Final Report
Key Comparison SIM.EM.RF-K5b.CL Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
H. Silva and G. Monasterios RF & Microwaves Metrology Laboratory Instituto Nacional de Tecnolog´ıa Industrial Argentina
September 13, 2016
Contents
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
1 Introduction
3
1.1 Motivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Measured Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 Relation with CCEM.RF-K5b.CL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 Traveling standards
4
2.1 Description of the standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.2 Details of the traveling standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2.3 Photograph of traveling standards . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
3 Participants and organization
5
3.1 Participants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3.2 Schedule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
4 Discussion about organization of the comparison
8
5 Measurement methods
8
6 Standards behavior
9
7 Treatment of measurement data from participants
9
7.1 Evaluation of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
7.2 Linking to CCEM.RF-K5b.CL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
8 Conclusions
14
Bibliography
16
Annex A: Results
17
A.1 3 dB Attenuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
A.2 20 dB Attenuator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
A.3 Matched load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
A.4 Mismatched load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Annex B: Uncertainty budget
53
B.1 INTI Uncertainty Budgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
B.2 NIST Uncertainty Budgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
B.3 NRC Uncertainty Budgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
B.4 CENAM Uncertainty Budgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
B.5 NPLI Uncertainty Budgets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Annex C: Participants reports
88
C.1 INTI Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
C.2 NIST Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
C.3 NRC Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
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SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
C.4 CENAM Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 C.5 NPLI Report . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
Annex D: Pin Depth measurements
99
Annex E: Electrical stability of standards
101
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2 GHz - 18 GHz - Type N Connector
1 Introduction
1.1 Motivations
This RMO 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 the National Metrology Institutes (NMIs) in America.
Through this key comparison, SIM demonstrates NMIs achievements in high frequency measurements by linking their results to key values resulting from previous CCEM-organized comparison. This link is provided by laboratories that participated in both comparisons.
INTI has proposed and piloted this first RF SIM comparison, which consists in S-parameter measurements in the frequency range from 2 GHz to 18 GHz in an unbalanced coaxial 50Ω system with Type N connector.
1.2 Measured Quantities
Scattering parameters of Type N connector devices were measured from 2 GHz to 18 GHz (inclusive) in 1 GHz steps. For one-port devices (matched and mismatched loads) the measurand was the complex-valued reflection coefficient S11. The matched load (VSWR=1.0) and mismatched load (VSWR=2.0) were chosen to perform reflection measurements at low and high magnitude values respectively.
For two-port devices (3 dB and 20 dB attenuators) the measurands were the four complex-valued Sparameters (S11, S21, S12 and S22). The values of 3 dB and 20 dB were chosen to cover transmission coefficients at high and low magnitude values respectively.
The Technical Protocol [5] established that participants had to report S-parameters 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 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 S-parameter was reported in the form of combined standard uncertainty of the real part u(x), imaginary part u(y) and correlation coefficient between them r(x, y) (see section 7.1 for further details). For two-port devices, the male port was referred as port number 1 for the purposes of this report.
1.3 Relation with CCEM.RF-K5b.CL
The results of this regional key comparison were linked to those corresponding to the CCEM Key Comparison [3] through laboratories acting as “linking” [1] [2]. This enabled SIM laboratories’ results to be linked to both CCEM comparison key values and the results of laboratories that participated in that comparison. The traveling standards were chosen based on those used in the
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SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
CCEM comparison making possible to link both of them. The linking method is detailed in section 7.2.
2 Traveling standards
2.1 Description of the standards
The selected standards are commercially available devices covering low and high reflection and transmission coefficients. These standards are similar to those used in the CCEM Key Comparison [3]. They cover the most important cases that arise in the measurement of S-parameters. They were bought to be used specially for this comparison.
2.2 Details of the 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
2.3 Photograph of traveling standards
Figure 1: One-port devices 4
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Figure 2: Two-port devices
3 Participants and organization
3.1 Participants
Hernando Silva / Guillermo Monasterios Instituto Nacional de tecnolog´ıa Industrial (INTI)
RF & Microwaves Laboratory San Mart´ın - Buenos Aires ARGENTINA
Ronald Ginley National Institute of Standards and Technology (NIST)
Radio Frequency Electronics Group (672.01) Boulder - Colorado
UNITED STATES OF AMERICA 5
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Alain Michaud National Research Council (NRC)
Ottawa - Ontario CANADA
Susana Padilla / Israel Garc´ıa Centro Nacional de Metrolog´ıa (CENAM)
Scattering Parameters Laboratory El Marqu´es - Quer´etaro MEXICO
Pramendra Singh Negi National Physical Laboratory (NPLI) LF & HF Voltage, Current and Microwave Standards
New Delhi INDIA
Jin-seob Kang Korea Research Institute of Standards and Science (KRISS) Center for Electromagnetic Wave Division of Physical Metrology
Daejeon SOUTH KOREA
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3.2 Schedule
The original schedule proposed in September 2012 had to be modified for different reasons. Firstly, KRISS (Korea) and NPLI (India) asked the pilot laboratory if they could participate in this comparison. That request was submitted to SIM’s authorities, who allowed them to participate, so the total number of participants increased to six. Both KRISS and NPLI were scheduled to measure the comparison traveling standards at the end of the original participants list.
Secondly, CENAM had to postpone its participation for personal reasons, so they conducted their measurements after NIST and NRC instead of measuring the traveling standards before them. As a result, CENAM was the last NMI among SIM members to participate.
After SIM members made their measurements and because of long delays at this stage (see Section 4), the period allowed for the temporary exportation was coming to an end, so the pilot laboratory had to ask for the standards back to INTI (Argentina).
After a series of control measurements at the pilot laboratory, the traveling standards were sent to Asia. This is how the original concept of circulation for the standards like a “ring” became more like a “star”.
The following table depicts the resulting schedule, the dates on which each laboratory received and dispatched the traveling standards, and the date on which they sent the results to the pilot laboratory.
Laboratory
Arrival of standards Dispatch of standards Submitt of data
INTI (Argentina). 1st measurement CENAM (Mexico) NIST (USA) NRC (Canada) CENAM (Mexico)
INTI (Argentina) 1st control NPLI (India) KRISS (Korea)
INTI (Argentina) 2nd control
Nov. 2012 Jan. 2013 Jul. 2013 Dec. 2013 Jan. 2014 Jul. 2014 Sep. 2014 Feb. 2015
Nov. 2012 Dec. 2012 Jun. 2013 Nov. 2013 Jan. 2014 Jun. 2014 Aug. 2014 Jan. 2015
-
(See 3.2) Dec. 2013 Aug. 2015 May. 2014
Dec. 2014
-
Table 2: Participants’ measurement dates
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SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
4 Discussion about organization of the comparison
In this section the pilot laboratory wants to remark some issues encountered during the process of managing this key comparison. It is written with the objective to make more dynamic the future comparisons that will take place within SIM.
After all the participants took their measurements, some of them did not send their data to the pilot to compute their results. After a request to meet a predefined deadline, the pilot did not have any other choice but to exclude KRISS from the comparison because they did not send their measurement results. This was agreed with SIM authorities, so an end was officially reached for the measurement stage. This caused a significant delay in the beginning of the redaction of the “Draft A Report”. Regarding the pin-depth measurements, the necessity to get these values was to assure the mechanical stability of the standards after every shipment. This is why the pilot had to know these values when each laboratory received the traveling standards to avoid possible delays due to potentially damaged devices. Some participants sent this data together with the measurement results much later. Luckily the standards remained stable during all the comparison process. Unlike other comparisons, there were no noticeable delays arising from customs issues in any country the traveling standards passed through.
5 Measurement methods
All participants performed their measurements with a VNA (Vector Network Analyzer) based system. In this key comparison, the 2-port devices were defined with the male port as port 1 and the female port as port 2. This was stated in the technical protocol [5].
Below are defined the methods each laboratory used to measure S-parameters. The complete report from each laboratory is included in Annex C.
Laboratory
Hardware
Calibration kit
Calibration method
INTI (Argentina) VNA Rohde & Schwarz ZVK Agilent 85054B/R&S ZV-Z21
NIST (USA)
VNA (model not specified)
5 air-lines
NRC (Canada) VNA Agilent PNA E8364C
HP 85054D + air-line
CENAM (Mexico)
VNA Agilent E8363C
HP 85054B
NPLI (India)
VNA Wiltron 37247B
Anritsu 3653 + air-line
SOLT (sliding) Multical LRL (not specified)
TRL 1 SOLT
Table 3: Participants’ measurement methods
1CENAM performed its measurements with a VNA calibrated either with TRL and SOLT methods. CENAM has decided to include the TRL method results in this report.
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6 Standards behavior
In order to check the mechanical stability of the traveling standards, participants were asked to provide pin-depth measurements of each device. In this manner, if a problem had arisen with any of the traveling standards during the shipping, the pilot laboratory could have found a solution or taken a decision about how to proceed.
Annex D shows pin-depth measurements of each participant. It does not show a significant variation of the inner conductor distance in relation to the reference plane (pin-depth). In addition, to help with the determination of a possible damage in the standards’ inner conductor, the pilot assumed that each laboratory made visual inspection of each device before starting the measurements.
At the end of the comparison, the pilot laboratory did not find any damage to the connectors. Just a premature wearing of the threads of the male connectors was found after the first measurement loop took place. This does not have any influence in the electrical performance, but it demonstrates a degraded test port connector at one or more laboratory setups.
To ensure the electrical stability of the traveling standards, the pilot laboratory performed two control measurements after the first loop and at the end of the comparison (see table 2). The results of these measurements are summarized in Annex E. They show a good agreement taking into consideration the uncertainties of each measurement. The differences in the uncertainties among different years are primary influenced by slight variations of the uncertainties pilot’s budgets, and are not an indicator of a variation of the standards (e.g.: connector repeatability).
7 Treatment of measurement data from participants
7.1 Evaluation of results
The analysis of the results has been done for S11 (one-port devices) and S21 (two-port devices) at frequencies of 2 GHz, 9 GHz and 18 GHz. These measurands and frequencies were chosen to cover the low, medium and high frequency range in transmission and reflection measurements. In addition, this measurands match with those reported in [4], allowing the linking with CCEM Key Comparison.
As stated in section 1.2, each measured complex S-parameter should 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 should also be given (or, alternatively, the correlation coefficient r(x, y)). This value was assumed to be zero if it was not included in the laboratory report.
The uncertainties in the real and imaginary parts, u(x) and u(y), together with the covariance
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SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
coefficient u(x, y), determine a 2×2 covariance matrix Vi associated to the complex-valued measurand [13]:
Vi =
u2(x) u(y, x)
u(x, y) u2(y)
(2)
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)
(3)
In the above matrices, u(x, y) = u(y, x) and r(x, y) = r(y, x), these matrices are symmetric. In order to evaluate and compare the data reported by laboratories taking part in this comparison exercise, the following quantities were calculated for each measurand in a similar way to [4], based on the guidelines in [1]:
7.1.1 Comparison reference value
The comparison reference value (CRV) is determined using an unweighted mean of the measurement
results reported by the participants:
1N
zm = N zi
(4)
i=1
where zm is the complex CRV, zi is the complex value reported by laboratory i and N is the total number of participants in the comparison exercise. Consistency test has not been applied in this comparison and all reported values contributed the same amount to the computation of the CRV.
The CRV uncertainties are determined by a 2 × 2 matrix covariance:
Vm =
u2(xm) u(ym, xm)
u(xm, ym) u2(ym)
(5)
where:
u2(xm)
=
1 N (N −
1)
N
(xi − xm)2
(6)
i=1
u2(ym)
=
1 N (N −
1)
N
(yi − ym)2
(7)
i=1
1
N
u(xm, ym) = N (N − 1) (xi − xm)(yi − ym)
(8)
i=1
In (6), (7) and (8), 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.
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7.1.2 Degrees of equivalence 7.1.2.1 With respect to the CRV
The degree of equivalence (DoE) di for laboratory i with respect to the CRV is given by:
di = zi − zm
(9)
The covariance matrix associated with this DoE for the unweighted mean CRV computation (as presented in section 7.1.1) is obtained by means of the expression in [10]:
2
Vdi = Vm + (1 − N )Vi
(10)
where Vi is the covariance matrix (2) resulting from measurement uncertainties reported by the participants.
7.1.2.2 Bilateral DoE
The degree of equivalence dij between participants i and j, or bilateral DoE, is given by:
dij = zi − zj
(11)
where zi and zj are the measurement values reported by laboratories i and j, respectively.
Assuming that zi and zj are uncorrelated, the covariance matrix of this bilateral DoE is simply
obtained by:
Vdij = Vi + Vj
(12)
where Vi and Vj are the covariance matrices resulting from the measurement uncertainties reported by each laboratory.
7.1.2.3 Dimension reduction of DoE
The degrees of equivalence defined above 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 expressions detailed in [10]:
y = |d|
(13)
dy = |d| (dT Vd−1d)−1k2
(14)
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 sufficient high [13], then k = 2, 45. In (14), 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.
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7.2 Linking to CCEM.RF-K5b.CL
7.2.1 DoE respect to KCRV The following methodology for linking the results of this SIM comparison with those from the CCEM.RF-K5b.CL was applied introducing a set of correction factors ci:
where:
ci = dLi,ccem − dLi,sim
(15)
- Li refers to a laboratory i that participated in both CCEM and SIM comparisons, acting as a link between them.
- dLi,sim is the degree of equivalence di (9) for the linking laboratory Li. - dLi,ccem is the degree of equivalence respect to the KCRV for the linking laboratory Li. This complex value is obtained from the data included in [4].
According to [11], the final correction factor between both comparisons c results from a weighted mean between the ci factor of each linking laboratory. Additionally, its consistency has to be evaluated. Taking note that ci are complex-valued magnitudes, the weighted mean c are obtained by means of the following expression [10]:
n
c = VT−1
Vd−i 1ci
i=1
(16)
Where Vdi represents the 2 × 2 covariance matrix associated with the reproducibility (stability) of each linking laboratory and it is assumed to be the stated covariance matrix (2), n is the number
of linking laboratories and VT is obtained from the expression:
n
VT =
Vd−i 1
i=1
(17)
The covariance matrix Vc associated with c is:
Vc = VT−1
(18)
Consistency test over c is accomplished by means of the factor RB2 analog to the “Birge Ratio” [12, Appendix 2]:
RB2
=
(Y
− X.c)T V −1(Y (2n − 2)
− X.c)
(19)
where:
c1
Y
=
...
cn 2n×1
I1
X
=
...
In 2n×2
Vdi . . . 0
V
=
...
...
...
0 . . . Vdn 2n×2n
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I1 . . . In are 2 × 2 identity matrices. V is a matrix formed by Vdi as sub-matrices in the diagonal and the off-diagonal components are all zero (i.e. is assumed the absent of any correlation among ci of linking laboratories). Additionally V has to be a positive definite matrix.
Three laboratories participated in CCEM and SIM RMO key comparisons so there are three possible linking laboratories. The weighted mean (16) was obtained taking into account only ci of linking laboratories whose DoE respect to the KCRV (CCEM.RF-K5b.CL) and the CRV (SIM comparison) appear to be consistent. For this reason, to link the results of transmission coefficient of the 3 dB attenuator, only NIST and NPLI were used as linking laboratories. In the case of reflection coefficient of the matched load, only NRC and NIST data was used. Finally, to link the results of transmission coefficient of the 20 dB attenuator, all three linking laboratories might be used as links but only the data of SIM laboratories NRC and NIST was used.
If a bivariate normal distribution of ci is assumed: (2n−2)RB2 ∼ χ2(2n−2)
This property is used to test the consistency of weighted mean result by means of the hypothesis that “there is no significant difference between the observed variance and the variance deduced using the laboratories reproducibility estimates” [11].
If (2n−2)RB2 > χ2(2n−2, 0,05), then the hypothesis is rejected at 95 % of confidence level. If two linking laboratories are used, then n = 2 and χ2 2, 0,05 = 5, 99.
Finally, the condition not to reject the hypothesis is RB2 < 2, 995.
This condition and the positive definite of V have been verified successfully in all measurands linked to the CCEM comparison: S21 of the 3 dB and 20 dB attenuator and S11 of the matched load at 2 GHz, 9 GHz and 18 GHz.
For a laboratory lsim that participated only in this SIM comparison, its degree of equivalence dlsim,KCRV with respect to the KCRV from the CCEM comparison can be calculated as follows:
dlsim,KCRV = dlsim + c
(20)
where dlsim is the degree of equivalence of laboratory lsim with respect to the CRV (9) from this SIM comparison.
The following expression represents the covariance matrix associated with dlsim,KCRV :
where:
Vdlsim,KCRV = Vlsim + VKCRV + Vc
(21)
- Vlsim is the laboratory lsim covariance matrix (2). - VKCRV is the covariance matrix associated with the KCRV and is obtained from the data included in [4].
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- Vc is the covariance matrix associated with c.
In addition, the expression (21) assumes the absence of any correlation between its terms as well as transfer uncertainties due to drift or instabilities associated to traveling devices. The degrees of equivalence dlsim,KCRV also require a reduction in the number of dimensions. This is accomplished as explained in 7.1.2.3.
7.2.2 Bilateral DoE
Bilateral linking between laboratory lsim, that only participated in SIM comparison, and laboratory kccem, that only participated in CCEM2 comparison, was accomplished by the expression:
where:
dlsim,kccem = dlsim,KCRV − dk,ccem
(22)
- dlsim,KCRV is the DoE with respect to KCRV of laboratory lsim obtained in 7.2.1. - dk,ccem is the DoE with respect to KCRV of laboratory kccem, obtained from the data included in [4].
The terms presented in (22) are correlated; for this reason it is necessary to take the correlation
between its terms into account to find the covariance matrix associated with dlsim,kccem. This is done by using the properties of covariance matrices detailed in [9]:
where:
V = V + V − 2 V dlsim,kccem
dlsim ,K C RV
dk,ccem
KCRV
(23)
- Vdlsim,KCRV is taken from (21). - Vdk,ccem is the covariance matrix associated with dk,ccem and is obtained from the data included in [4]. - VKCRV is the covariance matrix associated with KCRV and is obtained from the data included in [4].
Finally, dlsim,kccem are reduced in the number of dimensions as explained in 7.1.2.3.
8 Conclusions
Degrees of equivalence with respect to reference values and bilateral DoE between participant laboratories have shown good consistency with the exceptions of NPLI in reflection measurements, and INTI for 3 dB attenuator S21 measurement at 18 GHz. Moreover, the linked DoE from SIM laboratories to key reference values from CCEM comparison, and the linked bilateral DoE from SIM laboratories with CCEM comparison participating laboratories, have also shown good consistency.
2Acronyms of CCEM participants have been kept as stated in the “CCEM Key Comparison Final Report” for ease of comparison.
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A variety of VNA calibration methods have been applied by participants, allowing to test the performance of different type of S-parameter measurement systems based on vector network analyzers. The purpose of this first SIM comparison in RF & microwave parameters was to show the ability of the region laboratories in this field. The authors encourage other SIM’s laboratories to participate and pilot comparison exercises in high frequency parameters, which will enable them to test their methods and foster valuable exchange of information among colleagues.
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References
[1] Measurement comparisons in the context of the CIPM MRA. CIPM MRA-D-05, Version 1.5, March 2014.
[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 Coefficients 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 Coefficients by Broad-Band Methods, 2-18 GHz - Type N Connector, Final Report of the Pilot Laboratory”, May 2010.
[5] H.Silva, G. Monasterios “SIM.EM.RF-K5b.CL Technical Protocol: Scattering Coefficients by Broad-Band Methods 2-18 GHz - Type N Connector”, version 1, September 2012.
[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] K. Yhland, J. Stenarson, “A Simplified treatment of uncertainties in complex quantities”,
CPEM 2004 Conference Digest, London, June 2004, pp 652-653. [9] M.Benjamin; H.Silva; G.Monasterios; N.Tempone,“Multivariate statistics applied to assess
measurement uncertainty of complex reflection coefficient”, CPEM 2014 Conference Digest, R´ıo de Janeiro, August 2014, pp 18-19. [10] M.Zeier, “On the analysis of multidimensional quantities in measurement comparison”, CPEM 2006 Conference Digest, Torino, July 2006, pp 458-459. [11] F.Delahaye; T.J.Witt, “Linking the results of 10 pF capacitance key comparisons CCEM-K4 and EUROMET 345”, BIPM key comparison database, CCEM-K4 Results. [12] R.Kacker; R.Datla; A.Parr,“Combined result and associated uncertainty from interlaboratory evaluations based on the ISO Guide”, Metrologia, 2002, 39, 279-293. [13] N.M.Riddler; M.J.Salter, “An approach to the treatment of uncertainty in complex Sparameter measurements”, Metrologia, 2002, 39, pp 295-302. [14] “EA Guidelines on the Evaluation of Vector Network Analysers (VNA)”. Euramet /cg-12/v 2.0, March 2011.
16
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Annex A: Results
A.1 3 dB Attenuator
Lab i
INTI NIST NRC CENAM NPLI
Re(S21)
-0,64269 -0,64308 -0,64496 -0,64255 -0,64459
Measurement and combined standard uncertainty
S21 of 3 dB Attenuator at 2 GHz
u(Re(S21))
combined 1-sigma
I m(S21 )
u(I m(S21 ))
combined 1-sigma
0,00029
-0,28534
0,00029
0,00191
-0,28578
0,00341
0,00250
-0,28618
0,00250
0,00083
-0,28619
0,00145
0,00121
-0,28749
0,00121
Table 4
r(x, y)
0,00 0,00 0,00 -0,89 0,07
Re(xi) 0,64357
Reference Value (CRV)
S21 of 3 dB Attenuator at 2 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
u(I m(xi ))
combined 1-sigma
0,00050
-0,28620
0,00036
Table 5
r(x,y) 0,63
17
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Figure 3: 3 dB Attenuator - Measurements of S21 along with CRV and its expanded uncertainty
(k = 2, 45) at 2 GHz
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0012 0,0006
0,0014 0,0045
0,0014 0,0010
0,0049 0,0017
0,0016
0,0027
INTI
y
dy
0,0006
0,0060
0,0024 0,0009
0,0062 0,0027
0,0029
0,0032
NIST
y
dy
0,0006 -
0,0060 -
0,0019 0,0007
0,0078 0,0061
0,0023
0,0069
Table 6: 3 dB Attenuator - DoE of S21 at 2 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0024
0,0062
0,0019
0,0078
-
-
0,0024
0,0064
0,0014
0,0068
CENAM
y
dy
0,0009 0,0007 0,0024
-
0,0027 0,0061 0,0064
-
0,0024
0,0032
NPLI
y
dy
0,0029 0,0023 0,0014 0,0024
0,0032 0,0069 0,0068 0,0032
-
-
Table 7: 3 dB Attenuator - DoE of S21 at 2 GHz
18
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Figure 4: 3 dB Attenuator - DoE of S21 respect to CRV at 2 GHz
INTI CENAM
KCRV
y
dy
0,0018 0,0032
0,0012 0,0031
NMIA
y
dy
0,0017 0,0034
0,0010 0,0036
SPRING
y
dy
0,0020 0,0048
0,0012 0,0038
SCL
y
dy
0,0016 0,0173 0,0010 0,0134
Table 8: 3 dB Attenuator - CCEM/SIM Linked DoE of S21 at 2 GHz
INTI CENAM
SNIIM
y
dy
0,0033 0,0100 0,0041 0,0106
NIM
y
dy
0,0045 0,0044 0,0038 0,0049
CSIR-NML
y
dy
0,0021 0,0034
0,0015 0,0034
NMIJ
y
dy
0,0021 0,0049 0,0013 0,0055
Table 9: 3 dB Attenuator - CCEM/SIM Linked DoE of S21 at 2 GHz
INTI CENAM
SP
y
dy
0,0023 0,0051 0,0015 0,0055
LNE
y
dy
0,0027 0,0031 0,0019 0,0037
NPL
y
dy
0,0030 0,0029 0,0021 0,0037
Table 10: 3 dB Attenuator - CCEM/SIM Linked DoE of S21 at 2 GHz
Note: Since a step change in the 3 dB attenuator measurements was observed in the CCEM comparison, it had to be split into two different sub-comparisons, each one with its own KCRV [4, Section 5]. Given that linking laboratories belong to only one of these subsets, the 3 dB attenuator was linked to that particular subset.
19
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Lab i
INTI NIST NRC CENAM NPLI
Re(S21)
0,70093 0,69911 0,70440 0,70330 0,70035
Measurement and combined standard uncertainty
S21 of 3 dB Attenuator at 9 GHz
u(Re(S21))
combined 1-sigma
I m(S21 )
u(I m(S21 ))
combined 1-sigma
0,00076
0,14791
0,00076
0,00404
0,15026
0,01137
0,00250
0,14761
0,00250
0,00127
0,14710
0,00377
0,00232
0,14899
0,00232
Table 11
r(x, y)
0,00 0,00 0,00 -0,33 0,24
Re(xi) 0,70162
Reference Value (CRV)
S21 of 3 dB Attenuator at 9 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
u(I m(xi ))
combined 1-sigma
0,00097
0,14837
0,00056
Table 12
r(x,y) -0,86
Figure 5: 3 dB Attenuator - Measurements of S21 along with CRV and its expanded uncertainty
(k = 2, 45) at 9 GHz
20
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0008 0,0031 0,0029 0,0021 0,0014
0,0017 0,0097 0,0054 0,0042 0,0048
INTI
y
dy
0,0030 0,0035 0,0025 0,0012
0,0149 0,0064 0,0038 0,0054
NIST
y
dy
0,0030 -
0,0059 0,0052 0,0018
0,0149 -
0,0128 0,0126 0,0150
Table 13: 3 dB Attenuator - DoE of S21 at 9 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0035 0,0059
0,0012 0,0043
0,0064 0,0128
0,0070 0,0080
CENAM
y
dy
0,0025 0,0052 0,0012
0,0035
0,0038 0,0126 0,0070
0,0072
NPLI
y
dy
0,0012 0,0018 0,0043 0,0035
-
0,0054 0,0150 0,0080 0,0072
-
Table 14: 3 dB Attenuator - DoE of S21 at 9 GHz
Figure 6: 3 dB Attenuator - DoE of S21 respect to CRV at 9 GHz 21
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI CENAM
KCRV
y
dy
0,0035 0,0055
0,0057 0,0072
NMIA
y
dy
0,0051 0,0055
0,0076 0,0071
SPRING
y
dy
0,0049 0,0059
0,0071 0,0066
SCL
y
dy
0,0053 0,0245
0,0076 0,0230
Table 15: 3 dB Attenuator - CCEM/SIM Linked DoE of S21 at 9 GHz
INTI CENAM
SNIIM
y
dy
0,0012 0,0115 0,0036 0,0118
NIM
y
dy
0,0065 0,0070 0,0081 0,0102
CSIR-NML
y
dy
0,0040 0,0090 0,0062 0,0107
NMIJ
y
dy
0,0048 0,0062 0,0068 0,0086
Table 16: 3 dB Attenuator - CCEM/SIM Linked DoE of S21 at 9 GHz
INTI CENAM
SP
y
dy
0,0057 0,0088 0,0075 0,0113
LNE
y
dy
0,0050 0,0055 0,0070 0,0080
NPL
y
dy
0,0076 0,0054 0,0094 0,0084
Table 17: 3 dB Attenuator - CCEM/SIM Linked DoE of S21 at 9 GHz
22
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Lab i
INTI NIST NRC CENAM NPLI
Re(S21)
0,67553 0,67825 0,67902 0,68265 0,68290
Measurement and combined standard uncertainty
S21 of 3 dB Attenuator at 18 GHz
u(Re(S21))
combined 1-sigma
I m(S21 )
u(I m(S21 ))
combined 1-sigma
0,00125
-0,20365
0,00125
0,00695
-0,19654
0,02156
0,00250
-0,19898
0,00250
0,00349
-0,19027
0,00655
0,00352
-0,19898
0,00352
Table 18
r(x, y)
0,00 0,00 0,00 0,74 0,02
Re(xi) 0,67967
Reference Value (CRV)
S21 of 3 dB Attenuator at 18 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
u(I m(xi ))
combined 1-sigma
0,00139
-0,19768
0,00218
Table 19
r(x,y) 0,69
Figure 7: 3 dB Attenuator - Measurements of S21 along with CRV and its expanded uncertainty
(k = 2, 45) at 18 GHz
23
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0073 0,0018 0,0015 0,0080 0,0035
0,0063 0,0168 0,0076 0,0146 0,0070
INTI
y
dy
0,0076 0,0058 0,0152 0,0087
0,0368 0,0068 0,0174 0,0092
NIST
y
dy
0,0076 -
0,0026 0,0077 0,0053
0,0368 -
0,0410 0,0308 0,0212
Table 20: 3 dB Attenuator - DoE of S21 at 18 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0058 0,0026
0,0094 0,0039
0,0068 0,0410
0,0184 0,0106
CENAM
y
dy
0,0152 0,0077 0,0094
0,0087
0,0174 0,0308 0,0184
0,0158
NPLI
y
dy
0,0087 0,0053 0,0039 0,0087
-
0,0092 0,0212 0,0106 0,0158
-
Table 21: 3 dB Attenuator - DoE of S21 at 18 GHz
Figure 8: 3 dB Attenuator - DoE of S21 respect to CRV at 18 GHz 24
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI CENAM
KCRV
y
dy
0,0093 0,0092
0,0068 0,0175
NMIA
y
dy
0,0129 0,0097
0,0037 0,0117
SPRING
y
dy
0,0181 0,0217
0,0042 0,0256
SCL
y
dy
0,0138 0,0334
0,0013 0,0325
Table 22: 3 dB Attenuator - CCEM/SIM Linked DoE of S21 at 18 GHz
INTI CENAM
SNIIM
y
dy
0,0088 0,0142 0,0067 0,0207
NIM
y
dy
0,0132 0,0099 0,0102 0,0124
CSIR-NML
y
dy
0,0091 0,0125 0,0081 0,0187
NMIJ
y
dy
0,0106 0,0096 0,0067 0,0150
Table 23: 3 dB Attenuator - CCEM/SIM Linked DoE of S21 at 18 GHz
INTI CENAM
SP
y
dy
0,0108 0,0137 0,0071 0,0181
LNE
y
dy
0,0091 0,0087 0,0083 0,0153
NPL
y
dy
0,0116 0,0090 0,0045 0,0150
Table 24: 3 dB Attenuator - CCEM/SIM Linked DoE of S21 at 18 GHz
25
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
A.2 20 dB Attenuator
Lab i
INTI NIST NRC CENAM NPLI
Re(S21)
-0,08619 -0,08639 -0,08700 -0,08625 -0,08677
Measurement and combined standard uncertainty
S21 of 20 dB Attenuator at 2 GHz
u(Re(S21))
combined 1-sigma
I m(S21 )
u(I m(S21 ))
combined 1-sigma
0,00014 0,00031 0,00250 0,00013 0,00037
-0,05135 -0,05135 -0,05141 -0,05133 -0,05159
0,00014 0,00046 0,00250 0,00019 0,00037
Table 25
r(x, y)
0,00 0,00 0,00 -0,96 -0,14
Re(xi) -0,08652
Reference Value (CRV)
S21 of 20 dB Attenuator at 2 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
u(I m(xi ))
combined 1-sigma
0,00016
-0,05141
0,00005
Table 26
r(x,y) 0,64
26
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Figure 9: 20 dB Attenuator - Measurements of S21 along with CRV and its expanded uncertainty
(k = 2, 45) at 2 GHz
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0003 0,0001
0,0005 0,0007
0,0005 0,0003
0,0048 0,0004
0,0003
0,0007
INTI
y
dy
0,0002
0,0008
0,0008 0,0001
0,0061 0,0005
0,0006
0,0009
NIST
y
dy
0,0002 -
0,0008 -
0,0006 0,0001
0,0062 0,0008
0,0004
0,0012
Table 27: 20 dB Attenuator - DoE of S21 at 2 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0008
0,0061
0,0006
0,0062
-
-
0,0008
0,0061
0,0003
0,0062
CENAM
y
dy
0,0001 0,0001 0,0008
-
0,0005 0,0008 0,0061
-
0,0006
0,0009
NPLI
y
dy
0,0006 0,0004 0,0003 0,0006
0,0009 0,0012 0,0062 0,0009
-
-
Table 28: 20 dB Attenuator - DoE of S21 at 2 GHz
27
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Figure 10: 20 dB Attenuator - DoE of S21 respect to CRV at 2 GHz
INTI CENAM
KCRV
y
dy
0,0002 0,0008 0,0001 0,0008
NPL
y
dy
0,0002 0,0009 0,0001 0,0009
PTB
y
dy
0,0001 0,0011 0,0000 0,0014
NMI-VSL
y
dy
0,0002 0,0011 0,0001 0,0011
Table 29: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 2 GHz
INTI CENAM
INRIM
y
dy
0,0002 0,0011
0,0002 0,0012
METAS
y
dy
0,0001 0,0010
0,0000 0,0011
CMI
y
dy
0,0002 0,0011 0,0001 0,0011
UME
y
dy
0,0003 0,0013 0,0002 0,0013
Table 30: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 2 GHz
INTI CENAM
NMIA
y
dy
0,0001 0,0009 0,0001 0,0011
SPRING
y
dy
0,0002 0,0014 0,0001 0,0014
SCL
y
dy
0,0002 0,0020 0,0001 0,0021
SNIIM
y
dy
0,0005 0,0014 0,0004 0,0015
Table 31: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 2 GHz
28
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI CENAM
NIM
y
dy
0,0003 0,0012
0,0003 0,0012
CSIR
y
dy
0,0003 0,0009
0,0002 0,0009
NMIJ
y
dy
0,0002 0,0011
0,0001 0,0012
SP
y
dy
0,0001 0,0010
0,0001 0,0010
Table 32: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 2 GHz
INTI CENAM
LNE
y
dy
0,0002 0,0011 0,0001 0,0011
Table 33: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 2 GHz
29
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Lab i
INTI NIST NRC CENAM NPLI
Re(S21)
0,06970 0,06965 0,07135 0,07032 0,07032
Measurement and combined standard uncertainty
S21 of 20 dB Attenuator at 9 GHz
u(Re(S21))
combined 1-sigma
I m(S21 )
u(I m(S21 ))
combined 1-sigma
0,00015
0,07181
0,00015
0,00122
0,07165
0,00119
0,00250
0,07177
0,00250
0,00036
0,07154
0,00036
0,00098
0,07217
0,00098
Table 34
r(x, y)
0,00 0,00 0,00 -0,98 -0,70
Re(xi) 0,07027
Reference Value (CRV)
S21 of 20 dB Attenuator at 9 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
u(I m(xi ))
combined 1-sigma
0,00031
0,07179
0,00011
Table 35
r(x,y) 0,10
Figure 11: 20 dB Attenuator - Measurements of S21 along with CRV and its expanded uncertainty
(k = 2, 45) at 9 GHz
30
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0006 0,0006 0,0011 0,0002 0,0004
0,0008 0,0024 0,0048 0,0007 0,0013
INTI
y
dy
0,0002 0,0016 0,0007 0,0007
0,0029 0,0061 0,0008 0,0014
NIST
y
dy
0,0002 -
0,0017 0,0007 0,0009
0,0029 -
0,0068 0,0031 0,0032
Table 36: 20 dB Attenuator - DoE of S21 at 9 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0016 0,0017
0,0011 0,0011
0,0061 0,0068
0,0062 0,0068
CENAM
y
dy
0,0007 0,0007 0,0011
0,0006
0,0008 0,0031 0,0062
0,0017
NPLI
y
dy
0,0007 0,0009 0,0011 0,0006
-
0,0014 0,0032 0,0068 0,0017
-
Table 37: 20 dB Attenuator - DoE of S21 at 9 GHz
Figure 12: 20 dB Attenuator - DoE of S21 respect to CRV at 9 GHz 31
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI CENAM
KCRV
y
dy
0,0005 0,0027
0,0004 0,0027
NPL
y
dy
0,0005 0,0027
0,0005 0,0027
PTB
y
dy
0,0004 0,0028
0,0005 0,0028
NMI-VSL
y
dy
0,0004 0,0029
0,0004 0,0028
Table 38: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 9 GHz
INTI CENAM
INRIM
y
dy
0,0009 0,0027 0,0005 0,0027
METAS
y
dy
0,0005 0,0028 0,0004 0,0029
CMI
y
dy
0,0004 0,0030 0,0005 0,0030
UME
y
dy
0,0006 0,0029 0,0004 0,0028
Table 39: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 9 GHz
INTI CENAM
NMIA
y
dy
0,0005 0,0027 0,0005 0,0028
SPRING
y
dy
0,0002 0,0033 0,0006 0,0035
SCL
y
dy
0,0007 0,0054 0,0004 0,0054
SNIIM
y
dy
0,0001 0,0030 0,0006 0,0032
Table 40: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 9 GHz
INTI CENAM
NIM
y
dy
0,0002 0,0027 0,0005 0,0029
CSIR
y
dy
0,0006 0,0029
0,0003 0,0029
NMIJ
y
dy
0,0006 0,0027
0,0004 0,0027
SP
y
dy
0,0004 0,0029 0,0004 0,0029
Table 41: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 9 GHz
INTI CENAM
LNE
y
dy
0,0011 0,0030 0,0010 0,0030
Table 42: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 9 GHz
32
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Lab i
INTI NIST NRC CENAM NPLI
Re(S21)
0,03707 0,03670 0,03688 0,03568 0,03719
Measurement and combined standard uncertainty
S21 of 20 dB Attenuator at 18 GHz
u(Re(S21))
combined 1-sigma
I m(S21 )
u(I m(S21 ))
combined 1-sigma
0,00017
0,09130
0,00017
0,00290
0,09125
0,00125
0,00250
0,09148
0,00250
0,00085
0,09211
0,00041
0,00377
0,09308
0,00377
Table 43
r(x, y)
0,00 0,00 0,00 -0,95 -0,53
Re(xi) 0,03671
Reference Value (CRV)
S21 of 20 dB Attenuator at 18 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
u(I m(xi ))
combined 1-sigma
0,00027
0,09185
0,00034
Table 44
r(x,y) 0,04
Figure 13: 20 dB Attenuator - Measurements of S21 along with CRV and its expanded uncertainty
(k = 2, 45) at 18 GHz
33
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0007 0,0006 0,0004 0,0011 0,0013
0,0008 0,0025 0,0048 0,0017 0,0053
INTI
y
dy
0,0004 0,0003 0,0016 0,0018
0,0068 0,0061 0,0022 0,0076
NIST
y
dy
0,0004 -
0,0003 0,0013 0,0019
0,0068 -
0,0076 0,0046 0,0083
Table 45: 20 dB Attenuator - DoE of S21 at 18 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0003 0,0003
0,0014 0,0016
0,0061 0,0076
0,0065 0,0097
CENAM
y
dy
0,0016 0,0013 0,0014
0,0018
0,0022 0,0046 0,0065
0,0065
NPLI
y
dy
0,0018 0,0019 0,0016 0,0018
-
0,0076 0,0083 0,0097 0,0065
-
Table 46: 20 dB Attenuator - DoE of S21 at 18 GHz
Figure 14: 20 dB Attenuator - DoE of S21 respect to CRV at 18 GHz 34
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI CENAM
KCRV
y
dy
0,0004 0,0042
0,0021 0,0045
NPL
y
dy
0,0004 0,0046
0,0019 0,0047
PTB
y
dy
0,0005 0,0044
0,0021 0,0047
NMI-VSL
y
dy
0,0004 0,0044
0,0020 0,0047
Table 47: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 18 GHz
INTI CENAM
INRIM
y
dy
0,0013 0,0042 0,0029 0,0046
METAS
y
dy
0,0004 0,0045 0,0020 0,0047
CMI
y
dy
0,0001 0,0056 0,0017 0,0052
UME
y
dy
0,0009 0,0053 0,0025 0,0057
Table 48: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 18 GHz
INTI CENAM
NMIA
y
dy
0,0004 0,0035 0,0020 0,0043
SPRING
y
dy
0,0004 0,0052 0,0014 0,0052
SCL
y
dy
0,0012 0,0097 0,0028 0,0087
SNIIM
y
dy
0,0007 0,0040 0,0009 0,0049
Table 49: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 18 GHz
INTI CENAM
NIM
y
dy
0,0011 0,0045 0,0025 0,0051
CSIR
y
dy
0,0014 0,0046
0,0030 0,0049
NMIJ
y
dy
0,0004 0,0041
0,0020 0,0045
SP
y
dy
0,0003 0,0039 0,0019 0,0047
Table 50: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 18 GHz
INTI CENAM
LNE
y
dy
0,0007 0,0032 0,0023 0,0042
Table 51: 20 dB Attenuator - CCEM/SIM Linked DoE of S21 at 18 GHz
35
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
A.3 Matched load
Lab i
INTI NIST NRC CENAM NPLI
Re(S11)
-0,00037 -0,00067 0,00051 0,00119 0,00278
Measurement and combined standard uncertainty
S11 of Matched load at 2 GHz
u(Re(S11))
combined 1-sigma
I m(S11 )
u(I m(S11 ))
combined 1-sigma
0,00248 0,00234 0,00520 0,00091 0,00333
-0,00088 -0,00134 -0,00098 -0,00106 -0,00543
0,00248 0,00333 0,00520 0,00133 0,00333
Table 52
r(x, y)
0,00 0,00 0,00 0,05 0,85
Re(xi) 0,00069
Reference Value (CRV)
S11 of Matched load at 2 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
0,00062
-0,00194
u(I m(xi ))
combined 1-sigma
0,00088
Table 53
r(x,y) -0,83
36
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Figure 15: Matched load - Measurements of S11 along with CRV and its expanded uncertainty
(k = 2, 45) at 2 GHz
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0015 0,0015
0,0053 0,0050
0,0010 0,0010
0,0101 0,0024
0,0041
0,0036
INTI
y
dy
0,0006
0,0095
0,0009 0,0016
0,0141 0,0065
0,0055
0,0069
NIST
y
dy
0,0006 -
0,0095 -
0,0012 0,0019
0,0141 0,0062
0,0053
0,0077
Table 54: Matched load - DoE of S11 at 2 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0009
0,0141
0,0012
0,0141
-
-
0,0007
0,0129
0,0050
0,0134
CENAM
y
dy
0,0016 0,0019 0,0007
-
0,0065 0,0062 0,0129
-
0,0046
0,0046
NPLI
y
dy
0,0055 0,0053 0,0050 0,0046
0,0069 0,0077 0,0134 0,0046
-
-
Table 55: Matched load - DoE of S11 at 2 GHz
37
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Figure 16: Matched load - DoE of S11 respect to CRV at 2 GHz
INTI CENAM
KCRV
y
dy
0,0006 0,0080 0,0009 0,0057
NPL
y
dy
0,0010 0,0084 0,0006 0,0063
PTB
y
dy
0,0009 0,0089 0,0023 0,0065
NMI-VSL
y
dy
0,0025 0,0104 0,0026 0,0117
Table 56: Matched load - CCEM/SIM Linked DoE of S11 at 2 GHz
INTI CENAM
INRIM
y
dy
0,0028 0,0153 0,0019 0,0147
METAS
y
dy
0,0011 0,0093 0,0005 0,0075
CMI
y
dy
0,0004 0,0141 0,0013 0,0126
UME
y
dy
0,0018 0,0159 0,0014 0,0151
Table 57: Matched load - CCEM/SIM Linked DoE of S11 at 2 GHz
INTI CENAM
NMIA
y
dy
0,0009 0,0095
0,0013 0,0068
SPRING
y
dy
0,0018 0,0164
0,0014 0,0121
SCL
y
dy
0,0010 0,0122 0,0018 0,0103
SNIIM
y
dy
0,0021 0,0094
0,0017 0,0085
Table 58: Matched load - CCEM/SIM Linked DoE of S11 at 2 GHz
38
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI CENAM
NIM
y
dy
0,0005 0,0082 0,0011 0,0060
CSIR
y
dy
0,0006 0,0100
0,0011 0,0082
NMIJ
y
dy
0,0005 0,0086
0,0012 0,0064
SP
y
dy
0,0007 0,0103 0,0015 0,0079
Table 59: Matched load - CCEM/SIM Linked DoE of S11 at 2 GHz
INTI CENAM
LNE
y
dy
0,0004 0,0132 0,0019 0,0114
Table 60: Matched load - CCEM/SIM Linked DoE of S11 at 2 GHz
39
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Lab i
INTI NIST NRC CENAM NPLI
Re(S11)
-0,00403 -0,00264 -0,00119 -0,00404 -0,01441
Measurement and combined standard uncertainty
S11 of Matched load at 9 GHz
u(Re(S11))
combined 1-sigma
I m(S11 )
u(I m(S11 ))
combined 1-sigma
0,00284
0,01550
0,00284
0,00349
0,01770
0,00438
0,00600
0,02339
0,00600
0,00222
0,01643
0,00151
0,00551
0,02265
0,00551
Table 61
r(x, y)
0,00 0,00 0,00 -0,74 -0,51
Re(xi) -0,00526
Reference Value (CRV)
S11 of Matched load at 9 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
0,00235
0,01913
u(I m(xi ))
combined 1-sigma
0,00163
Table 62
r(x,y) -0,35
Figure 17: Matched load - Measurements of S11 along with CRV and its expanded uncertainty
(k = 2, 45) at 9 GHz
40
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0038 0,0030 0,0059 0,0030 0,0098
0,0070 0,0092 0,0121 0,0053 0,0127
INTI
y
dy
0,0026 0,0084 0,0009 0,0126
0,0122 0,0163 0,0077 0,0176
NIST
y
dy
0,0026 -
0,0059 0,0019 0,0128
0,0122 -
0,0181 0,0099 0,0173
Table 63: Matched load - DoE of S11 at 9 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0084 0,0059
0,0075 0,0132
0,0163 0,0181
0,0149 0,0192
CENAM
y
dy
0,0009 0,0019 0,0075
0,0121
0,0077 0,0099 0,0149
0,0169
NPLI
y
dy
0,0126 0,0128 0,0132 0,0121
-
0,0176 0,0173 0,0192 0,0169
-
Table 64: Matched load - DoE of S11 at 9 GHz
Figure 18: Matched load - DoE of S11 respect to CRV at 9 GHz 41
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI CENAM
KCRV
y
dy
0,0042 0,0111
0,0034 0,0089
NPL
y
dy
0,0032 0,0113
0,0023 0,0090
PTB
y
dy
0,0068 0,0115
0,0059 0,0096
NMI-VSL
y
dy
0,0046 0,0224
0,0037 0,0217
Table 65: Matched load - CCEM/SIM Linked DoE of S11 at 9 GHz
INTI CENAM
INRIM
y
dy
0,0055 0,0166 0,0047 0,0159
METAS
y
dy
0,0057 0,0142 0,0048 0,0135
CMI
y
dy
0,0058 0,0159 0,0049 0,0152
UME
y
dy
0,0048 0,0200 0,0040 0,0199
Table 66: Matched load - CCEM/SIM Linked DoE of S11 at 9 GHz
INTI CENAM
NMIA
y
dy
0,0053 0,0121 0,0044 0,0109
SPRING
y
dy
0,0037 0,0187 0,0028 0,0179
SCL
y
dy
0,0043 0,0268 0,0035 0,0265
SNIIM
y
dy
0,0051 0,0112 0,0047 0,0096
Table 67: Matched load - CCEM/SIM Linked DoE of S11 at 9 GHz
INTI CENAM
NIM
y
dy
0,0061 0,0110 0,0059 0,0098
CSIR
y
dy
0,0037 0,0125
0,0028 0,0111
NMIJ
y
dy
0,0044 0,0106
0,0042 0,0094
SP
y
dy
0,0047 0,0126 0,0046 0,0118
Table 68: Matched load - CCEM/SIM Linked DoE of S11 at 9 GHz
INTI CENAM
LNE
y
dy
0,0032 0,0155 0,0027 0,0142
Table 69: Matched load - CCEM/SIM Linked DoE of S11 at 9 GHz
42
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Lab i
INTI NIST NRC CENAM NPLI
Re(S11)
0,02690 0,02616 0,03261 0,02836 0,01336
Measurement and combined standard uncertainty
S11 of Matched load at 18 GHz
u(Re(S11))
combined 1-sigma
I m(S11 )
u(I m(S11 ))
combined 1-sigma
0,00341
0,05679
0,00341
0,00473
0,05333
0,00685
0,00800
0,06458
0,00800
0,00263
0,05670
0,00174
0,00601
0,06596
0,00601
Table 70
r(x, y)
0,00 0,00 0,00 0,31 0,76
Re(xi) 0,02548
Reference Value (CRV)
S11 of Matched load at 18 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
u(I m(xi ))
combined 1-sigma
0,00323
0,05947
0,00246
Table 71
r(x,y) -0,37
Figure 19: Matched load - Measurements of S11 along with CRV and its expanded uncertainty
(k = 2, 45) at 18 GHz
43
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0030 0,0062 0,0088 0,0040 0,0137
0,0097 0,0144 0,0163 0,0086 0,0103
INTI
y
dy
0,0035 0,0097 0,0015 0,0163
0,0185 0,0213 0,0104 0,0112
NIST
y
dy
0,0035 -
0,0130 0,0040 0,0180
0,0185 -
0,0249 0,0160 0,0158
Table 72: Matched load - DoE of S11 at 18 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0097 0,0130
0,0090 0,0193
0,0213 0,0249
0,0204 0,0231
CENAM
y
dy
0,0015 0,0040 0,0090
0,0176
0,0104 0,0160 0,0204
0,0088
NPLI
y
dy
0,0163 0,0180 0,0193 0,0176
-
0,0112 0,0158 0,0231 0,0088
-
Table 73: Matched load - DoE of S11 at 18 GHz
Figure 20: Matched load - DoE of S11 respect to CRV at 18 GHz 44
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI CENAM
KCRV
y
dy
0,0022 0,0133
0,0037 0,0120
NPL
y
dy
0,0038 0,0138
0,0053 0,0128
PTB
y
dy
0,0036 0,0134
0,0051 0,0123
NMI-VSL
y
dy
0,0049 0,0193
0,0064 0,0186
Table 74: Matched load - CCEM/SIM Linked DoE of S11 at 18 GHz
INTI CENAM
INRIM
y
dy
0,0041 0,0186 0,0054 0,0173
METAS
y
dy
0,0027 0,0170 0,0039 0,0151
CMI
y
dy
0,0022 0,0190 0,0031 0,0170
UME
y
dy
0,0032 0,0219 0,0042 0,0203
Table 75: Matched load - CCEM/SIM Linked DoE of S11 at 18 GHz
INTI CENAM
NMIA
y
dy
0,0006 0,0165 0,0014 0,0138
SPRING
y
dy
0,0011 0,0212 0,0018 0,0155
SCL
y
dy
0,0022 0,0278 0,0036 0,0272
SNIIM
y
dy
0,0062 0,0144 0,0075 0,0134
Table 76: Matched load - CCEM/SIM Linked DoE of S11 at 18 GHz
INTI CENAM
NIM
y
dy
0,0058 0,0137 0,0073 0,0126
CSIR
y
dy
0,0066 0,0171
0,0066 0,0155
NMIJ
y
dy
0,0045 0,0152
0,0041 0,0138
SP
y
dy
0,0028 0,0185 0,0028 0,0172
Table 77: Matched load - CCEM/SIM Linked DoE of S11 at 18 GHz
INTI CENAM
LNE
y
dy
0,0033 0,0195 0,0019 0,0187
Table 78: Matched load - CCEM/SIM Linked DoE of S11 at 18 GHz
45
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
A.4 Mismatched load
Lab i
INTI NIST NRC CENAM NPLI
Re(S11)
0,31844 0,31613 0,31924 0,31774 0,32436
Measurement and combined standard uncertainty
S11 of Mismatched load at 2 GHz
u(Re(S11))
combined 1-sigma
I m(S11 )
u(I m(S11 ))
combined 1-sigma
0,00300 0,00359 0,00520 0,00109 0,00582
0,08359 0,08477 0,08498 0,08620 0,08470
0,00300 0,00344 0,00520 0,00160 0,00582
Table 79
r(x, y)
0,00 0,00 0,00 0,42 -0,44
Re(xi) 0,31918
Reference Value (CRV)
S11 of Mismatched load at 2 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
u(I m(xi ))
combined 1-sigma
0,00139
0,08485
0,00041
Table 80
r(x,y) -0,13
46
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Figure 21: Mismatched load - Measurements of S11 along with CRV and its expanded uncertainty
(k = 2, 45) at 2 GHz
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0015 0,0031
0,0059 0,0076
0,0001 0,0020
0,0100 0,0032
0,0052
0,0106
INTI
y
dy
0,0026
0,0114
0,0016 0,0027
0,0147 0,0081
0,0060
0,0142
NIST
y
dy
0,0026 -
0,0114 -
0,0031 0,0021
0,0155 0,0095
0,0082
0,0159
Table 81: Mismatched load - DoE of S11 at 2 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0016
0,0147
0,0031
0,0155
-
-
0,0019
0,0130
0,0051
0,0188
CENAM
y
dy
0,0027 0,0021 0,0019
-
0,0081 0,0095 0,0130
-
0,0068
0,0146
NPLI
y
dy
0,0060 0,0082 0,0051 0,0068
0,0142 0,0159 0,0188 0,0146
-
-
Table 82: Mismatched load - DoE of S11 at 2 GHz
47
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Figure 22: Mismatched load - DoE of S11 respect to CRV at 2 GHz
48
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Lab i
INTI NIST NRC CENAM NPLI
Re(S11)
-0,31298 -0,31491 -0,31733 -0,31458 -0,32919
Measurement and combined standard uncertainty
S11 of Mismatched load at 9 GHz
u(Re(S11))
combined 1-sigma
I m(S11 )
u(I m(S11 ))
combined 1-sigma
0,00455
0,15726
0,00455
0,00434
0,15502
0,00416
0,00800
0,16852
0,00800
0,00274
0,15565
0,00148
0,00881
0,16247
0,00881
Table 83
r(x, y)
0,00 0,00 0,00 0,58 -0,53
Re(xi) -0,31780
Reference Value (CRV)
S11 of Mismatched load at 9 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
u(I m(xi ))
combined 1-sigma
0,00293
0,15978
0,00255
Table 84
r(x,y) -0,44
Figure 23: Mismatched load - Measurements of S11 along with CRV and its expanded uncertainty
(k = 2, 45) at 9 GHz
49
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0054 0,0056 0,0087 0,0052 0,0117
0,0118 0,0110 0,0163 0,0080 0,0178
INTI
y
dy
0,0030 0,0121 0,0023 0,0170
0,0152 0,0226 0,0129 0,0254
NIST
y
dy
0,0030 -
0,0137 0,0007 0,0161
0,0152 -
0,0221 0,0116 0,0270
Table 85: Mismatched load - DoE of S11 at 9 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0121 0,0137
0,0132 0,0133
0,0226 0,0221
0,0198 0,0251
CENAM
y
dy
0,0023 0,0007 0,0132
0,0161
0,0129 0,0116 0,0198
0,0249
NPLI
y
dy
0,0170 0,0161 0,0133 0,0161
-
0,0254 0,0270 0,0251 0,0249
-
Table 86: Mismatched load - DoE of S11 at 9 GHz
Figure 24: Mismatched load - DoE of S11 respect to CRV at 9 GHz 50
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Lab i
INTI NIST NRC CENAM NPLI
Re(S11)
0,00093 -0,00211 0,00409 -0,00329 -0,01595
Measurement and combined standard uncertainty
S11 of Mismatched load at 18 GHz
u(Re(S11))
combined 1-sigma
I m(S11 )
u(I m(S11 ))
combined 1-sigma
0,00660
0,29499
0,00660
0,00521
0,29549
0,00740
0,01000
0,30607
0,01000
0,00257
0,29595
0,00244
0,00881
0,31020
0,00881
Table 87
r(x, y)
0,00 0,00 0,00 -0,83 0,62
Re(xi) -0,00326
Reference Value (CRV)
S11 of Mismatched load at 18 GHz
u(Re(xi))
combined 1-sigma
I m(xi )
u(I m(xi ))
combined 1-sigma
0,00342
0,30054
0,00317
Table 88
r(x,y) -0,51
Figure 25: Mismatched load - Measurements of S11 along with CRV and its expanded uncertainty
(k = 2, 45) at 18 GHz
51
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
INTI NIST NRC CENAM NPLI
CRV
y
dy
0,0070 0,0052 0,0092 0,0046 0,0159
0,0159 0,0163 0,0199 0,0073 0,0144
INTI
y
dy
0,0031 0,0115 0,0043 0,0227
0,0207 0,0294 0,0177 0,0209
NIST
y
dy
0,0031 -
0,0123 0,0013 0,0202
0,0207 -
0,0297 0,0150 0,0204
Table 89: Mismatched load - DoE of S11 at 18 GHz
INTI NIST NRC CENAM NPLI
NRC
y
dy
0,0115 0,0123
0,0125 0,0205
0,0294 0,0297
0,0246 0,0298
CENAM
y
dy
0,0043 0,0013 0,0125
0,0191
0,0177 0,0150 0,0246
0,0156
NPLI
y
dy
0,0227 0,0202 0,0205 0,0191
-
0,0209 0,0204 0,0298 0,0156
-
Table 90: Mismatched load - DoE of S11 at 18 GHz
Figure 26: Mismatched load - DoE of S11 respect to CRV at 18 GHz 52
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Annex B: Uncertainty budget
B.1 INTI Uncertainty Budgets
B.1.1 Reflection measurements
Uncertainty region of complex input quantities was considered circular, that is: u(xi) = u(re(xi)) = u(im(xi)) and cov(re(xi), im(xi)) = 0. According to [8] , if the uncertainty region of the input quantities satisfies these properties, the uncertainty region of the measurand will satisfy the same properties, namely: u(s11) = u(re(s11)) = u(im(s11)) and cov(re(s11), im(s11)) = 0. For this reason, the real and imaginary uncertainty components are identical.
Due to the correlation between effective directivity and effective source match [14], real and imaginary standard deviation (square root of variances) of their distributions were linearly added to get a worst case circular uncertainty region (see [9] for further details).
Quantity
Eff. Directivity Eff. Test p. match
Linear sum Linearity Repeatability
Standard Uncertainty
u(xi)
0,00248
0,00290
Probability distribution (Bidimentional)
Ring Ring
0,00000 0,00007
Ring
urep= u2rep(re(xi)) + u2rep(im(xi))
Matched load at 2 GHz
Sensitivity coefficient
ci
1
Uncertainty contribution
ciu(xi)
0,00248
|Γm|2 1
0,00000 0,00248 0,00000
1
utotal
0,00007 0,00248
53
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Eff. Directivity Eff. Test p. match
Linear sum Linearity Repeatability
Standard Uncertainty
u(xi)
0,00283
0,00198
Probability distribution (Bidimentional)
Ring Ring
0,00003 0,00025
Ring
urep= ur2ep(re(xi)) + u2rep(im(xi))
Matched load at 9 GHz
Sensitivity coefficient
ci
1
Uncertainty contribution
ciu(xi)
0,00283
|Γm|2 1
0,00000 0,00283 0,00003
1
utotal
0,00025 0,00284
Quantity
Eff. Directivity Eff. Test p. match
Linear sum Linearity Repeatability
Standard Uncertainty
u(xi)
0,00332
0,00820
Probability distribution (Bidimentional)
Ring Ring
0,00003 0,00058
Ring
urep= u2rep(re(xi)) + u2rep(im(xi))
Matched load at 18 GHz
Sensitivity coefficient
ci
1
Uncertainty contribution
ciu(xi)
0,00332
|Γm|2 1
0,00003 0,00336 0,00003
1
utotal
0,00058 0,00341
54
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Eff. Directivity Eff. Test p. match
Linear sum Tracking Linearity
Repeatability
Standard Uncertainty
u(xi)
0,00262
0,00339
Probability distribution (Bidimentional)
Ring Ring
0,00050 0,00000 0,00018
Disc Ring
urep= u2rep(re(xi)) + ur2ep(im(xi))
Mismatched load at 2 GHz
Sensitivity coefficient
ci
1
Uncertainty contribution
ciu(xi)
0,00262
|Γm|2 |Γm|
0,00037 0,02985 0,00016
1
0,00000
1
utotal
0,00018 0,00300
Quantity
Eff. Directivity Eff. Test p. match
Linear sum Tracking Linearity
Repeatability
Standard Uncertainty
u(xi)
0,00431
0,00184
Probability distribution (Bidimentional)
Ring Ring
0,00050 0,00000 0,00031
Disc Ring
urep= u2rep(re(xi)) + ur2ep(im(xi))
Mismatched load at 9 GHz
Sensitivity coefficient
ci
1
Uncertainty contribution
ciu(xi)
0,00431
|Γm|2 |Γm|
0,00023 0,00454 0,00018
1
0,00000
1
utotal
0,00031 0,00455
55
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Eff. Directivity Eff. Test p. match
Linear sum Tracking Linearity
Repeatability
Standard Uncertainty
u(xi)
0,00566
0,01054
Probability distribution (Bidimentional)
Ring Ring
0,00050 0,00023 0,00054
Disc Ring
urep= u2rep(re(xi)) + u2rep(im(xi))
Mismatched load at 18 GHz
Sensitivity coefficient
ci
1
Uncertainty contribution
ciu(xi)
0,00566
|Γm|2 |Γm|
0,00092 0,00657 0,00015
1
0,00023
1
utotal
0,00054 0,00660
56
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
B.1.2 Transmission measurements
Uncertainty estimation in transmission measurement was performed considering only the magnitude of measurand. If the condition u(|S21|) |S21| is fulfilled, we can assume a circular uncertainty region of the measurand, where u(|S21|) = u(re(S21)) = u(im(S21)) and cov(re(S21), im(S21)) = 0.
Quantity Mtm
Standard Uncertainty
u(xi)
0,00020
Probability distribution Σ U-type
Sensitivity coefficient
ci
8, 686
Uncertainty contribution
ciu(xi)
0,00174 dB
Linearity
0,00168 dB
Rectangular
1
0,00168 dB
Stability
0,00100 dB
Gaussian
1
0,00100 dB
Cable flex
0,00172 dB
Gaussian
1
0,00172 dB
Repeatability 0,00181 dB
urep
1
0,00181 dB
u(|S21|)total u(|S21|)total
0,00362 dB 0,00029
3 dB Attenuator S21 at 2 GHz
Quantity
Mtm Linearity Stability Cable flex Repeatability
Standard Uncertainty
u(xi)
0,00039
Probability distribution Σ U-type
Sensitivity coefficient
ci
8, 686
Uncertainty contribution
ciu(xi)
0,00335 dB
0,00613 dB
Rectangular
1
0,00613 dB
0,00100 dB
Gaussian
1
0,00100 dB
0,00298 dB
Gaussian
1
0,00298 dB
0,00522 dB
urep
1
0,00522 dB
u(|S21|)total u(|S21|)total
0,00926 dB 0,00076
3 dB Attenuator S21 at 9 GHz
57
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Mtm Linearity Stability Cable flex Repeatability
Standard Uncertainty
u(xi)
0,00129
Probability distribution Σ U-type
Sensitivity coefficient
ci
8, 686
Uncertainty contribution
ciu(xi)
0,01122 dB
0,00168 dB
Rectangular
1
0,00168 dB
0,00200 dB
Gaussian
1
0,00200 dB
0,00083 dB
Gaussian
1
0,00083 dB
0,01013 dB
urep
1
0,01013 dB
u(|S21|)total u(|S21|)total
0,01536 dB 0,00125
3 dB Attenuator S21 at 18 GHz
Quantity
Mtm Linearity Stability Cable flex Isolation Repeatability
Standard Uncertainty
u(xi)
0,00003
Probability distribution Σ U-type
Sensitivity coefficient
ci
8, 686
Uncertainty contribution
ciu(xi)
0,00022 dB
0,01162 dB
Rectangular
1
0,01162 dB
0,00100 dB
Gaussian
1
0,00100 dB
0,00172 dB
Gaussian
1
0,00172 dB
0,00088 dB
Gaussian
1
0,00088 dB
0,00183 dB
urep
1
0,00183 dB
u(|S21|)total u(|S21|)total
0,01196 dB 0,00014
20 dB Attenuator S21 at 2 GHz
58
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Mtm Linearity Stability Cable flex Isolation Repeatability
Standard Uncertainty
u(xi)
0,00018
Probability distribution Σ U-type
Sensitivity coefficient
ci
8, 686
Uncertainty contribution
ciu(xi)
0,00156 dB
0,01162 dB
Rectangular
1
0,01162 dB
0,00100 dB
Gaussian
1
0,00100 dB
0,00298 dB
Gaussian
1
0,00298 dB
0,00100 dB
Gaussian
1
0,00100 dB
0,00434 dB
urep
1
0,00434 dB
u(|S21|)total u(|S21|)total
0,01293 dB 0,00015
20 dB Attenuator S21 at 9 GHz
Quantity
Mtm Linearity Stability Cable flex Isolation Repeatability
Standard Uncertainty
u(xi)
0,00093
Probability distribution Σ U-type
Sensitivity coefficient
ci
8, 686
Uncertainty contribution
ciu(xi)
0,00804 dB
0,00751 dB
Rectangular
1
0,00751 dB
0,00200 dB
Gaussian
1
0,00200 dB
0,00083 dB
Gaussian
1
0,00083 dB
0,00525 dB
Gaussian
1
0,00525 dB
0,00890 dB
urep
1
0,00890 dB
u(|S21|)total u(|S21|)total
0,01524 dB 0,00017
20 dB Attenuator S21 at 18 GHz
59
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
B.2 NIST Uncertainty Budgets
Uncertainties were obtained for magnitude and phase coordinates of measurand, then the uncertainties for real and imaginary components were obtained through a proper coordinates transformation.
B.2.1 Reflection measurements
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0017 0,0006 0,0001 36,35 0,03 2,45
magnitude magnitude magnitude phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude Expanded Unc. Phase
0,0036 72,74
Matched load at 2 GHz
(deg)
60
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0018 0,0012 0,0005 5,55 0,07 0,87
magnitude magnitude magnitude phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude Expanded Unc. Phase
0,0044 11,11
Matched load at 9 GHz
(deg)
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0019 0,0032 0,0004 1,77 0,18 1,18
magnitude magnitude magnitude phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude Expanded Unc. Phase
Matched load 18 GHz
0,0074 3,68
(deg)
61
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0017 0,0006 0,0000 0,30 0,03 0
magnitude magnitude magnitude phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude Expanded Unc. Phase
0,0036 0,6
Mismatched load at 2 GHz
(deg)
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0018 0,0012 0,0001 0,33 0,07 0,01
magnitude magnitude magnitude phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude Expanded Unc. Phase
0,0044 0,67
Mismatched load at 9 GHz
(deg)
62
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0019 0,0032 0,0001 0,47 0,18 0,03
magnitude magnitude magnitude phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude Expanded Unc. Phase
0,0074 1,01
Mismatched load at 18 GHz
(deg)
63
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
B.2.2 Transmission measurements
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0020 0,0080 0,0030 0,12 0,08 0,05
magnitude(dB) magnitude(dB) magnitude(dB)
phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude Expanded Unc. Phase
0,016 0,30
3 dB Attenuator S21 at 2 GHz
(dB) (deg)
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0040 0,0110 0,0400 0,44 0,14 0,08
magnitude(dB) magnitude(dB) magnitude(dB)
phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude
0,04
Expanded Unc. Phase
0,93
3 dB Attenuator S21 at 9 GHz
(dB) (deg)
64
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0060 0,0180 0,0090 0,87 0,27 0,09
magnitude(dB) magnitude(dB) magnitude(dB)
phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude Expanded Unc. Phase
0,039 1,82
3 dB Attenuator S21 at 18 GHz
(dB) (deg)
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0020 0,0080 0,0010 0,12 0,08 0,05
magnitude(dB) magnitude(dB) magnitude(dB)
phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude Expanded Unc. Phase
0,016 0,30
20 dB Attenuator S21 at 2 GHz
(dB) (deg)
65
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0040 0,0110 0,0470 0,44 0,14 0,06
magnitude(dB) magnitude(dB) magnitude(dB)
phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude Expanded Unc. Phase
0,047 0,93
20 dB Attenuator S21 at 9 GHz
(dB) (deg)
Uncertainty contribution
Type B - due to imperfections in air line standards and test ports (1 sigma)
Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma) Type B - due to imperfections in air line
standards and test ports (1 sigma) Type A - due to connector variability, long term system variations, power meter resolution, and system noise during calibration (1 sigma) Type A - evaluated from repeat measurements
of the device under test (1 sigma)
Estimated value 0,0060 0,0180 0,0210 0,87 0,27 0,02
magnitude(dB) magnitude(dB) magnitude(dB)
phase (deg) phase (deg) phase (deg)
Expanded Unc. Magnitude Expanded Unc. Phase
0,042 1,82
20 dB Attenuator S21 at 18 GHz
(dB) (deg)
66
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
B.3 NRC Uncertainty Budgets
B.3.1 Small reflection coeficient
The next tables give the error budget for the well matched terminations. There is no phase, and the uncertainty on both components (Re,Im) are equal and assumed to be not correlated. This condition applies in the case of the termination #55719 at 2, 9, and 18 GHz respectively.
Matched termination #55719 uncertainty at 2 GHz
Airlines standards Connector Repeatability Combined Uncertainty
0,005 0,001 0,0052
rect Gauss k=1
Matched termination #55719 uncertainty at 9 GHz
Airlines standards Connector Repeatability Combined Uncertainty
0,005 0,002 0,006
rect Gauss k=1
Matched termination #55719 uncertainty at 18 GHz
Airlines standards Connector Repeatability Combined Uncertainty
0,005 0,004 0,008
rect Gauss k=1
67
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
B.3.2 Large reflection coeficient
When the reflection coefficient is large, then the phase of the reflection coefficient becomes more important. It is linked to the length of the calibration standards. We have performed many calibrations/measurements cycles with different experimental configurations, and we find that the phase varies for the high frequencies. The standard deviation for the phase of the mismatch termination is about one degree (N=7). We include this uncertainty component that we call “length of short/lines”.
The next tables give the error budget in the case of the mismatched termination #9006 at 2, 9, and 18 GHz respectively.
Mismatch termination #9006 uncertainty at 2 GHz
Airlines standards Connector Repeatability Combined Uncertainty
0,005 0,001 0,0052
rect Gauss k=1
Mismatch termination #9006 uncertainty at 9 GHz
Airlines standards Connector Repeatability Length of short/lines Combined Uncertainty
0,005 0,002 0,004 0,008
rect Gauss rect k=1
Mismatch termination #9006 uncertainty at 18 GHz
Airlines standards Connector Repeatability Length of short/lines Combined Uncertainty
0,005 0,004 0,008 0,010
rect Gauss rect k=1
68
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
B.3.3 Large transmission coefficient
In the case of the transmission, the uncertainty is largely due to the connector repeatability. The system is characterized by comparison to a similar measurement using a matched source and matched receiver. This uncertainty can also be compared to the deviation of a single connector during a power factor calibration. Also a THRU measurement can be performed before and after the measurement and give an idea of the performance of the cables, etc... The measurements that appear “stable” are sometimes difficult to reproduce.
The next tables give the uncertainty for the transmission coefficients of the 3 dB attenuator #66530 and 20 dB attenuator #66597 at 2, 9, and 18 GHz.
Transmission uncertainty at 2 GHz for (3 dB) att. #66530
Connector Repeatability Combined Uncertainty
0,0025 0,0025
Gauss k=1
Transmission uncertainty at 9 GHz for (3 dB) att. #66530
Connector Repeatability Combined Uncertainty
0,0025 0,0025
Gauss k=1
Transmission uncertainty at 18 GHz for (3 dB) att. #66530
Connector Repeatability Combined Uncertainty
0,0025 0,0025
Gauss k=1
Transmission uncertainty at 2 GHz for (20 dB) att. #66597
Connector Repeatability Combined Uncertainty
0,0025 0,0025
Gauss k=1
Transmission uncertainty at 9 GHz for (20 dB) att. #66597
Connector Repeatability Combined Uncertainty
0,0025 0,0025
Gauss k=1
Transmission uncertainty at 18 GHz for (20 dB) att. #66597
Connector Repeatability Combined Uncertainty
0,0025 0,0025
Gauss k=1
69
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
B.4 CENAM Uncertainty Budgets
B.4.1 Reflection measurements (TRL -METHOD)
Quantity
Effective Directivity Effective Test Port
Match Linear sum of the directivity and test
port match Reflection Tracking
Linearity System Repeatability
Connector Repeatability Ambient Conditions Reference Line Repeat measurements
Standard Uncertainty Mag[u(xi)]
0,0009005
Probability Distribution U-shaped
0,0015293
U-shaped
Sensitivity Coefficient
ci
1
Uncertainty contribution Mag[ciu(xi)]
0,0009005
0,000003 0,000000004
U-shaped
0,0011547 0,0002228 0,0001155
Rectangular Rectangular Rectangular
0,0016 0,0016
1
0,0000385
Gaussian
1
0,0002659
Rectangular
1
0,0005245
Rectangular
1
0,0000260
Gaussian
1
Magnitude combined uncertainty (k = 1):
0,0009005
0,000002 0,000000 0,000115
0,000038
0,000266 0,000524 0,000026
0,00108
Matched load at 2 GHz
Quantity
Magnitude of reflection
coefficient 0.0016 at 2 GHz Thermal
coefficient in phase Repeat
measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
42,37
Gaussian
1
42,37
0,12
Rectangular
1
0,81
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
Matched load at 2 GHz
0,12
0,81 42,38 0,0009 0,0013
70
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Effective Directivity Effective Test Port
Match Linear sum of the directivity and test
port match Reflection Tracking
Linearity System Repeatability
Connector Repeatability Ambient Conditions Reference Line Repeat measurements
Standard Uncertainty Mag[u(xi)]
0,0017967
Probability Distribution U-shaped
0,0018175
U-shaped
Sensitivity Coefficient
ci
1
Uncertainty contribution Mag[ciu(xi)]
0,0017967
0,000286 0,000000520
U-shaped
0,0011547 0,0001413 0,0001155
Rectangular Rectangular Rectangular
0,0169 0,0169
1
0,0000427
Gaussian
1
0,0002659
Rectangular
1
0,0005245
Rectangular
1
0,0000546
Gaussian
1
Magnitude combined uncertainty (k = 1):
0,0017973
0,000020 0,000002 0,000115
0,000043
0,000266 0,000524 0,000055
0,00190
Matched load at 9 GHz
Quantity
Magnitude of reflection
coefficient 0.0169 at 9 GHz Thermal
coefficient in phase Repeat
measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
6,43
Gaussian
1
6,43
0,12
Rectangular
1
0,16
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
Matched load at 9 GHz
0,12
0,16 6,44 0,0022 0,0015
71
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Effective Directivity Effective Test Port
Match Linear sum of the directivity and test
port match Reflection Tracking
Linearity System Repeatability
Connector Repeatability Ambient Conditions Reference Line Repeat measurements
Standard Uncertainty Mag[u(xi)]
0,0020393
Probability Distribution U-shaped
0,0024802
U-shaped
Sensitivity Coefficient
ci
1
Uncertainty contribution Mag[ciu(xi)]
0,0020393
0,004021 0,000009972
U-shaped
0,0017321 0,0005094 0,0005196
Rectangular Rectangular Rectangular
0,0634 0,0634
1
0,0000796
Gaussian
1
0,0003989
Rectangular
1
0,0005245
Rectangular
1
0,0001171
Gaussian
1
Magnitude combined uncertainty (k = 1):
0,0020493
0,000110 0,000032 0,000520
0,000080
0,000399 0,000524 0,000117
0,00222
Matched load at 18 GHz
Quantity
Magnitude of reflection
coefficient 0.0634 at 18 GHz Thermal coefficient in phase Repeat
measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
2,01
Gaussian
1
2,01
0,12
Rectangular
1
0,14
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
Matched load at 18 GHz
0,12
0,14 2,02 0,0026 0,0017
72
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Effective Directivity Effective Test Port
Match Linear sum of the directivity and test
port match Reflection Tracking
Linearity System Repeatability
Connector Repeatability Ambient Conditions Reference Line Repeat measurements
Standard Uncertainty Mag[u(xi)]
0,0009005
Probability Distribution U-shaped
0,0015293
U-shaped
Sensitivity Coefficient
ci
1
Uncertainty contribution Mag[ciu(xi)]
0,0009005
0,108386 0,000165752
U-shaped
0,0011547 0,0000385 0,0001155
Rectangular Rectangular Rectangular
0,3292 0,3292
1
0,0000385
Gaussian
1
0,0002659
Rectangular
1
0,0005245
Rectangular
1
0,0000283
Gaussian
1
Magnitude combined uncertainty (k = 1):
0,0010663
0,000380 0,000013 0,000115
0,000038
0,000266 0,000524 0,000028
0,00128
Mismatched load at 2 GHz
Quantity
Magnitude of reflection
coefficient 0.0016 at 2 GHz Thermal
coefficient in phase Repeat
measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
0,223
Gaussian
1
0,223
0,115
Rectangular
1
0,005
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
Mismatched load at 2 GHz
0,115
0,005 0,251 0,0011 0,0016
73
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Effective Directivity Effective Test Port
Match Linear sum of the directivity and test
port match Reflection Tracking
Linearity System Repeatability
Connector Repeatability Ambient Conditions Reference Line Repeat measurements
Standard Uncertainty Mag[u(xi)]
0,0017967
Probability Distribution U-shaped
0,0018175
U-shaped
Sensitivity Coefficient
ci
1
Uncertainty contribution Mag[ciu(xi)]
0,0017967
0,123184 0,000223893
U-shaped
0,0011547 0,0000363 0,0001155
Rectangular Rectangular Rectangular
0,3510 0,3510
1
0,0000427
Gaussian
1
0,0002659
Rectangular
1
0,0005245
Rectangular
1
0,0000334
Gaussian
1
Magnitude combined uncertainty (k = 1):
0,0020206
0,000405 0,000013 0,000115
0,000043
0,000266 0,000524 0,000033
0,00215
Mismatched load at 9 GHz
Quantity
Magnitude of reflection
coefficient 0.0169 at 9 GHz Thermal
coefficient in phase Repeat
measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
0,350
Gaussian
1
0,350
0,115
Rectangular
1
0,018
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
Mismatched load at 9 GHz
0,115
0,018 0,369 0,0027 0,0015
74
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Effective Directivity Effective Test Port
Match Linear sum of the directivity and test
port match Reflection Tracking
Linearity System Repeatability
Connector Repeatability Ambient Conditions Reference Line Repeat measurements
Standard Uncertainty Mag[u(xi)]
0,0020393
Probability Distribution U-shaped
0,0024802
U-shaped
Sensitivity Coefficient
ci
1
Uncertainty contribution Mag[ciu(xi)]
0,0020393
0,087601 0,000217268
U-shaped
0,0017321 0,0002249 0,0005196
Rectangular Rectangular Rectangular
0,2960 0,2960
1
0,0000796
Gaussian
1
0,0003989
Rectangular
1
0,0005245
Rectangular
1
0,0000789
Gaussian
1
Magnitude combined uncertainty (k = 1):
0,0022566
0,000513 0,000067 0,000520
0,000080
0,000399 0,000524 0,000079
0,00246
Mismatched load at 18 GHz
Quantity
Magnitude of reflection
coefficient 0.0634 at 18 GHz Thermal coefficient in phase Repeat
measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
0,477
Gaussian
1
0,477
0,115
Rectangular
1
0,051
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
Mismatched load at 18 GHz
0,115
0,051 0,494 0,0026 0,0024
75
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
B.4.2 Transmission measurements (TRL -METHOD)
Quantity
Linearity Mismatch calculated
Cross-talk Transmission
Tracking System Repeatability Connector Repeatability Cable flexure Ambient Conditions Repeat measurements
Standard Uncertainty Mag[u(xi)]
[dB]
0.0000346 dB/dB 0,0007110 0,0000566
Probability Distribution
Rectangular U-shaped
Rectangular
0,0035281
Rectangular
Sensitivity Coefficient
ci
3,06 1 1
1
0,0006087
Gaussian
1
0,0003757
Gaussian
1
0,0008660
Rectangular
1
0,0023094
Rectangular
1
0,0002662
Gaussian
1
Magnitude combined uncertainty (k = 1):
Uncertainty contribution Mag[ciu(xi)]
[dB] 0,000106 0,000711 0,000057
0,003528
0,000609
0,000376
0,000866 0,002309
0,000266
0,00443
3 dB Attenuator S21 at 2 GHz
Quantity
Magnitude of transmission
coefficient Thermal coefficient
in phase Uncertainty in phase
standard Stability of the cable
Repeat measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
0,029
Gaussian
1
0,029
0,115
Rectangular
1
0,0010
Gaussian
1
0,058
Rectangular
1
0,003
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
0,115
0,001 0,058 0,003 0,132 0,0008 0,0014
3 dB Attenuator S21 at 2 GHz
76
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Linearity Mismatch calculated
Cross-talk Transmission
Tracking System Repeatability Connector Repeatability Cable flexure Ambient Conditions Repeat measurements
Standard Uncertainty Mag[u(xi)]
[dB]
0.0000346 dB/dB 0,0013700 0,0000554
Probability Distribution
Rectangular U-shaped
Rectangular
0,0144250
Rectangular
Sensitivity Coefficient
ci
2,87 1 1
1
0,0019679
Gaussian
1
0,0005112
Gaussian
1
0,0008660
Rectangular
1
0,0023094
Rectangular
1
0,0003702
Gaussian
1
Magnitude combined uncertainty (k = 1):
Uncertainty contribution Mag[ciu(xi)]
[dB] 0,000099 0,001370 0,000055
0,014425
0,001968
0,000511
0,000866 0,002309
0,000370
0,01484
3 dB Attenuator S21 at 9 GHz
Quantity
Magnitude of transmission
coefficient Thermal coefficient
in phase Uncertainty in phase
standard Stability of the cable
Repeat measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
0,098
Gaussian
1
0,098
0,115
Rectangular
1
0,004
Gaussian
1
0,260
Rectangular
1
0,024
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
0,115
0,004 0,260 0,024 0,302 0,0013 0,0038
3 dB Attenuator S21 at 9 GHz
77
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Linearity Mismatch calculated
Cross-talk Transmission
Tracking System Repeatability Connector Repeatability Cable flexure Ambient Conditions Repeat measurements
Standard Uncertainty Mag[u(xi)]
[dB]
0.0001848 dB/dB 0,0030026 0,0000562
Probability Distribution
Rectangular U-shaped
Rectangular
0,0266956
Rectangular
Sensitivity Coefficient
ci
2,99 1 1
1
0,0098988
Gaussian
1
0,0006047
Gaussian
1
0,0017321
Rectangular
1
0,0034641
Rectangular
1
0,0002906
Gaussian
1
Magnitude combined uncertainty (k = 1):
Uncertainty contribution Mag[ciu(xi)]
[dB] 0,000553 0,003003 0,000056
0,026696
0,009899
0,000605
0,001732 0,003464
0,000291
0,02890
3 dB Attenuator S21 at 18 GHz
Quantity
Magnitude of transmission
coefficient Thermal coefficient
in phase Uncertainty in phase
standard Stability of the cable
Repeat measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
0,191
Gaussian
1
0,191
0,115
Rectangular
1
0,009
Gaussian
1
0,520
Rectangular
1
0,062
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
0,115
0,009 0,520 0,062 0,569 0,0035 0,0066
3 dB Attenuator S21 at 18 GHz
78
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Linearity Mismatch calculated
Cross-talk Transmission
Tracking System Repeatability Connector Repeatability Cable flexure Ambient Conditions Repeat measurements
Standard Uncertainty Mag[u(xi)]
[dB]
0.0000346 dB/dB 0,0001208 0,0003969
Probability Distribution
Rectangular U-shaped
Rectangular
0,0005033
Rectangular
Sensitivity Coefficient
ci
19,97 1 1
1
0,0006087
Gaussian
1
0,0003757
Gaussian
1
0,0008660
Rectangular
1
0,0023094
Rectangular
1
0,0003259
Gaussian
1
Magnitude combined uncertainty (k = 1):
Uncertainty contribution Mag[ciu(xi)]
[dB] 0,000691 0,000121 0,000397
0,000503
0,000609
0,000376
0,000866 0,002309
0,000326
0,00276
20 dB Attenuator S21 at 2 GHz
Quantity
Magnitude of transmission
coefficient Thermal coefficient
in phase Uncertainty in phase
standard Stability of the cable
Repeat measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
0,018
Gaussian
1
0,018
0,115
Rectangular
1
0,0010
Gaussian
1
0,058
Rectangular
1
0,004
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
0,115
0,001 0,058 0,004 0,130 0,00013 0,00019
20 dB Attenuator S21 at 2 GHz
79
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Linearity Mismatch calculated
Cross-talk Transmission
Tracking System Repeatability Connector Repeatability Cable flexure Ambient Conditions Repeat measurements
Standard Uncertainty Mag[u(xi)]
[dB]
0.0000346 dB/dB 0,0006583 0,0003971
Probability Distribution
Rectangular U-shaped
Rectangular
0,0020125
Rectangular
Sensitivity Coefficient
ci
19,97 1 1
1
0,0019679
Gaussian
1
0,0005112
Gaussian
1
0,0008660
Rectangular
1
0,0023094
Rectangular
1
0,0005102
Gaussian
1
Magnitude combined uncertainty (k = 1):
Uncertainty contribution Mag[ciu(xi)]
[dB] 0,000691 0,000658 0,000397
0,002013
0,001968
0,000511
0,000866 0,002309
0,000510
0,00395
20 dB Attenuator S21 at 9 GHz
Quantity
Magnitude of transmission
coefficient Thermal coefficient
in phase Uncertainty in phase
standard Stability of the cable
Repeat measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
0,026
Gaussian
1
0,026
0,115
Rectangular
1
0,004
Gaussian
1
0,260
Rectangular
1
0,022
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
0,115
0,004 0,260 0,022 0,286 0,00036 0,00036
20 dB Attenuator S21 at 9 GHz
80
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Quantity
Linearity Mismatch calculated
Cross-talk Transmission
Tracking System Repeatability Connector Repeatability Cable flexure Ambient Conditions Repeat measurements
Standard Uncertainty Mag[u(xi)]
[dB]
0.0001848 dB/dB 0,0022239 0,0004032
Probability Distribution
Rectangular U-shaped
Rectangular
0,0037161
Rectangular
Sensitivity Coefficient
ci
20,11 1 1
1
0,0098988
Gaussian
1
0,0006047
Gaussian
1
0,0017321
Rectangular
1
0,0034641
Rectangular
1
0,0007994
Gaussian
1
Magnitude combined uncertainty (k = 1):
Uncertainty contribution Mag[ciu(xi)]
[dB] 0,003716 0,002224 0,000403
0,003716
0,009899
0,000605
0,001732 0,003464
0,000799
0,01211
20 dB Attenuator S21 at 18 GHz
Quantity
Magnitude of transmission
coefficient Thermal coefficient
in phase Uncertainty in phase
standard Stability of the cable
Repeat measurements
Standard Uncertainty Phase[u(xi)]
[Degrees]
Probability Distribution
Sensitivity Coefficient
ci
Uncertainty contribution Phase[ciu(xi)]
[Degrees]
0,080
Gaussian
1
0,080
0,115
Rectangular
1
0,009
Gaussian
1
0,520
Rectangular
1
0,055
Gaussian
1
Phase combined uncertainty (k = 1): Real component combined uncertainty (k = 1): Imaginary component combined uncertainty (k = 1):
0,115
0,009 0,520 0,055 0,541 0,00085 0,00041
20 dB Attenuator S21 at 18 GHz
81
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
B.5 NPLI Uncertainty Budgets
Both in reflection and transmission s-parameters measurement, the real and imaginary components are considered to have the same uncertainty u(re(sab)) = u(im(sab)).
B.5.1 Reflection measurements
Contribution
Effective Dir. Eff.TPmtch Sum Corr.Qnt. Tracking Linearity System Rep Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,004687 0,0312
0,001588 3,62E-05 0,000348 0,000323
0,002 0,000927
0,004687 1,16E-06 0,004688 9,68E-06 2,21E-07 2,12E-06 1,97E-06 1,22E-05 0,000927
U
1,414
U
1,414
U
1,414 0,003316
R
1,732 5,59E-06
R
1,732 1,27E-07
G
2
1,06E-06
G
2
9,84E-07
R
1,732 7,04E-06
t
3,16
0,000293
0,003329
Matched load at 2 GHz
Contribution
Effective Dir. Eff.TPmtch Sum Corr.Qnt. Tracking Linearity System Rep Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,007732 0,0329
0,008214 4,52E-05 0,000195 0,000395
0,002 0,001519
0,007732 2,37E-05 0,007756 0,000221 1,21E-06 5,23E-06 1,06E-05 5,37E-05 0,001519
U
1,414
U
1,414
U
1,414 0,005485
R
1,732 0,000127
R
1,732
7E-07
G
2
2,61E-06
G
2
5,3E-06
R
1,732
3,1E-05
t
3,16
0,000481
0,005508
Matched load at 9 GHz
82
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Contribution
Effective Dir. Eff.TPmtch Sum Corr.Qnt. Tracking Linearity System Rep Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,008164 0,0435
0,00279 5,41E-05 0,001589 0,001473
0,002 0,003322
0,008164 0,000197 0,008361 0,000188 3,64E-06 0,000107 9,91E-05 0,000135 0,003322
U
1,414
U
1,414
U
1,414 0,005913
R
1,732 0,000108
R
1,732
2,1E-06
G
2
5,35E-05
G
2
4,96E-05
R
1,732 7,77E-05
t
3,16
0,001051
0,006008
Matched load at 18 GHz
Contribution
Effective Dir. Eff.TPmtch Sum Corr.Qnt. Tracking Linearity System Rep Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,004687
0,004687
U
1,414
0,0312
0,003506325
U
1,414
0,008193325
U
1,414 0,0057944
0,001587703 0,000532253
R
1,732 0,0003073
0,000727304 0,000243817
R
1,732 0,0001408
0,000348341 0,000116776
G
2
5,839E-05
0,000322723 0,000108188
G
2
5,409E-05
0,002
0,000670469
R
1,732 0,0003871
0,000683317 0,000683317
t
3,16 0,0002162
0,0058217
Mismatched load at 2 GHz
Contribution
Effective Dir. Eff.TPmtch Sum Corr.Qnt. Tracking Linearity System Rep Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,007732
0,007732
U
1,414
0,0329
0,004433728
U
1,414
0,012165728
U
1,414 0,0086038
0,008213906 0,00301534
R
1,732 0,001741
0,000908868 0,000333647
R
1,732 0,0001926
0,000194736 7,14879E-05
G
2
3,574E-05
0,00039492 0,000144976
G
2
7,249E-05
0,002
0,000734204
R
1,732 0,0004239
0,001667015 0,001667015
t
3,16 0,0005275
0,0088067
Mismatched load at 9 GHz
83
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Contribution
Effective Dir. Eff.TPmtch Sum Corr.Qnt. Tracking Linearity System Rep Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,008164
0,008164
U
1,414
0,0435
0,004196884
U
1,414
0,012360884
U
1,414 0,0087418
0,002789687 0,000866511
R
1,732 0,0005003
0,001090328 0,000338669
R
1,732 0,0001955
0,001588579 0,000493432
G
2
0,0002467
0,001472931 0,000457511
G
2
0,0002288
0,002
0,000621225
R
1,732 0,0003587
0,002468228 0,002468228
t
3,16 0,0007811
0,0088068
Mismatched load at 18 GHz
84
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
B.5.2 Transmission measurements
Contribution
Linearity TPmtch(M*S11) LDmtch(GAMA-L*S22) TP LM(M*GAMA-L) Mmtch CrossTlk System Rep Noise Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,000459 0,032305 0,00631 0,000204
3,16E-06 0,000184 4,08E-05 0,0003 0,000244 0,002072
0,000459 0,001064 0,000206 0,000204 0,001372 3,16E-06 0,000184 4,08E-05
0,0003 0,000244 0,002072
G
2
0,00023
U
1,414
0,00097
R
1,732 1,83E-06
G
2
9,21E-05
G
2
2,04E-05
G
2
0,00015
R
1,732 0,000141
t
3,16
0,000656
0,001215
3 dB Attenuator S21 at 2 GHz
Contribution
Linearity TPmtch(M*S11) LDmtch(GAMA-L*S22) TP LM(M*GAMA-L) Mmtch CrossTlk System Rep Noise Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,000574 0,033951 0,007943 0,00027
4,47E-06 0,001557 4,08E-05 0,0003 0,000244 0,004255
0,000574 0,001828 0,000421 0,00027 0,002388 4,47E-06 0,001557 4,08E-05
0,0003 0,000244 0,004255
G
2
0,000287
U
1,414 0,001689
R
1,732 2,58E-06
G
2
0,000778
G
2
2,04E-05
G
2
0,00015
R
1,732 0,000141
t
3,16
0,001346
0,002323
3 dB Attenuator S21 at 9 GHz
85
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Contribution
Linearity TPmtch(M*S11) LDmtch(GAMA-L*S22) TP LM(M*GAMA-L) Mmtch CrossTlk System Rep Noise Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,000688 0,052631 0,009772 0,000526
5,62E-06 0,001109 4,08E-05 0,0003 0,000244 0,004447
0,000688 0,003062 0,001127 0,000526 0,004461 5,62E-06 0,001109 4,08E-05
0,0003 0,000244 0,004447
G
2
0,000344
U
1,414 0,003155
R
1,732 3,25E-06
G
2
0,000554
G
2
2,04E-05
G
2
0,00015
R
1,732 0,000141
t
3,16
0,001407
0,003522
3 dB Attenuator S21 at 18 GHz
Contribution
Linearity TPmtch(M*S11) LDmtch(GAMA-L*S22) TP LM(M*GAMA-L) Mmtch CrossTlk System Rep Noise Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,000196 0,032305 0,00631 0,000204
2,24E-05 0,000184 5,75E-05 0,0003 3,45E-05 0,000623
0,000196 0,000288 3,9E-05 0,000204 0,00033 2,24E-05 0,000184 5,75E-05
0,0003 3,45E-05 0,000623
G
2
0,000098
U
1,414 0,000233
R
1,732 1,29E-05
G
2
9,21E-05
G
2
2,88E-05
G
2
0,00015
R
1,732 1,99E-05
t
3,16
0,000197
0,000368
20 dB Attenuator S21 at 2 GHz
86
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Contribution
Linearity TPmtch(M*S11) LDmtch(GAMA-L*S22) TP LM(M*GAMA-L) Mmtch CrossTlk System Rep Noise Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,00023 0,033951 0,007943 0,00027
3,16E-05 0,001557 5,75E-05 0,0003 3,45E-05 0,00113
0,00023 0,000472 0,000136 0,00027 0,00061 3,16E-05 0,001557 5,75E-05
0,0003 3,45E-05 0,00113
G
2
0,000115
U
1,414 0,000432
R
1,732 1,83E-05
G
2
0,000778
G
2
2,88E-05
G
2
0,00015
R
1,732 1,99E-05
t
3,16
0,000358
0,000979
20 dB Attenuator S21 at 9 GHz
Contribution
Linearity TPmtch(M*S11) LDmtch(GAMA-L*S22) TP LM(M*GAMA-L) Mmtch CrossTlk System Rep Noise Cable fix Amb.condn Conn. Rep. C.S.Unc.
Estimate Uncertainity Distribution Divisor Std. Unc.
0,000264 0,052631 0,009772 0,000514
3,98E-05 0,001109 5,75E-05 0,0003 3,45E-05 0,001314
0,000264 0,004805 0,000419 0,000514 0,005234 3,98E-05 0,001109 5,75E-05
0,0003 3,45E-05 0,001314
G
2
0,000132
G
1,414 0,003702
R
1,732
2,3E-05
G
2
0,000554
G
2
2,88E-05
G
2
0,00015
R
1,732 1,99E-05
t
3,16
0,000416
0,003771
20 dB Attenuator S21 at 18 GHz
87
SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods
2 GHz - 18 GHz - Type N Connector
Annex C: Participants reports
C.1 INTI Report
Previous check The traveling standards pin-depth were measured and connectors were carefully inspected to ensure a good mechanical condition.
Hardware The measurements were performed using a Rohde & Schwarz ZVK Vector Network Analyzer which covers a frequency range up to 40 GHz. A 12-term model was solved to find the error terms of the VNA based setup. The calibration of the VNA was performed with the SOLT method. An Agilent 85054B calibration kit was used for high reflection calibration standards and a R&S ZV-Z21 calibration kit for low reflection calibration standards. Both kits have Type-N connectors. In addition, 2 Type-N sliding loads from Maury up to 18 GHz were used.
Measurements The measured values were error corrected with the VNA firmware. In addition, all the raw data were taken from the VNA and processed with a software implemented by INTI, which gave the same results.
Reported results are obtained as the mean of ten measurements, performing a new calibration of the VNA among them. The mean value includes both system and connector repeatability. After calibration, a set of verification devices traced to PTB were measured to verify the calibration accuracy.
According to the technical protocol, the S-parameters of each device in the real and imaginary form with its associated combined uncertainty were reported.
The ambient laboratory temperature during the measurements was (23 ± 1)◦C.
Uncertainty and traceability Uncertainties of S-parameters were calculated assuming equal real and imaginary components.
The uncertainties of the VNA were calculated based on EURAMET cg-12 [14].
The SOLT method uses definitions of the standards obtained by a TRL method which has better uncertainties.
Our traceability in S-parameters depends on dimensional characteristics of a set of coaxial air lines. Our air lines were measured at the Dimensional Metrology Laboratory at INTI to obtain traceability to the SI base unit of length (m).
Linearity of the system was measured with a step attenuator calibrated by INTI at 1 GHz.
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C.2 NIST Report
We used a commercial vector network analyzer (VNA) for the measurements. We calibrated the VNA using our own multical LRL software which utilizes multiple airline standards (we used 5) to give the best possible combination of airlines at each frequency. The calibration was verified with in-house check standards. We then measured the devices using a pattern for one-ports of three connects on port #1 and three connects on port #2. The final result for each device is an average of all connects. For two–ports, we made three connects in the “forward” direction, reversed the device and made three more connects. The final results for the two-port S-parameters are the averages of all connects accounting for forward and reverse directions.
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C.3 NRC Report
METHOD The measurement was performed on a PNA Agilent model E8364C (10 MHz to 50 GHz) network analyzer. This instrument has two (2.4 mm) ports on the front panel. This instrument is a regular production unit that has NO special option such as extended dynamic range or extra power amplifier etc... However, it is equipped with external loop cables, allowing the replacement of the couplers by external ones. No computer was attached to the instrument and the instrument firmware was used for the zeroing and measurement. The zeroing standards are taken from a HP calibration kit model 85054D plus some other standards. This kit is a regular production unit with no special option. No sliding load was available to perform this measurement. Instead we used a set of air-lines form Maury Microwave. The lines are 3 cm, 4.28 cm, 5 cm, and 7.5 cm. These zeroing standards are currently used in our laboratory. Several zeroing/measurement cycles were performed in different configuration/operating conditions. The reason for doing this was that we wanted to ensure that the results are reproducible, and that no obvious “mistake” was done. We did not use any “check/verification standards”, such as a previously measured attenuator of the same type, in order to check or correct our results. However we performed the obvious tests such as checking the phase of a short, the insertion loss of the THRU, etc. Although we performed many zeroing/measurement cycles, we did not average or modify the output results from the network analyzer.
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C.4 CENAM Report
CENAM (M´exico) Measurements
1. Measurements method
The measurements were performed on a commercial Vector Network Analyzer (VNA). The VNA used for this set of measurements was an Agilent E8363C. The calibration of the VNA was performed with the TRL method using precision coaxial airlines and with the SOLT method using a Hewlett Packard 85054B calibration kit. As it is known, the TRL method consists of three fundamental measurement steps: 1.- THRU- A standard transmission line is inserted between test port 1 and test port 2 of the network analyzer. The Thru used is a 5 cm airline. 2.- REFLECT- One-port and high reflective identical devices are connected to each of the two test ports of the network analyzer. 2.- LINE- Two standard transmission lines are inserted between test port 1 and test port 2 of the network analyzer, with a different length to that used in the THRU connection. One of the airlines used has 6 cm of length and the other has 7.5 cm of length. The SOLT method (Short-Open-Load-Thru) requires a 50 Ω Load, the ones used are a lowband load up to 2 GHz and a sliding load for higher frequencies.
2. Traceability
The set of beadless precision air-lines in Type-N connector used are measured dimensionally, traceable to the SI base unit of length (m) realized at CENAM. The electrical characteristics of the transmission lines are calculated from the physical dimensions. The precision air-lines are used as primary calculable standards. The coaxial terminations from the 85054B calibration kit were characterized prior by means of a TRL method. The calibration coefficients of the sets of coaxial terminations are obtained from the reflection coefficient measurements and whose values are applied automatically in the Vector Network Analyzer. The coaxial terminations are used as working standards.
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Figure 1. Structure of traceability
3. Measurements
The measurements were performed using a VNA system, the setup and configuration is summarized in the following tables:
Type of VNA: Type of calibration kit: Method of VNA calibration:
Sweep type:
Averaging Factor: IF Bandwidth: Power level: Other:
E8363C Reference airline kit –precision N 85054B Type N Calibration kit TRL, Short-Open-Load/Sliding load-Thru (two ports measurements), Short-Open-Load/Sliding load (one port measurements) Frequency list From 2 GHz to 18 GHz in step of 1 GHz 20 10 Hz -17 dBm • Adapter NMD 2.4 mm (female) to Type N (male), Manufacturer: MMC • Adapter NMD 2.4 mm (female) to Type N (female), Manufacturer: MMC • Test Port Cable 8946C25, Manufacturer: Maury Microwave
Table 1. VNA measurement system at CENAM
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One port measurement setup Note: The one port devices with male connectors were connected to port 2 of the Vector Network Analyzer and an S22 measurement carried out , this is equivalent to measuring S11.
Two port measurement setup
DUT orientation:
A test port adapter NMD 2.4 mm to Type N (female) was connected to port 2 of the VNA. The VNA was calibrated with this configuration using the TRL method. After that, the Matched load and Mismatched load were measured. These measurements were repeated to get 5 sets of measurements for each frequency and for each device. The standard was disconnected, rotated by about 120◦ and reconnected for each measurement. The VNA was re-calibrated, the standard was disconnected, rotated by about 180◦ and reconnected. The VNA was calibrated using SOL (Short-OpenLoad/Load sliding) method. After the calibration, the measurements of reflection coefficient were performed. These measurements were repeated to get 4 sets of measurements at each frequency for each device. The standard was disconnected, rotated by about 180◦ and reconnected for each measurement. The VNA was recalibrated, the standard was disconnected, rotated by about 180◦ and reconnected. A single test port cable was connected to port 1 of VNA and on the other end a test port adapter NMD 2.4 mm to Type N (male) was connected. A test port adapter NMD 2.4 mm to Type N (female) is connected to port 2 of VNA. The VNA was calibrated with this configuration using the TRL method. After the calibration, the S-parameters of the 3 dB and 20 dB attenuators were measured. The Sparameters measurements were repeated to get a total of 6 sets data for each frequency and for each attenuator. The standard was disconnected, rotated by about 120◦ and reconnected for each measurement. The VNA was re-calibrated, the standard was disconnected, rotated by about 120◦ and reconnected. The VNA was calibrated using SOLT (Short-OpenLoad/Load sliding-Thru) method. After the calibration the attenuators were measured. These measurements were repeated to get 4 sets of measurements for each frequency and for each device. The standard was disconnected, rotated by about 180◦ and reconnected for each measurement. The VNA was re-calibrated, the standard was disconnected, rotated by about 180◦ and reconnected. Port 1 Type-N (male) Port 2 Type-N (female)
Table 2. VNA measurement setup at CENAM 93
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Laboratory temperature Laboratory relative humidity
23 ◦C with variations not larger than ± 1 ◦C 35 % with variations not larger than ± 15 %
Table 4. Environment conditions at CENAM
4. Measurement Uncertainties
The Type B uncertainty for the reflection coefficient measurements for one port devices, UV RC1 port, has been calculated using the following formula:
UV RC1 port =
(D + M Γ)2 + (T Γ)2 + (LΓ)2 + (A)2 + (RV RC )2
2
3
3
3
3
(1)
where: D Effective directivity of VNA M Effective source match of VNA T Effective reflection tracking of VNA L System derivation from linearity A Airline reflection RV RC represents all the Random contributions: system repeatability, connector repeatability, effects of ambient conditions. Γ Magnitude of the reflection coefficient of the 1-port DUT
The Type B uncertainty on UV RC2 port reflection coefficient for two port devices has been calculated using the formula:
UV RC2 port =
(D + M Γ)2 (T Γ)2 (LΓ)2 (A)2
+
+
+
+
ΓLS221 2 +
2ΓM ΓLS221 2 + (RV RC )2 (2)
2
3
3
3
2
2
3
where:
ΓL Effective load match S21 Magnitude of the forward transmission coefficient of the two port device under calibration RV RC represents all the Random contributions: system repeatability, connector repeatability, effects of ambient conditions and effects of the cable flexure.
For the transmission measurements uncertainty:
UT M =
(LS21)2 + (I)2 + (TT M )2 + (MT M )2 + (RdB)2
3
3
3
2
3
(3)
where: I is the estimated/measured cross-talk MT M is the calculated error term due to mismatch TT M Effective transmission tracking of VNA
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RdB represents all the random contributions: system repeatability, connector repeatability, effects of ambient conditions and effects of the cable flexure.
The Type A uncertainty is the dispersion of the experimental data. Therefore, the combined uncertainty Uc has been calculated as square sum between Type B and Type A
The combined uncertainty for the phase of reflection coefficient measurements of one port devices has been evaluated with the following equation:
u (arg (Γ)) =
arcsin
UcΓ |Γ|
2
×
180 π
+ (CTphase)2 + (Rphase)2
(4)
1
3
n
where:
UcΓ combined uncertainty on reflection coefficient for one port devices CTphase Thermal coefficient in phase Rphase repeat measurements in phase n number of measurements
The combined uncertainty for the phase of reflection coefficient measurements of two port devices has been evaluated with the following equation:
u (arg (S11)) =
arcsin
UcS11 |S11|
1
×
180 π
2
+ (CTphase)2 + (Cable)2 + (Rphase)2
3
3
n
(5)
where:
UcS11 combined uncertainty on reflection coefficient for two port devices Cable represent the cable flexure
u (arg (S21)) =
arcsin
10 UcdB 20
−1
×
180 π
2
+ (CTphase)2 + (Cable)2 + (Rphase)2
(6)
1
3
3
n
where: UcdB combined uncertainty on transmission coefficient
The results are in magnitude and phase format. To evaluate the uncertainties in real and imaginary format the following method was used:
The vector of input quantities: X = (r, φ) The vector of output quantities: Y = (rcos φ, rsin φ )
Two transformations f1 and f2 are defined as:
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f1 (r, φ) = r cos φ f2 (r, φ) = r sin φ
The Jacobian matrix of the transformations is:
where:
∂f1 ∂r
=
cos φ
J=
∂f1 ∂f1
∂r ∂φ ∂f2 ∂f2
∂r ∂φ
∂f1 ∂φ
=
−rsin φ
∂f2 ∂r
=
sin φ
∂f2 ∂φ
=
rcos φ
In matrix form, the law of propagation of uncertainty states that:
J=
cos φ sin φ
−rsin φ rcos φ
Where V (X) is the covariance matrix of the input and V (Y ) is the covariance matrix of the output
V (X) =
u (x1) is the uncertainty in magnitude u (x2) is the uncertainty in phase u (x1, x2) = u (x1) u (x2) r (x1, x2) r (x1, x2) is the correlation coefficient
u2 (x1) u (x1, x2) u (x2, x1) u2 (x2)
The covariance matrix of the output has been calculated as follows:
V (Y ) =
u2 (y1) u (y1, y2) u (y2, y1) u2 (y2)
where:
V (Y ) =
cos φ −rsin φ sin φ rcos φ
u2 (x1) u (x1, x2) u (x2, x1) u2 (x2)
cos φ sin φ −rsin φ rcos φ
u2 (y1) = cos φ (cos φ ) u2 (x1) + (−rsin φ ) (u (x2, x1)) − rsin φ (cos φ ) (u (x1, x2)) + (−rsin φ ) u2 (x2)
u2 (y2) = sin φ (sin φ ) u2 (x1) + (rcos φ ) (u (x2, x1)) + rcos φ (sin φ ) (u (x1, x2)) + (rcos φ ) u2 (x2)
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u (y1, y2) = sin φ (cos φ ) u2 (x1) + (−rsin φ ) (u (x2, x1)) + rcos φ (cos φ ) (u (x1, x2)) + (−rsin φ ) u2 (x2)
u (y2, y1) = cos φ (sin φ ) u2 (x1) + (rcos φ ) (u (x2, x1)) − rsin φ (sin φ ) (u (x1, x2)) + (rcos φ ) u2 (x2)
u (y1) is the uncertainty of real part u (y2) is the uncertainty of imaginary part
The correlation coefficient of the output variables has been calculated using the following formula:
r (y1, y2)
=
u (y1, y2) u (y1) × u (y2)
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C.5 NPLI Report
Scattering Coefficients by Broad-Band Methods
SIM.EM.RF-K5b.CL
NPLI(India) Measurements
Environmental conditions: Temperature: (23 ± 1)◦C
Relative Humidity: (50 ± 10) % RH
Measurement description: The traveling standards received for the comparison were checked for their pin depths. The S-parameters of the traveling standards have been measured using a Vector Network Analyser (WILTRON VNA 37247B) System, which has been calibrated using a Type N Calibration kit, Model no.3653 and the precision coaxial airline for full 12-term, 1601 data points. The calibration method used was the SOLT one in Type-N connector for the desired 17 frequencies points from 2 to 18 GHz. The respective S-parameters of one port and two port components have been recorded in the real and imaginary form, Sab = x + jy. The S-parameters of each traveling standard have been measured ten times by connect-disconnect at the desired frequencies points. The mean value of the real and imaginary components of S-parameter has been reported for each standard. The combined standard uncertainty for the real and imaginary components i.e. u(x) and u(y) and the correlation coefficient r(x, y) have been calculated and reported accordingly [1, 2 & 3].
Traceability route: The S parameter measurement (S21/S12) is traceable to the 30 MHz WBCO attenuator of NPL India through transfer standard coaxial attenuators and (S11/S22) measurement is traceable to the Dimension metrology at NPL India through transfer standards coaxial airlines and calibration kit components.
References: 1. “Guidelines on the Evaluation of Vector Network Analyzers(VNA)”, Calibration Guide
Euramet cg-12 Version 2.0 (03/2011). 2. N.M.Ridler and M.J.Salter, “An approach to the treatment of uncertainty in complex S-
parameter measurements”, Metrologia, 2002, 39, pp 295-302. 3. Song Meng and Yueyan Shan, “Measurement uncertainty of complex valued microwave
quantities”, Progress in Electromagnetics Research, Vol. 136, 421-433, 2013.
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Annex D: Pin Depth measurements
The following tables show the reported values of pin depth in the order they were measured.
Some participants reported the pin depth as a delta measurement together with the reference depth used to zero the connector gage. In one case, a different offset from the rest was used, so in order to compare the reported values, depths were converted to absolute values (pin depth definition) based on the reference depth provided by each laboratory which expressed the pin depth as a delta value.
Not all laboratories reported pin depth measurements.
Device: 3 dB Attenuator
INTI (1st measurement) NIST NRC
CENAM INTI (1st control)
NPLI INTI (2nd control)
Pin depth [mm] Male port
5,284 -
5,281 5,284 5,283 5,292 5,283
Pin depth [mm] Female port
5,226 -
5,238 5,229 5,232 5,238 5,239
Table 91: Pin depth measurements - 3 dB Attenuator
Device: 20 dB Attenuator
INTI (1st measurement) NIST NRC
CENAM INTI (1st control)
NPLI INTI (2nd control)
Pin depth [mm] Male port
5,284 -
5,288 5,289 5,290 5,301 5,286
Pin depth [mm] Female port
5,232 -
5,238 5,232 5,239 5,250 5,239
Table 92: Pin depth measurements - 20 dB Attenuator
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Device: Matched Load
INTI (1st measurement) NIST NRC
CENAM INTI (1st control)
NPLI INTI (2nd control)
Pin depth [mm]
5,273 -
5,270 5,272 5,271 5,283 5,264
Table 93: Pin depth measurements - Matched Load
Device: Mismatched Load
INTI (1st measurement) NIST NRC
CENAM INTI (1st control)
NPLI INTI (2nd control)
Pin depth [mm]
5,264 -
5,264 5,266 5,264 5,276 5,264
Table 94: Pin depth measurements - Mismatched Load
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Annex E: Electrical stability of standards
The following figures show the measurements of each device made by the pilot laboratory, along with the expanded uncertainty associated with the measurement, normalized to the mean value of the measurements obtained at the beginning and at two control measurements at the respective frequencies. Each measurement is offset slightly in the figures for ease of viewing.
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Figure 27: Matched Load. Real part of S11 measured at INTI.
Figure 28: Matched Load. Imaginary part of S11 measured at INTI. 102
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Figure 29: Mismatched Load. Real part of S11 measured at INTI.
Figure 30: Mismatched Load. Imaginary part of S11 measured at INTI. 103
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Figure 31: 3 dB attenuator. Real part of S21 measured at INTI.
Figure 32: 3 dB attenuator. Imaginary part of S21 measured at INTI. 104
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Figure 33: 20 dB attenuator. Real part of S21 measured at INTI.
Figure 34: 20 dB attenuator. Imaginary part of S21 measured at INTI. 105
Ver+/-
