Technical Protocol
Key Comparison SIM.EM.RFK5b.CL Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
H. Silva and G. Monasterios RF & Microwaves Metrology Laboratory Instituto Nacional de Tecnolog´ıa Industrial Argentina
Version 1.0, September 21, 2012
SIM.EM.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand 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.RFK5b.CL . . . . . . . . . . . . . . . . . . . . . . . . 6
5 Organization
7
5.1 Pilot laboratory contacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
5.2 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.3 Time schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
5.4 Transportation and ﬁnancial 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.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
1 Introduction
This key comparison is based on the responsibility of the Interamerican 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 ﬁrst comparison on RF within the SIM, which consists in Sparameter 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 Sparameters in a frequency range up to 18 GHz.
2.2 Details of traveling standards
The speciﬁcations of the standards are given below:
Description
Attenuator Attenuator Matched Load Mismatched Load
Nominal Value
3 dB 20 dB 50 Ω (VSWR=1.0) VSWR=2.0
Model
HP 8491B(opt.003) HP 8491B(opt.020)
HP 909F Maury 2562G
Serial Number
MY39266530 MY39266597
55719 9006
Connector
Male/Female Male/Female
Male Male
Table 1: Traveling standards
2
2.3 Photograph of traveling standards
SIM.EM.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
Figure 1: Oneport devices
Figure 2: Twoport 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 oneport devices (matched and mismatched loads) the measurand is the complexvalued reﬂection coeﬃcient S11. The VSWR 1.0 (matched) load and VSWR 2.0 (mismatched) load were chosen to
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SIM.EM.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
perform reﬂection measurements with low and high magnitude values.
When measuring twoport devices (3 dB and 20 dB attenuators) the measurands are the four complexvalued Sparameters (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 Sparameters must be informed in the form:
Sab = x + jy
(1)
where x and y are the real and imaginary parts of the reported Sparameter, subindex a corresponds to reﬂected or transmitted wave port and subindex b correspond√s to incident wave port. Both the real and imaginary parts are expressed in linear units, and j = −1 is the imaginary unit. The uncertainty of each measured Sparameter must be given in the form of combined standard uncertainty of the real part u(x), imaginary part u(y) and correlation coeﬃcient between them, u(x, y) (see section 7 for further details).
Note: For twoport 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 oneport devices) and S21 (for twoport 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:
1N
zm = N zi
(2)
i=1
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(ym, xm)
u(xm, ym) u2(ym)
(3)
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SIM.EM.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
where:
u2(xm)
=
1 N (N −
1)
N
(xi − xm)2
(4)
i=1
u2(ym)
=
1 N (N −
1)
N
(yi − ym)2
(5)
i=1
1
N
u(xm, ym) = N (N − 1) (xi − ym)(xi − ym)
(6)
i=1
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:
2
Vdi = Vm + (1 − 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.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
4.2.3 Dimension reduction of DoE
The degrees of equivalence previously deﬁned are complexvalued 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 = d
(11)
dy = d (dT Vd−1d)−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% conﬁdence level. Assuming that d follows a bivariate Gaussian distribution and the degrees of freedom are suﬃciently high [11], then k = 2.45. In (12), dy is the distance from y to the conﬁdence boundary through the origin of the coordinate system and is referred to as a conﬁdence indicator.
4.3 Proposal for linking to CCEM.RFK5b.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.RFK5b.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.RFK5b.CL comparison.
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SIM.EM.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand 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.RFK5b.CL comparison (if any abnormal instability or drift is observed during the course of the comparison, equations (3) and (15) should both be modiﬁed 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´ıa Industrial Av. General Paz 5445  Ediﬁcio 42 B1650KNA  San Mart´ın Provincia de Buenos Aires Repu´blica Argentina
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SIM.EM.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand 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 INTI
Country
Name
Argentina Hernando Silva
NRCINMS Canada Alain Michaud
KRISS
Korea JinSeob Kang
CENAM Mexico Susana Padilla
NIST
USA Ronald Ginley
Department RF & Microwave Metrology Laboratory
Center for Electromagnetic Wave Scattering Parameters
Laboratory Radio Frequency Electronics Group
(818.01)
email hsilva@inti.gov.ar Alain.michaud@nrccnrc.gc.ca jinskang@kriss.re.kr spadilla@cenam.mx
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 diﬃculties in keeping the agreed schedule, the pilot laboratory should be contacted immediately by email to agree on how to proceed.
Institute INTI In transit CENAM In transit
NIST
In transit NRCINMS In transit KRISS In transit INTI
Country Argentina
Mexico

USA
Canada
Korea
Argentina
Start date
November 5, 2012 December 10, 2012 January 28, 2013
March 4, 2013 April 8, 2013
Finish date October 22, 2012 Novembre 26, 2012
January 14, 2013
February 18, 2013 March 25, 2013
Comments Initial measurements
Includes two extra weeks for christmas & new year holidays
Final measurements
Table 3: Proposed time schedule
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SIM.EM.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
5.4 Transportation and ﬁnancial 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 conﬁrmation 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 Sparameter 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 coeﬃcient 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 coeﬃcient
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SIM.EM.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
u(x, y) determine a 2×2 covariance matrix Vi for the uncertainty of a complexvalued measurand [11]:
Vi =
u2(x) u(y, x)
u(x, y) u2(y)
(16)
or, in terms of the correlation coeﬃcient:
u2(x)
r(x, y)u(x)u(y)
Vi = 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 widespread 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 ﬁles, a Word format ﬁle for the descriptions and an Excel format ﬁle 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 oneport 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 ﬁrst 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.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand 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.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
References
[1] Measurement comparisons in the context of the CIPM MRA. CIPM MRAD05, 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.RFK5b.CL Technical Protocol: Scattering Coeﬃcients by BroadBand Methods, 218 GHz  Type N Connector”, Version 1, August 2003.
[4] C.P.Eio, “CCEM Key Comparison CCEM.RFK5b.CL (GTRF/923) Scattering Coeﬃcients by BroadBand Methods, 218 GHz  Type N Connector, Final Report of the Pilot Laboratory”, May 2010.
[5] R.Judaschke, “CCEM.RFK25.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 587588.
[7] M.G.Cox, “The evaluation of key comparison data”, Metrologia, 2002, 39, pp 589595. [8] M.Zeier, “On the analysis of multidimensional quantities in measurement comparison”, CPEM
2006 Conference Digest, Torino, July 2006, pp 458459. [9] F.Delahaye; T.J.Witt, “Linking the results of 10 pF capacitance key comparisons CCEMK4
and EUROMET 345”, Precision Electromagnetic Measurements, 2002. Conference Digest 2002 Conference on , vol., no., pp. 526527, 2002. [10] B.Wood; A.Steele; R.Douglas, “Linking methodology with application to CCEMK4 and EUROMET 345”, CCEM/WGKC 0117. [11] N.M.Riddler; M.J.Salter, “An approach to the treatment of uncertainty in complex Sparameter measurements”, Metrologia, 2002, 39, pp 295302. [12] “EA Guidelines on the Evaluation of Vector Network Analysers (VNA)”. Euramet /cg12/v 2.0, March 2011.
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SIM.EM.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
Annex A: Results
Laboratory: ....... Traveling standard: .......
Frequency GHz
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Measurand Sa,b
u(Re(S11)) combined 1sigma
u(I m(S11 ))
r(x,y)
combined 1sigma
Table 4: Table of results
Device
Attenuator 3 dB Attenuator 20 dB
Matched Load Mismatched Load
Pin depth [µm] Male port
Pin depth [µm] Female port

Table 5: Pin depth measurements
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SIM.EM.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
Annex B: Uncertainty budget
Laboratory: ....... Traveling standard: ....... Sa,b @2 GHz
Standard
Sensitivity Uncertainty
Quantity Uncertainty Probability distribution coeﬃcient contribution
u(xi)
ci
ciu(xi)



Utotal
Table 6: Uncertainty budget  2 GHz
Sa,b @9 GHz
Standard
Sensitivity Uncertainty
Quantity Uncertainty Probability distribution coeﬃcient contribution
u(xi)
ci
ciu(xi)



Utotal
Table 7: Uncertainty budget  9 GHz
Sa,b @18 GHz
Standard
Sensitivity Uncertainty
Quantity Uncertainty Probability distribution coeﬃcient contribution
u(xi)
ci
ciu(xi)



Utotal
Table 8: Uncertainty budget  18 GHz
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SIM.EM.RFK5b.CL Technical Protocol Scattering Coeﬃcients by BroadBand Methods
2 GHz  18 GHz  Type N Connector
Annex C: Description of the measurement method
Laboratory: ....... Please ﬁll out the lines below including a description of the measurement method, traceability route and instruments used in the present comparison: ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. ................................................................................................. .................................................................................................
This and any other relevant information provided by your laboratory will be included in the ﬁnal report.
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Ver+/