waveguideIt is necessary to specify whether the
standardselected is coaxial or waveguide. Coaxial transmis-sion
line has a linear phase response as
Waveguide transmission line exhibits dispersivephase response as
follows:
where
Selection of WAVEGUIDE computes offset delayusing the dispersive
response, of rectangular wave-guide only, as a function of
frequency as
This emphasizes the importance of entering fco asthe LOWER
FREQUENCY.
Selection of COAXIAL assumes linear response ofoffset delay.
1-(fco/f)2 Delay (seconds) Linear delay =
1-(/co)2 g =
2(radians)g=
22f(delay)(radians) ==
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17
NoteMathematical operations on measurements (anddisplayed data)
after calibration are not correctedfor dispersion.
Enter WAVEGUIDE into the standard definitiontable for all four
standards.
Standard labelsLabels are entered through the title menu and
maycontain up to 10 characters. Standard Labels areentered to
facilitate menu driven calibration.Labels that describe and
differentiate each stan-dard should be used. This is especially
true formultiple standards of the same type.
When sexed connector standards are labeled, male(M) or female
(F), the designation refers to the testport connector sexnot the
connector sex of thestandard. Further, it is recommended that the
labelinclude information carried on the standard suchas the serial
number of the particular standard toavoid confusing multiple
standards which are simi-lar in appearance.
The labels for the four standards in the waveguideexample are;
#1-PSHORT1, #2-PSHORT2, #3-PLOAD,and #4-THRU.
Assign classesIn the previous section, define standards, the
characteristics of calibration standards werederived. Class
assignment organizes these stan-
dards for computation of the various error modelsused in
calibration. The Agilent 8510 requires afixed number of standard
classes to solve for the nterms used in the error models (n = 1, 3,
or 12).That is, the number of calibration error termsrequired by
the 8510 to characterize the measure-ment system (1-Port, 2-Port,
etc.) equals the num-ber of classes utilized.
Standard ClassesA single Standard Class is a standard or group
of(up to 7) standards that comprise a single calibra-tion step. The
standards within a single class areassigned to locations A through
G as listed on theClass Assignments table. It is important to
notethat a class must be defined over the entire fre-quency range
that a calibration is made, eventhough several separate standards
may be requiredto cover the full measurement frequency range. Inthe
measurement calibration process, the order ofstandard measurement
within a given class is notimportant unless significant frequency
overlapexists among the standards used. When two stan-dards have
overlapping frequency bands, the laststandard to be measured will
be used by the 8510.The order of standard measurement between
dif-ferent classes is not restricted, although the 8510requires
that all standards that will be used withina given class are
measured before proceeding tothe next class. Standards are
organized into speci-fied classes which are defined by a
StandardsClass Assignment table. See Table 2 for the
classassignments table for the waveguide calibration kit.
-
18
S11 A,B,C and S22 A,B,CS11 A, B,C and S22 A,B,C correspond to
the S11 andS22 reflection calibrations for port 1 and port
2respectively. These three classes are used by theAgilent 8510 to
solve for the systematic errors;directivity, source match, and
reflection tracking.The three classes used by the 7-mm cal kit
arelabeled short, open, and loads. Loads refersto a group of
standards which is required to com-plete this standard class. A
class may include a setof standards of which there is more than
oneacceptable selection or more than one standardrequired to
calibrate the desired frequency range.
Table 2 contains the class assignment for the WR-62 waveguide
cal kit. The 1/8 offset short (stan-dard #1) is assigned to S11A.
The 3/8 offset short(standard #2) is assigned to S11B. The
matchedload (standard #3) is assigned to S11C.
Forward transmission match and thruForward Transmission (Match
and Thru) classescorrespond to the forward (port 1 to port 2)
trans-mission and reflection measurement of thedelay/thru standard
in a FULL 2-PORT or ONE-PATH 2-PORT calibration. During
measurementcalibration the response of the match standard isused to
find the systematic Load Match error term.Similarly the response of
the thru standard is usedto characterize transmission tracking.
The class assignments for the WR-62 waveguide calkit are as
follows. The thru (standard #4) isassigned to both FORWARD
TRANSMISSION andFORWARD MATCH.
Reverse transmission match and thruReverse Transmission (Match
and Thru) classescorrespond to the reverse transmission and
reflec-tion measurement of the delay/thru standard.For S-parameter
test sets, this is the port 2 to port 1transmission path. For the
reflection/transmissiontest sets, the device is reversed and is
measured inthe same manner using the forward
transmissioncalibration.
The class assignments for the WR-62 waveguide calkit are as
follows. The thru (Standard #4) isassigned to both REVERSE
TRANSMISSION andREVERSE MATCH.
IsolationIsolation is simply the leakage from port 1 to port
2internal to the test set.
To determine the leakage signals (crosstalk), eachport should be
terminated with matched loadswhile measuring S21 and S12.
The class assignments for forward and reverse iso-lation are
both loads (standard #3).
Frequency responseFrequency Response is a single class which
corre-sponds to a one-term error correction that charac-terizes
only the vector frequency response of thetest configuration.
Transmission calibration typi-cally uses a thru and reflection
calibration typi-cally uses either an open or a short.
NoteThe Frequency Response calibration is not a sim-ple
frequency normalization. A normalizedresponse is a mathematical
comparison betweenmeasured data and stored data. The important
dif-ference is, that when a standard with non-zerophase, such as an
offset short, is remeasured aftercalibration using Frequency
Response, the actualphase offset will be displayed, but its
normalizedresponse would display zero phase offset (meas-ured
response minus stored response).
Therefore, the WR-62 waveguide calibration kit classassignment
includes standard #1, standard #2, andstandard #4.
-
19
TRL ThruTRL Thru corresponds to the measurement of
theS-parameters of a zero-length or short thru connec-tion between
port 1 and port 2. The Thru, Reflectand Line classes are used
exclusively for the threesteps of the TRL 2-PORT calibration.
Typically, adelay/thru with zero (or the smallest) OffsetDelay is
specified as the TRL Thru standard.
TRL ReflectTRL Reflect corresponds to the S11 and S22
meas-urement of a highly reflective 1-port device. TheReflect
(typically an open or short circuit) must bethe same for port 1 and
2. The reflection coeffi-cient magnitude of the Reflect should be
close to 1but is not specified. The phase of the
reflectioncoefficient need only be approximately specified(within
90 degrees).
TRL LineTRL Line corresponds to the measurement of
theS-parameters of a short transmission line. Theimpedance of this
Line determines the referenceimpedance for the subsequent
error-correctedmeasurements. The insertion phase of the Lineneed
not be precisely defined but may not be thesame as (nor a multiple
of pi) the phase of theThru.
TRM ThruRefer to TRL Thru section.
TRM ReflecRefer to TRL Reflec section.
TRM MatchTRM Match corresponds to the measurement of
theS-parameters of a matched load. The input reflec-tion of this
Match determines the reference imped-ance for the subsequent
error-correctedmeasurements. The phase of the Match does notneed to
be precisely defined.
AdapterThis class is used to specify the adapters used forthe
adapter removal process. The standard num-ber of the adapter or
adapters to be characterizedis entered into the class assignment.
Only an esti-mate of the adapters Offset Delay is required
(within 90 degrees). A simple way to estimatethe Offset Delay of
any adapter would be as fol-lows. Perform a 1-port calibration
(Response or S11 1-PORT) and then connect the adapter to thetest
port. Terminate the adapter with a short cir-cuit and then measure
the Group Delay. If theshort circuit is not an offset short, the
adaptersOffset Delay is simply l/2 of the measured delay. If the
short circuit is offset, its delay must be sub-tracted from the
measured delay.
Modifying a cal set with connector compensationConnector
compensation is a feature that providesfor compensation of the
discontinuity found at theinterface between the test port and a
connector.The connector here, although mechanically com-patible, is
not the same as the connector used forthe calibration. There are
several connector fami-lies that have the same characteristic
impedance,but use a different geometry. Examples of suchpairs
include:
3.5 mm / 2.92 mm3.5 mm / SMASMA / 2.92 mm2.4 mm / 1.85 mm
The interface discontinuity is modeled as alumped,
shunt-susceptance at the test port refer-ence plane. The
susceptance is generated from acapacitance model of the form:
C=C0 + C1 x f + C2 x f2 + C3 x f3
where f is the frequency. The coefficients are pro-vided in the
default Cal Kits for a number of typi-cally used connector-pair
combinations. To addmodels for other connector types, or to change
thecoefficients for the pairs already defined in a CalKit, use the
Modifying a Calibration Kit proce-dure in the Calibrating for
System Measurementschapter of the 8510 network analyzer
systemsOperating and Programming Manual (part number08510-90281).
Note that the definitions in thedefault Cal Kits are additions to
the StandardClass Adapter, and are Standards of type OPEN.
-
20
Each adapter is specified as a single delay/thrustandard and up
to seven standards numbers canbe specified into the adapter
class.
Standard Class labelsStandard Class labels are entered to
facilitatemenu-driven calibration. A label can be any user-selected
term which best describes the device orclass of devices that the
operator should connect.Predefined labels exist for each class.
These labelsare
S11A, S11B, S11C, S22A, S22B, S22C, FWD TRANS,FWD MATCH, REV
TRANS, REV MATCH,RESPONSE, FWD ISOLATION, REV ISOLATION,THRU,
REFLECT, LINE, and ADAPTER.
The class labels for the WR-62 waveguide calibra-tion kit are as
follows; S11A and S22APSHORT1;S11B and S22BPSHORT2; S11C and
S22CPLOAD;FWD TRANS, FWD MATCH, REV TRANS and REVMATCHPTHRU; and
RESPONSERESPONSE.
TRL optionsWhen performing a TRL 2-PORT calibration, cer-tain
options may be selected. CAL Z is used tospecify whether
skin-effect-related impedance vari-ation is to be used or not. Skin
effect in lossytransmission line standards will cause a
frequency-dependent variation in impedance. This variationcan be
compensated when the skin loss (offsetloss) and the mechanically
derived impedance(Offset Z0) are specified and CAL Z0: SYSTEM
Z0selected. CAL Z0: LINE Z0 specifies that the imped-ance of the
line is equal to the Offset Z0 at all frequencies.
The phase reference can be specified by the Thruor Reflect
during the TRL 2-PORT calibration. SETREF: THRU corresponds to a
reference plane set byThru standard (or the ratio of the physical
lengthsof the Thru and Line) and SET REF: REFLECT cor-responds to
the Reflect standard.
LOWBAND FREQUENCY is used to select the mini-mum frequency for
coaxial TRL calibrations. Belowthis frequency (typically 2 to 3
GHz) full 2-port calibrations are used.
NoteThe resultant calibration is a single cal set combining the
TRL and conventional full 2-portcalibrations. For best results, use
TRM calibrationto cover frequencies below TRL cut-off
frequency.
Calibration kit labelA calibration kit label is selected to
describe theconnector type of the devices to be measured. If anew
label is not generated, the calibration kit labelfor the kit
previously contained in that calibrationkit register (CAL 1 or CAL
2) will remain. The pre-defined labels for the two calibration kit
registersare:
Calibration kit 1 Cal 1 Agilent 85050B7-mm B.1
Calibration kit 2 Cal 2 Agilent 85052B3.5-mm B.1
-
21
Again, cal kit labels should be chosen to bestdescribe the
calibration devices. The B.1 defaultsuffix corresponds to the kits
mechanical revision(B) and mathematical revision (1).
NoteTo prevent confusion, if any standard definitionsin a
calibration kit are modified but a new kit labelis not entered, the
default label will appear withthe last character replaced by a *.
This is not thecase if only a class is redefined without changing
astandard definition.
The WR-62 waveguide calibration kit can belabeled simply P
BAND.
Enter standards/classesThe specifications for the Standard
Definitiontable and Standard Class Assignments table can beentered
into the 8510 through front panel menu-driven entry or under
program control by an exter-nal controller. The procedure for entry
of standarddefinitions, standard labels, class assignments,class
labels, and calibration kit label is describedin Appendix A.
NoteDO NOT exit the calibration kit modificationprocess without
saving the calibration kit defini-tions in the appropriate register
in the 8510.Failure to save the redefined calibration kit
willresult in not saving the new definitions and theoriginal
definitions for that register will remain.Once this process is
completed, it is recommendedthat the new calibration kit should be
saved ontape.
Verify performanceOnce a measurement calibration using a
particularcalibration kit has been generated, its performanceshould
be checked before making device measure-ments. To check the
accuracy that can be obtainedusing the new calibration kit, a
device with a welldefined frequency response (preferably unlike
anyof the standards used) should be measured. It isimportant to
note that the verification device mustnot be one of the calibration
standards. Calibratedmeasurement of one of the calibration
standards ismerely a measure of repeatability.
A performance check of waveguide calibration kitsis often
accomplished by measuring a zero lengthshort or a short at the end
of a straight section ofwaveguide. The measured response of this
deviceon a polar display should be a dot at 1 180. Thedeviation
from the known is an indication of theaccuracy. To achieve a more
complete verificationof a particular measurement calibration,
(includingdynamic accuracy) accurately known verificationstandards
with a diverse magnitude and phaseresponse should be used. NBS
traceable or Agilentstandards are recommended to achieve
verifiablemeasurement accuracy. Further, it is recommend-ed that
verification standards with known but dif-ferent phase and
magnitude response than any ofthe calibration standards be used to
verify per-formance of the 8510.
-
22
User modified cal kits and Agilent 8510 specificationsAs noted
previously, the resultant accuracy of the8510 when used with any
calibration kit is depend-ent on how well its standards are defined
and isverified through measurement of a device withtraceable
frequency response.
The published Measurement Specifications for the8510 Network
Analyzer system include calibrationwith Agilent calibration kits
such as the 85050B.Measurement calibrations made with user
definedor modified calibration kits are not subject to the8510
performance specifications although a proce-dure similar to the
standard verification proceduremay be used.
Modification examplesModeling a thru adapterThe MODIFY CAL KIT
function allows more precisedefinition of existing standards, such
as the thru.For example, when measuring devices with thesame sex
coaxial connectors, a set of thru stan-dards to adapt
non-insertable devices on each endis needed. Various techniques are
used to cancelthe effects of the thru adapters. However, usingthe
modify cal kit function to make a precise defi-nition of the thru
enables the 8510 to mathemati-cally remove the attenuation and
phase shift dueto the thru adapter. To model correctly a thruof
fixed length, accurate gauging (see OFFSETDELAY) and a precise
measurement of skin-lossattenuation (see OFFSET LOSS) are required.
Thecharacteristic impedance of the thru can befound from the inner
and outer conductor diame-ters and the permittivity of the
dielectric (see OFF-SET Z0).
Modeling an arbitrary impedance standardThe arbitrary impedance
standard allows the userto model the actual response of any one
port pas-sive device for use as a calibration standard.
Aspreviously stated, the calibration is mathematicallyderived by
comparing the measured response tothe known response which is
modeled through thestandard definition table. However, when
theknown response of a one-port standard is notpurely reflective
(short/open) or perfectly matched(load) but the response has a
fixed real impedance,then it can be modeled as an arbitrary
impedance.A load type standard has an assigned terminalimpedance
equal to the system Z0. If a given loadhas an impedance which is
other than the systemZ0, the load itself will produce a systematic
error insolving for the directivity of the measurement sys-tem
during calibration. A portion of the incidentsignal will be
reflected from the mismatched loadand sum together with the actual
leakage betweenthe reference and test channels within the
meas-urement system. However, since this reflection issystematic
and predictable (provided the terminat-ing impedance is known) it
may be mathematicallyremoved. The calibration can be improved if
thestandards terminal impedance is entered into thedefinition table
as an arbitrary impedance ratherthan as a load.
A procedure similar to that used for measurementof open circuit
capacitance (see method #3) couldbe used to make a calibrated
measurement of theterminal impedance.
-
23
Appendix ACalibration kit entry procedureCalibration kit
specifications can be entered intothe Agilent 8510 using the 8510
disk drive, a diskdrive connected to the system bus, by front
panelentry, or through program control by an
externalcontroller.
Disk procedureThis is an important feature since the 8510
caninternally store only two calibration kits at onetime while
multiple calibration kits can be storedon a single disk.
Below is the generic procedure to load or store cal-ibration
kits from and to the disk drive or diskinterface.
To load calibration kits from disk into the Agilent 85101.
Insert the calibration data disk into the 8510network analyzer (or
connect compatible disk driveto system bus).
2. Press the DISC key; select STORAGE IS: INTERNAL or EXTERNAL;
then press the followingdisplay softkeys:LOADCAL KIT 1-2CAL KIT 1
or CAL KIT 2 (This selection determineswhich of the 8510
non-volatile registers that thecalibration kit will be loaded
into.)FILE #_ or FILE NAME (Select the calibration kitdata to
load.) LOAD FILE.
3. To verify that the correct calibration kit wasloaded into the
instrument, press the CAL key. Ifproperly loaded, the calibration
kit label will beshown under CAL 1 or CAL 2 on the CRT
dis-play.
To store calibration kits from the Agilent 8510 onto a disk1.
Insert an initialized calibration data disk intothe 8510 network
analyzer or connect compatibledisk drive to the system bus.
2. Press the DISC key; select STORAGE IS: INTERNAL or EXTERNAL;
then press the followingCRT displayed softkeys:STORECAL KIT 1-2CAL
KIT 1 or CAL KIT 2 (This selection determineswhich of the 8510
non-volatile calibration kit regis-ters is to be stored.)FILE #_ or
FILE NAME (Enter the calibration kitdata file name.) STORE
FILE.
3. Examine directory to verify that file has beenstored. This
completes the sequence to store a cali-bration kit onto the
disk.
To generate a new cal kit or modify an existingone, either front
panel or program controlled entrycan be used.
In this guide, procedures have been given to definestandards and
assign classes. This section will listthe steps required for front
panel entry of the stan-dards and appropriate labels.
-
24
Front panel procedure: (P-band waveguide example)1. Prior to
modifying or generating a cal kit, storeone or both of the cal kits
in the 8510s non-volatile memory to a disk.
2. Select CAL menu, MORE.
3. Prepare to modify cal kit 2: press MODIFY 2.
4. To define a standard: press DEFINE STANDARD.
5. Enable standard no. 1 to be modified: press 1,X1.
6. Select standard type: SHORT.
7. Specify an offset: SPECIFY OFFSETS.
8. Enter the delay from Table 1: OFFSET DELAY,0.0108309, ns.
9. Enter the loss from Table 1: OFFSET LOSS, 0,X1.
10. Enter the Z0 from Table 1: OFFSET Z0, 50, X1.
11. Enter the lower cutoff frequency: MINIMUMFREQUENCY, 9.487
GHz.
12. Enter the upper frequency: MAXIMUM FRE-QUENCY, 18.97
GHz.
13. Select WAVEGUIDE.
14. Prepare to label the new standard: PRIORMENU, LABEL
STANDARD, ERASE TITLE.
15. Enter PSHORT 1 by using the knob, SELECTLETTER soft key and
SPACE soft key.
16. Complete the title entry by pressing TITLEDONE.
17. Complete the standard modification by press-ing STANDARD
DONE (DEFINED).
Standard #1 has now been defined for a 1/8 P-bandwaveguide
offset short. To define the remainingstandards, refer to Table 1
and repeat steps 4 -17.To define standard #3, a matched load,
specifyfixed.
The front panel procedure to implement the classassignments of
Table 2 for the P-band waveguidecal kit are as follows:
1. Prepare to specify a class: SPECIFY CLASS.
2. Select standard class S11A.
3. Inform the 8510 to use standard no. 1 for theS11A class of
calibration: l, X1, CLASS DONE(SPECIFIED).
-
25
4. Change the class label for S11A: LABEL CLASS,S11A, ERASE
TITLE.
5. Enter the label of PSHORT 1 by using the knob,the SELECT soft
key and the SPACE soft key.
6. Complete the label entry procedure: TITLEDONE, LABEL
DONE.
Follow a similar procedure to enter the remainingstandard
classes and labels as shown in the tablebelow:
Finally, change the cal kit label as follows:
1. Press LABEL KIT, ERASE TITLE.
2. Enter the title P BAND.
3. Press TITLE DONE, KIT DONE (MODIFIED). Themessage CAL KIT
SAVED should appear.
This completes the entire cal kit modification forfront panel
entry. An example of programmedmodification over the GPIB bus
through an exter-nal controller is shown in the Introduction
ToProgramming section of the Operating and Servicemanual (Section
III).
Standard Standard Classclass numbers label
S11B 2 PSHORT 2S11C 3 PLOADS22A 1 PSHORT 1S22B 2 PSHORT 2S22C 3
PLOADFWD TRANS 4 THRUFWD MATCH 4 THRUREV TRANS 4 THRUREV MATCH 4
THRURESPONSE 1,2,4 RESPONSE
-
26
Appendix BDimensional considerations in coaxial connectorsThis
appendix describes dimensional considera-tions and required
conventions used in determin-ing the physical offset length of
calibrationstandards in sexed coaxial connector families.
Precise measurement of the physical offset lengthis required to
determine the OFFSET DELAY of agiven calibration standard. The
physical offsetlength of one and two port standards is as
follows.
One port standardDistance between calibrationplane and
terminating impedance.
Two port standardDistance between the Port 1and Port 2
calibration planes.
The definition (location) of the calibration planein a
calibration standard is dependent on thegeometry and sex of the
connector type. The cali-bration plane is defined as a plane which
is per-pendicular to the axis of the conductor coincidentwith the
outer conductor mating surface. This mat-ing surface is located at
the contact points of theouter conductors of the test port and the
calibra-tion standard.
To illustrate this, consider the following connectortype
interfaces:
7-mm coaxial connector interfaceThe calibration plane is located
coincident toboth the inner and outer conductor mating sur-faces as
shown. Unique to this connector type isthe fact that the inner and
outer conductor matingsurfaces are located coincident as well as
havinghermaphroditic (sexless) connectors. In all othercoaxial
connector families this is not the case.
3.5-mm coaxial connector interfaceThe location of the
calibration plane in 3.5-mmstandards, both sexes, is located at the
outer con-ductor mating surface as shown.
Type-N coaxial connector interfaceThe location of the
calibration plane in Type-Nstandards is the outer conductor mating
surfacesas shown below.
NoteDuring measurement calibration using the Agilent85054 Type-N
Calibration Kit, standard labels forthe opens and shorts indicate
both the stan-dard type and the sex of the calibration test
port.The sex (M or F) indicates the sex of the test port,NOT the
sex of the standard. The calibration planein other coaxial types
should be defined at one ofthe conductor interfaces to provide an
easily veri-fied reference for physical length measurements.
-
27Female type-N Male type-N
7 mm Coaxial connector
Type-N coaxial connector interfaceThe location of the
calibration plane in Type-N standards is the outer conductor mating
surfaces as shown below.
Note: 1.0mm, 1.85mm and 2.4mm connectors not shown, but similar
to 3.5mm calibration planes.
-
28
-
29
Appendix CCal coefficients modelOffset devices like offset
shorts and offset opens canbe modeled by the following signal flow
graph :
Figure 1 Signal flow graph model of offset devices
The offset portion of the open or short, is modeledas a
perfectly uniform lossy air dielectric transmis-sion line. The
expected coefficient of reflection, ,of the open or short then can
be solved by signalflow graph technique.
Equation 1
The terms Zo, and are related to the calcoefficients - Offset
Zo, Offset Loss, and OffsetDelay - as follows:
Recall that
Equation 2
L L + 0R
-
30
Their first order approximations, R is small and G=0,
are:Equation 3
Since Equation 4
For coaxial devices
-
31
then:Equation 5
Equation 6
If the Offset delay=0, then the coefficient of reflection, =
L.
-
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