Traceable S-Parameter Measurements Up to 165 GHz Using 0.8 mm Coaxial Standards

936 IEEE MICROWAVE AND WIRELESS TECHNOLOGY LETTERS, VOL. 35, NO. 6, JUNE 2025 Traceable S-Parameter Measurements Up to 165 GHz Using 0.8 mm Coaxial Standards Andreas Schramm , Graduate Student Member, IEEE, Frauke Gellersen , Florian Rausche, and Karsten Kuhlmann Abstract—To extend SI-traceable calibration for coaxial measurements up to 165 GHz, seven calculable offset short standards in the 0.8 mm coaxial system are used. The standards are calculated based on dimensional measurements and used for an overdetermined least-squares calibration. Measurement results and uncertainty budgets are reported for a flush short and a broadband match. The repeatability of the interface and a minimal pin gap are investigated. Index Terms—Coaxial, least-squares calibration, offset-short, S-parameter, SI-traceability, vector network analyzer (VNA). I. INTRODUCTION CURRENT coaxial precision connectors (PC), such as the PC 1.0 mm, are standardized up to 110 GHz [1] and traceable to the Syst`eme International d’Unit´es (SI, International System of Units) up to 116.5 GHz [2]. The theoretical limit for single-mode operation is 135.9 GHz [1]. A logical progression is represented by PC 0.8 mm, which was first introduced by Anritsu Corporation approximately 10 years ago and is standardized in [1] since 2021. The theoretical limit of single-mode operation is 169.7 GHz [1]. To establish traceability to the SI, primary calibration standards are required whose scattering parameters (S-parameters) are traceable to the SI via dimensional measurements. Bead-less airlines commonly used in primary calibrations are not feasible at such small dimensions, because the handling of inner conductors with a diameter of 0.348 mm is challenging and impractical. Alternatively, traceability to the SI is established using seven offset short standards to solve an overdetermined system of equations. The characterization of their dimensions and estimates of material parameters such as dc conductivity and surface roughness enables the calculation of their reflection coefficient s11. A least-squares (LSQ) method according to [3] is used to optimize the estimates of the unknown material parameters of the standards by minimizing their residuals. A similar approach has been used for the SI-traceable calibration of PC 1.35 mm [4] and PC 1.0 mm [2]. Received 25 February 2025; revised 14 April 2025; accepted 14 April 2025. Date of publication 22 May 2025; date of current version 9 June 2025. This work is part of the project 23IND03 RF 4 6G focusing on advancing key quantities for 6G. The project 23IND03 RF 4 6G has received funding from the European Partnership on Metrology, co-financed from the European Union’s Horizon Europe Research and Innovation Programme and by the Participating States. (Corresponding author: Andreas Schramm.) The authors are with the Physikalisch-Technische Bundesanstalt (PTB), 38116 Brunswick, Germany (e-mail: [email protected]). This article was presented at the IEEE MTT-S International Microwave Symposium (IMS 2025), San Francisco, CA, USA, June 15–20, 2025. Digital Object Identifier 10.1109/LMWT.2025.3562419 Fig. 1. Primary offset shorts (standing) and verification flush short (lying). TABLE I NOMINAL OFFSET LINE LENGTHS FOR PC 0.8 MM CALIBRATION All the calculations regarding the definition of the standards presented in Section II and the vector network analyzer (VNA) calibration described in Sections III-B and III-C are performed using MATLAB and the METAS UncLib [5]. Simulations of connector effects are done using CST Microwave Studio. The evaluation of VNA uncertainties (drift, noise, and linearity) and connector repeatability follows the procedure implemented in METAS VNA Tools II [6] and the CG-12 [7]. II. CALIBRATION STANDARD DEFINITION During the development of the primary standards, the decision is made to only use plug standards. Compared with jack standards, the modeling of the connector interface is less complex and therefore more precise, as exemplified in [2, Figs. 4 and 7]. Fig. 1shows the seven offset shorts used for calibration and an additional flush short for verification. The offset lengths of ideal standards (smooth surface, perfect electric conductor) are optimized between 10 and 165 GHz using [8] and summarized in Table I. The dimensional characterization involves measuring the inner and outer conduct diameter as well as the physical lengths. The standards are then each divided into three parts: the connector SCis simulated using a 3D-full-wave simulation tool, and the offset line SLand short plane ssare calculated analytically based on [9]. Cascading of SC,SL, and ssyields s11. Material parameters including dc conductivity and surface roughness are used to calculate the frequency-dependent effective conductivity using [10]. Recent improvements allow the consideration of multiple layers of different materials [11]. The ©2025 The Authors. This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ SCHRAMM et al.: TRACEABLE S-PARAMETER MEASUREMENTS UP TO 165 GHz USING 0.8 mm COAXIAL STANDARDS 937 TABLE II FREQUENCY BANDS AND CALIBRATION SCHEMES OF THE PC 0.8 MM CALIBRATION influences of dimensional and material parameters as well as their uncertainties on s11 are discussed in [12]. The geometry of the interface–most importantly the inner and outer chamfers as depicted in [2, Fig. 4]– is challenging to characterize. The interface is therefore calculated using a 3D-full-wave simulation by including the measured pin and estimates for inner and outer chamfers. Uncertainties are propagated by repeated simulation of not only the nominal values but also the minimum and maximum values for each dimensional parameter. A strong influence of pin gap variation on the reflection s11 is observed for pin gap values smaller than 4 µm and pin depths smaller than 2 µm. All the offset shorts used in this work have a pin depth of 10–15 µm. No observable problems occurred during measurement. III. S-PARAMETER CALIBRATION S-parameter measurements of PC 0.8 mm are separated into three frequency bands. Table II summarizes the calibration setups used. In the first band, the setup is directly connected to the VNA using PC 1.85 mm. Frequency extensions for R 900 (WR 10) and R 1.4 k (WR 7) are used in the second and third frequency bands, respectively. By introducing cooling plates to these VNA extenders similar to [2], the warming and therefore the thermal expansion of the calibration standards, which would result in phase angle errors, is minimized. Where feasible, the same test port adapter (0.8–0.8) is used to connect the device under test (DUT) to ensure consistency while minimizing the amount of measurements necessary. The following adapters are used in each band: (1.85 −1.35) ↔(1.35 −0.8) ↔(0.8−0.8) ↔DUT (WR 10 −1.0) ↔(1.0−0.8) ↔(0.8−0.8) ↔DUT (WR 7 −0.8) ↔DUT. A specific averaging method is used in overlapping frequency ranges (e.g., 67–68 GHz and 110–115 GHz) to ensure that both the result and the weights w1≃cos2and w2≃sin2are continuous and free of jumps. Traceability of PC 0.8 mm to the SI is established using calculable offset short standards on VNA Port 1 and a zerolength thru connection to transfer the calibration to Port 2. A transfer calibration kit is characterized in this process, which can subsequently be used in transfer experiments to ensure traceability of additional calibration kits. Cable movements, which could cause errors in transmission measurements as Fig. 2. Repeatability of PC 0.8 mm. Measurements in the WR 10 band marked with ?were performed under fluctuating room temperatures. detailed in [13], are prevented in both the experiments, as no additional two-port DUTs are measured. A. Repeatability of the 0.8 mm Interface The repeatability of the connection significantly influences the achievable measurement uncertainty, particularly for small connectors. To assess the repeatability of PC 0.8 mm, each DUT is connected at least four times. The mean of these measurements is used in the calibration, and the repeatability ∆zτis calculated similar to CG-12 [7] for each DUT τ. The repeatability of the interface is determined by the mean ∆zτ and the standard deviation σ(∆zτ). Fig. 2summarizes the values ∆zτ+2·σ(∆zτ), so that approximately 95% of all the DUTs lie within that interval. According to CG-12 [7], an envelope represented by the unmarked black lines is defined. The second frequency band ranging from 67 to 110 GHz was measured two times, as the room temperature fluctuated by 2 ◦C in about 20 min during the first set of measurements. In comparison, the PC 1.85 mm measurements were conducted under stable conditions with fluctuations of 0.3◦C over several hours. This directly translates into worse repeatability of 4–6 dB in the WR 10 band as shown in Fig. 2. A suitable envelope for both the scenarios is determined and used in the evaluation of the corresponding measurement results. B. Primary Calibration In addition to the primary offset standards, a flush short for verification and a commercially available calibration kit are measured as DUTs. The experiment itself involves the calibration of Port 1 using plug standards and measuring plug DUTs. An LSQ method described in [3] is used from 14.5 to 165 GHz to optimize the material parameter estimates. To calibrate the range below 15.5 GHz, a broadband match and an open from the commercial calibration kit are polyfit using METAS VNA Tools II [6] and extrapolated to 10 MHz. By choosing a primary offset short matching the electrical length of the open, a one-port open-short-match (OSM) calibration is performed. In both the cases, Port 2 is characterized using the error terms of Port 1 and a zero-length thru connection comparable to [14]. The thru definition Tand its measurement Mallow to transfer the error terms from Port 1 (e1) to Port 2 (e2) following e2=(e1⊕T)1⊕M.(1) 938 IEEE MICROWAVE AND WIRELESS TECHNOLOGY LETTERS, VOL. 35, NO. 6, JUNE 2025 Fig. 3. Primary calibration result of a flush short (plug). Fig. 4. Uncertainty budget of the reflection magnitude of the flush short. The operation 1 denotes matrix inversion of a two-port and ⊕describes the cascading of two-ports. The calibration result of a flush short with plug connector is depicted in Fig. 3. It follows the expected behavior described in CG-12 [7]. A phase angle discontinuity, caused by temperature fluctuations described in Section III-A, is observed around 68 GHz in the WR 10 band. Expanded uncertainties (k=2) in reflection magnitude U(|s11|) of 0.002–0.019 and in phase angle U(∠(s11)) of 0.1◦–1.5◦are achieved for high-reflect DUTs. The highest uncertainty is present in the WR 10 band because of degraded repeatability during the measurement caused by temperature fluctuations. Three main conclusions can be drawn from the uncertainty budgets for magnitude in Fig. 4and phase angle in Fig. 5: 1) The main influence on the magnitude uncertainty is the connection repeatability. 2) Phase angle uncertainty is dominated by repeatability and the definition of the primary offset shorts: simulated connector effects and length measurement are major contributions. In addition, the VNA drift influences the phase uncertainty because of the extensive measurement plan involved with the primary experiment. 3) VNA linearity in LSQ calibration is negligible for high-reflect DUTs due to consistent receiver operation points. C. Transfer Calibration As detailed in Section III-B, an OSM transfer kit is calibrated as part of the primary experiment. From 10 MHz to 85.5 GHz, the transfer kit together with a zero-length thru is used for an unknown thru OSM (UOSM) calibration Fig. 5. Uncertainty budget of the reflection phase angle of the flush short. Fig. 6. Transfer calibration result of a match (jack). Fig. 7. Uncertainty budget of the reflection magnitude of the match. [15]. Above 84.5 up to 165 GHz triple-offset short (SSS) calibrations as described in [16] are performed for each port. The calibration result of a jack broadband match is shown in Fig. 6. The reflection magnitude across the whole frequency range is equal to or smaller than −20 dB. At around 152 and 156 GHz resonance effects caused by the beads in the DUT are observed. Expanded uncertainties (k=2) in reflection magnitude U(|s22|) of 0.006–0.031 and in phase angle U(∠(s11)) of 8◦–97◦are achieved for low-reflect DUTs. Three main conclusions can be drawn from the uncertainty budgets for magnitude in Fig. 7and phase angle in Fig. 8: 1) Magnitude and phase angle uncertainty are mainly influenced by the connection repeatability and the calibration standard definition obtained during primary calibration. 2) VNA linearity is nonnegligible for low-reflect DUTs, when mainly high reflects are used during cali- SCHRAMM et al.: TRACEABLE S-PARAMETER MEASUREMENTS UP TO 165 GHz USING 0.8 mm COAXIAL STANDARDS 939 Fig. 8. Uncertainty budget of the reflection phase angle of the match. bration. In this case, due to different receiver operation points, the linearity uncertainty contributions are not correlated and therefore do not cancel out. 3) Phase uncertainty increases rapidly as the magnitude approaches zero at lower frequencies. IV. CONCLUSION This letter details the successful establishment of SItraceable S-parameter measurements within the coaxial 0.8 mm precision connector system up to 165 GHz. Seven calculable offset short terminations of different offset length and a zero-length thru connection are used for primary calibration. Careful characterization of the offset short dimensions enables the calculation of their reflection coefficient s11. An overdetermined LSQ calibration is used to optimize unknown material parameters for modeling coated, rough surfaces. For high-reflect standards exemplified by a flush short with plug connector expanded uncertainties U(|s11|) of 0.002–0.019 and U(∠(s11)) of 0.1◦–1.5◦are achieved with k=2. In contrast, a match with jack connector and reflection |s11|smaller than −20 dB is examined as a low reflect standard up to 150 GHz. Expanded uncertainties U(|s11|) of 0.003–0.031 and U(∠(s11)) of 8◦–97◦with k=2 are observed. The main uncertainty contribution for highand low-reflect DUTs is the connection repeatability, though it is clearly influenced by the VNA drift in the WR 10 band due to room temperature fluctuations. During the experiments, a repeatability definition was established comparable to the procedure of CG-12 [7]. The coaxial 0.8 mm precision connector exhibits excellent metrological performance due to small achieved uncertainties, very good connection repeatability, and improved mechanical stability. Future work will result in smaller uncertainties especially in the WR 10 band and a higher frequency limit in calibration of up to 168 GHz. Furthermore, a comparison of these VNA-based primary calibration results with an optoelectronic measurement technique as presented in [17] is currently carried out. ACKNOWLEDGMENT The authors thank Rohde & Schwarz GmbH & Co. KG for valuable and productive discussions. SPINNER GmbH is to be thanked additionally for fabricating the necessary primary offset standards, DUTs and adapters. 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