| Título: | Final report : key vomparison SIM.EM.RF-K5b.CL. scattering coefficients by broad-band methods. 2 GHz - 18 GHz - type N connector |
| Fuente: | Metrología, 53 |
| Autor/es: | Silva, H.; Monasterios, G. |
| Materias: | Sistema Interamericano de Metrología; Dispersión; Banda ancha; Frecuencia; Microondas; Metrología; Mediciones; Frecuencímetros |
| Editor/Edición: | IOP Publishing; 2016 |
| Licencia: | https://creativecommons.org/licenses/by/3.0/ |
| Afiliaciones: | Silva, H. Instituto Nacional de Tecnología Industrial (INTI); Argentina Monasterios, G. Instituto Nacional de Tecnología Industrial (INTI); Argentina |
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| Resumen: | The first key comparison in microwave frequencies within the SIM (Sistema Interamericano de Metrología) region has been carried out. The measurands were the S-parameters of 50 ohm coaxial devices with Type-N connectors and were measured at 2 GHz, 9 GHz and 18 GHz. SIM.EM.RF-K5b.CL was the identification assigned and it was based on a parent CCEM key comparison named CCEM.RF-K5b.CL. For this reason, the measurements standards and their nominal values were selected accordingly, i.e. two one-port devices (a matched and a mismatched load) to cover low and high reflection coefficients and two attenuators (3dB and 20 dB) to cover low and high transmission coefficients. This key comparison has met the need for ensuring traceability in high-frequency measurements across America by linking SIM's results to CCEM. Six NMIs have participated in this comparison which was piloted by the Instituto Nacional de Tecnología Industrial (Argentina). A linking method of multivariate values was proposed and implemented in order to allow the linking of 2-dimensional results. |
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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 1 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 2 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 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 3 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 6 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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 7 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. 8 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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 9 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. 10 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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. 11 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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 12 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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]. 13 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector - 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. 14 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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. 15 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector References [1] Measurement comparisons in the context of the CIPM MRA. CIPM MRA-D-05, Version 1.5, 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. 88 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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. 89 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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. 90 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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. 91 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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 92 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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 94 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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: 95 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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) 96 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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) 97 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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. 98 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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 99 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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 100 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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. 101 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector Figure 27: Matched Load. Real part of S11 measured at INTI. Figure 28: Matched Load. Imaginary part of S11 measured at INTI. 102 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector Figure 29: Mismatched Load. Real part of S11 measured at INTI. Figure 30: Mismatched Load. Imaginary part of S11 measured at INTI. 103 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector 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 SIM.EM.RF-K5b.CL Final Report Scattering Coefficients by Broad-Band Methods 2 GHz - 18 GHz - Type N Connector Figure 33: 20 dB attenuator. Real part of S21 measured at INTI. Figure 34: 20 dB attenuator. Imaginary part of S21 measured at INTI. 105Ver+/- |
