Technical Protocol
Key Comparison SIM.EM.RF-K5b.CL
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
H. Silva and G. Monasterios
RF & Microwaves Metrology Laboratory
Instituto Nacional de Tecnolog a Industrial
Argentina
Version 1.0, September 21, 2012

SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Contents
1 Introduction 2
2 Traveling standards 2
2.1 Description of the standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.2 Details of traveling standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2.3 Photograph of traveling standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
3 Quantities to be measured 3
4 Evaluation of results 4
4.1 Comparison reference value . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
4.2 Degrees of equivalence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.2.1 DoE with respect to the CRV . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.2.2 Bilateral DoE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
4.2.3 Dimension reduction of DoE . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
4.3 Proposal for linking to CCEM.RF-K5b.CL . . . . . . . . . . . . . . . . . . . . . . . . 6
5 Organization 7
5.1 Pilot laboratory contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5.2 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.3 Time schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.4 Transportation and nancial aspects . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
5.5 Unpacking, handling and packing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
6 Measurement instructions 9
7 Uncertainty of measurement results 9
8 Report of results 10
9 Comparison report 10
Bibliography 12
Annex A: Results 13
Annex B: Uncertainty budget 14
Annex C: Description of the measurement method 15
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
1 Introduction
This key comparison is based on the responsibility of the Inter-american Metrology System (SIM)
through the CIPM Mutual Recognition Agreement (MRA) to ensure the measurement capabilities
of National Metrology Institutes (NMIs) in America.
Through a key comparison, the SIM provides metrology laboratories in the region the ability to
demonstrate their achievements in high frequency measurements by linking their results to CCEM
through a laboratory that has participated in both comparisons.
INTI proposes the realization and piloting of this rst comparison on RF within the SIM, which
consists in S-parameter measurements in the frequency range from 2 GHz to 18 GHz in an
unbalanced coaxial system with Type N connector.
2 Traveling standards
2.1 Description of the standards
The traveling standards were chosen based on those used in the CCEM Key Comparison [3] in
order to link both comparisons. These standards are commercially available devices covering some
of the most important cases that arise in the measurement of S-parameters in a frequency range
up to 18 GHz.
2.2 Details of traveling standards
The speci cations of the standards are given below:
Description Nominal Value Model Serial Number Connector
Attenuator 3 dB HP 8491B(opt.003) MY39266530 Male/Female
Attenuator 20 dB HP 8491B(opt.020) MY39266597 Male/Female
Matched Load 50 (VSWR=1.0) HP 909F 55719 Male
Mismatched Load VSWR=2.0 Maury 2562G 9006 Male
Table 1: Traveling standards
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
2.3 Photograph of traveling standards
Figure 1: One-port devices
Figure 2: Two-port devices
3 Quantities to be measured
Scattering parameters of Type N connector devices selected for this comparison will be measured
from 2 GHz to 18 GHz (inclusive) in 1 GHz steps.
For one-port devices (matched and mismatched loads) the measurand is the complex-valued re ection
coe cient S11. The VSWR 1.0 (matched) load and VSWR 2.0 (mismatched) load were chosen to
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
perform re ection measurements with low and high magnitude values.
When measuring two-port devices (3 dB and 20 dB attenuators) the measurands are the four
complex-valued S-parameters (S11,S21,S12 and S22). The values of 3 dB and 20 dB were chosen
to cover transmission measurements with high and low magnitude values.
The S-parameters must be informed in the form:
Sab = x+ jy (1)
where x and y are the real and imaginary parts of the reported S-parameter, subindex a corresponds
to re ected or transmitted wave port and subindex b corresponds to incident wave port. Both the
real and imaginary parts are expressed in linear units, and j =
p
1 is the imaginary unit.
The uncertainty of each measured S-parameter must be given in the form of combined standard
uncertainty of the real part u(x), imaginary part u(y) and correlation coe cient between them,
u(x; y) (see section 7 for further details).
Note: For two-port devices, the male port will be referred to as port number 1 for the purposes of
this protocol.
4 Evaluation of results
The analysis of the results will be done only for S11 (for one-port devices) and S21 (for two-port
devices) in 2 GHz, 9 GHz and 18 GHz to reduce the amount of data to be analyzed for the
comparison. This three frequencies were chosen to cover the low, medium and high frequency
range.
In order to evaluate and compare the data reported by laboratories taking part in this comparison
exercise, the following quantities will be calculated for each measurand in a way similar to [4], based
on the guidelines in [1]:
4.1 Comparison reference value
The comparison reference value or CRV will be determined using an unweighted mean of the
measurement results reported by the participants:
zm =
1
N
NX
i=1
zi (2)
where zm is the CRV and zi is the value reported by laboratory i and N is the total number of
participants in the comparison exercise.
Consistency test is not applied in this comparison and all reported values contribute the same
amount to the computation of the CRV.
The CRV uncertainties are determined by a 2 2 covariance matrix of the form:
Vm =

u2(xm) u(xm; ym)
u(ym; xm) u2(ym)

(3)
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
where:
u2(xm) =
1
N(N 1)
NX
i=1
(xi xm)
2 (4)
u2(ym) =
1
N(N 1)
NX
i=1
(yi ym)
2 (5)
u(xm; ym) =
1
N(N 1)
NX
i=1
(xi ym)(xi ym) (6)
In (4), (5) and (6) xm and ym are the real and imaginary parts of the CRV. xi and yi are the real
and imaginary parts of the individual reported values.
4.2 Degrees of equivalence
4.2.1 DoE with respect to the CRV
The degree of equivalence (or DoE) di for laboratory i with respect to the CRV is given by:
di = zi zm (7)
The covariance matrix of this DoE for the unweighted mean CRV computation (as presented in
section 4.1) is obtained by means of the expression:
Vdi = Vm + (1
2
N
)Vi (8)
where Vi is the covariance matrix resulting from measurement uncertainties reported by the participants
(see section 7 for further details).
4.2.2 Bilateral DoE
The degree of equivalence dij between participants i and j, or bilateral DoE, is given by:
dij = zi zj (9)
where zi and zj are the measurement values reported by lab i and lab j, respectively.
The covariance matrix of this bilateral DoE is simply obtained by:
Vdij = Vi + Vj (10)
where Vi and Vj are the covariance matrices resulting from measurement uncertainties reported by
each laboratory.
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
4.2.3 Dimension reduction of DoE
The degrees of equivalence previously de ned are complex-valued magnitudes. Proper evaluation
of the degrees of equivalence requires a reduction in the number of dimensions of these parameters.
This is accomplished by means of the expression detailed in [8]:
y = jdj (11)
dy = jdj
q
(dT V 1d d)
1k2 (12)
where d may be di for the degree of equivalence with respect to the CRV, or dij for the bilateral
DoE.
The factor k is a suitable coverage factor chosen to give a 95% con dence level. Assuming that d
follows a bivariate Gaussian distribution and the degrees of freedom are su ciently high [11], then
k = 2:45.
In (12), dy is the distance from y to the con dence boundary through the origin of the coordinate
system and is referred to as a con dence indicator.
4.3 Proposal for linking to CCEM.RF-K5b.CL
In accordance with the linking methods detailed in [9] and [10], the following methodology for
linking the results of this SIM comparison with those from the CCEM.RF-K5b.CL comparison [4]
is proposed for discussion by all participants, introducing a correction factor c :
c = dL;ccem dL;sim (13)
where:
- L refers to a laboratory that has participated in both CCEM and SIM comparisons, acting as a
link between them.
- dL;sim is the degree of equivalence with respect to the CRV from SIM comparison for linking
lab L.
- dL;ccem is the degree of equivalence with respect to the KCRV from CCEM comparison for linking
lab L.
The degree of equivalence di;ccem with respect to the KCRV from the CCEM comparison for lab i
in this SIM comparison can be calculated as follows:
di;ccem = di + c (14)
where di is the degree of equivalence of lab i with respect to the CRV from this SIM comparison.
The following expression would be adequate to obtain the covariance matrix of di;ccem:
Vdi;ccem = Vi + VKCRV + Vd (15)
where:
- Vi is the lab i covariance matrix.
- VKCRV is the KCRV covariance matrix from CCEM.RF-K5b.CL comparison.
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
- Vd is a covariance matrix associated with the imperfect reproducibility of the results of the linking
laboratory between CCEM and SIM comparison. This matrix should be supplied by the linking
laboratory.
In addition, the expression (15) requires the absence of any correlation between the covariance
matrices that appear in (15), and all the units must be the same.
As in section 4.2, transfer uncertainty due to drift or instabilities associated to traveling devices
is not considered in this proposal for the computation of the degree of equivalence with respect to
the KCRV from CCEM.RF-K5b.CL comparison (if any abnormal instability or drift is observed
during the course of the comparison, equations (3) and (15) should both be modi ed to include
this uncertainty contribution).
The degrees of equivalence di;ccem requires a reduction in the number of dimensions. This is
accomplished as explained in 4.2.3.
5 Organization
5.1 Pilot laboratory contacts
The pilot laboratory contacts are:
Hernando Silva (primary contact)
Email: metrologiarf@inti.gov.ar
Guillermo Monasterios (secondary contact)
Email: guillem@inti.gov.ar
Phone: +(5411)4724 6367
Fax: +(5411)4754 5194
INTI - Instituto Nacional de Tecnolog a Industrial
Av. General Paz 5445 - Edi cio 42
B1650KNA - San Mart n
Provincia de Buenos Aires
Rep ublica Argentina
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
5.2 Participants
The following institutes (in alphabetical order by country) will take part in this key comparison:
Institute Country Name Department e-mail
INTI Argentina Hernando Silva
RF & Microwave
Metrology Laboratory
hsilva@inti.gov.ar
NRC-INMS Canada Alain Michaud Alain.michaud@nrc-cnrc.gc.ca
KRISS Korea Jin-Seob Kang
Center for
Electromagnetic Wave
jinskang@kriss.re.kr
CENAM Mexico Susana Padilla
Scattering Parameters
Laboratory
spadilla@cenam.mx
NIST USA Ronald Ginley
Radio Frequency
Electronics Group
(818.01)
rginley@boulder.nist.gov
Table 2: List of participants
5.3 Time schedule
The expected time required for a participant to take the measurements and ship the traveling
standards to the next participant is 5 weeks.
The report with the results should be sent to the pilot laboratory within 1 month after taking the
measurements.
The pilot laboratory will measure the devices at the beginning and end of the comparison.
If there are any di culties in keeping the agreed schedule, the pilot laboratory should be contacted
immediately by email to agree on how to proceed.
Institute Country Start date Finish date Comments
INTI Argentina October 22, 2012 Initial measurements
In transit -
CENAM Mexico November 5, 2012 Novembre 26, 2012
In transit -
NIST USA December 10, 2012 January 14, 2013
Includes two extra weeks for
christmas & new year holidays
In transit -
NRC-INMS Canada January 28, 2013 February 18, 2013
In transit -
KRISS Korea March 4, 2013 March 25, 2013
In transit -
INTI Argentina April 8, 2013 Final measurements
Table 3: Proposed time schedule
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
5.4 Transportation and nancial aspects
Upon shipping the devices to the next laboratory, participants should notify the pilot laboratory
and the next participant laboratory by email.
Similarly upon arrival, the previous laboratory and the pilot laboratory should be informed.
Each participant is responsible for arranging and paying the transportation and insurance (including
customs clearance where necessary) of the devices since the arrival at their laboratory until arrival
at the subsequent laboratory.
The value of insurance can be assumed to be USD 3200.
5.5 Unpacking, handling and packing
On arrival at each participating laboratory, the traveling standards and packaging will be carefully
inspected for possible damage during shipment.
The pin depth of the center conductor should be checked on each element before starting with the
measurements to prevent damage, and report the results in the con rmation of receipt according
to Table 5 in Annex A.
If any damage is found, the pilot laboratory should be contacted immediately to agree on how to
proceed.
Extreme care should be taken when handling the traveling standards in order to avoid damaging the
center conductor pin and to maintain the stability of the devices in the course of the intercomparison.
Before the devices are shipped to the next laboratory the contents of the case should be checked
against the enclosed packing list.
6 Measurement instructions
Every participant laboratory is responsible to apply their own technical procedures to successfully
complete the measurements and to avoid damages of the traveling standards during the measurement
process.
7 Uncertainty of measurement results
As stated in section 3, each S-parameter measured must be reported in the form of a real part x
plus its combined standard uncertainty u(x), and an imaginary part y plus its combined standard
uncertainty u(y). If it is assumed that u(x) = u(y), then only a single value of uncertainty needs
to be given.
Additionally, the covariance u(x; y) between the real and imaginary parts of Sab may also be given
(or, alternatively, the correlation coe cient r(x; y)). This value will be assumed to be zero when
not included in the results report.
The real and imaginary parts uncertainties u(x) and u(y) together with the correlation coe cient
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
u(x; y) determine a 2 2 covariance matrix Vi for the uncertainty of a complex-valued measurand [11]:
Vi =

u2(x) u(x; y)
u(y; x) u2(y)

(16)
or, in terms of the correlation coe cient:
Vi =

u2(x) r(x; y)u(x)u(y)
r(y; x)u(x)u(y) u2(y)

(17)
In the above matrices, u(x; y) = u(y; x) and r(x; y) = r(y; x) so these matrices are symmetric.
The methods used to evaluate the measurement uncertainties are determined by each laboratory,
which shall report a detailed uncertainty budget for each measured value (see section 8). The
reference document [12] is a wide-spread guidance to deal with this task in the case of VNA
measurements.
8 Report of results
The results of the measurement quantities (Annex A), a detailed evaluation of the uncertainties for
each measurement (Annex B) and a short description of the method used for the measurements
(Annex C) should be reported with the format given in the annexes. The tables for this purpose
will be sent by email to all participants and will consist of two les, a Word format le for the
descriptions and an Excel format le for the data.
Note: According to Section 4, the only necessary data required to be reported in Annex B
(Uncertainty budget) corresponds to uncertainties of S11 in the case of one-port devices and S21 in
the case of attenuators at three frequencies: 2 GHz, 9 GHz and 18 GHz. This gives a total of 12
complex measurands, that is, 4 devices at 3 frequencies per device for subsequent analysis.
Reports should be sent to the pilot laboratory via email as an attachment and as a signed paper
version via conventional post.
9 Comparison report
Within 3 months after completion of the circulation, the pilot laboratory will prepare a rst
Draft A Report and send it to participants for comments.
This report will include:
- Measurement results of participating labs with their uncertainties.
- Computations of the CRV with their uncertainties.
- Computation of degrees of equivalence with respect to the CRV, Bilateral DoE, and degrees of
equivalence with respect to the KCRV from CCEM comparison.
- Uncertainty budgets for each measurand as reported by participants.
- A summary of the measurement techniques employed by each participating laboratory.
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
If any anomalous results are observed for some participants, it will be informed before the emission
of the Draft A Report to allow them to check their results.
Subsequently the procedure outlined in the CCEM guidelines [2] will be followed.
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
References
[1] Measurement comparisons in the context of the CIPM MRA. CIPM MRA-D-05, Version 1,
October 2010.
[2] CCEM guidelines for planning, organizing, conducting and reporting key, supplementary and
pilot comparisons, 2007, 30 pp.
[3] C.P.Eio; M.J.Maddock; N.M.Ridler; M.J.Salter, \CCEM.RF-K5b.CL Technical Protocol:
Scattering Coe cients by Broad-Band Methods, 2-18 GHz - Type N Connector", Version
1, August 2003.
[4] C.P.Eio, \CCEM Key Comparison CCEM.RF-K5b.CL (GT-RF/92-3) Scattering Coe cients
by Broad-Band Methods, 2-18 GHz - Type N Connector, Final Report of the Pilot Laboratory",
May 2010.
[5] R.Judaschke, \CCEM.RF-K25.W Technical Protocol:RF power from 33 to 50 GHz in
waveguide", May 2010.
[6] M.G.Cox, \The evaluation of key comparison data:An introduction", Metrologia, 2002, 39, pp
587-588.
[7] M.G.Cox, \The evaluation of key comparison data", Metrologia, 2002, 39, pp 589-595.
[8] M.Zeier, \On the analysis of multidimensional quantities in measurement comparison", CPEM
2006 Conference Digest, Torino, July 2006, pp 458-459.
[9] F.Delahaye; T.J.Witt, \Linking the results of 10 pF capacitance key comparisons CCEM-K4
and EUROMET 345", Precision Electromagnetic Measurements, 2002. Conference Digest 2002
Conference on , vol., no., pp. 526-527, 2002.
[10] B.Wood; A.Steele; R.Douglas, \Linking methodology with application to CCEM-K4 and
EUROMET 345", CCEM/WGKC 01-17.
[11] N.M.Riddler; M.J.Salter, \An approach to the treatment of uncertainty in complex S-
parameter measurements", Metrologia, 2002, 39, pp 295-302.
[12] \EA Guidelines on the Evaluation of Vector Network Analysers (VNA)". Euramet /cg-12/v
2.0, March 2011.
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Annex A: Results
Laboratory: .......
Traveling standard: .......
Frequency Measurand u(Re(S11)) u(Im(S11)) r(x,y)
GHz Sa;b combined 1-sigma combined 1-sigma
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Table 4: Table of results
Device
Pin depth [ m] Pin depth [ m]
Male port Female port
Attenuator 3 dB
Attenuator 20 dB
Matched Load -
Mismatched Load -
Table 5: Pin depth measurements
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Annex B: Uncertainty budget
Laboratory: .......
Traveling standard: .......
Sa;b @2 GHz
Standard
Probability distribution
Sensitivity Uncertainty
Quantity Uncertainty coe cient contribution
u(xi) ci ciu(xi)
- - - Utotal
Table 6: Uncertainty budget - 2 GHz
Sa;b @9 GHz
Standard
Probability distribution
Sensitivity Uncertainty
Quantity Uncertainty coe cient contribution
u(xi) ci ciu(xi)
- - - Utotal
Table 7: Uncertainty budget - 9 GHz
Sa;b @18 GHz
Standard
Probability distribution
Sensitivity Uncertainty
Quantity Uncertainty coe cient contribution
u(xi) ci ciu(xi)
- - - Utotal
Table 8: Uncertainty budget - 18 GHz
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SIM.EM.RF-K5b.CL Technical Protocol
Scattering Coe cients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Annex C: Description of the measurement method
Laboratory: .......
Please ll out the lines below including a description of the measurement method, traceability route
and instruments used in the present comparison:
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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This and any other relevant information provided by your laboratory will be included in the nal
report.
15