Traceable S-Parameter Measurements up to 165 GHz using 0.8mm Coaxial Standards

Traceable S-Parameter Measurements up to 165 GHz using 0.8 mm Coaxial Standards Andreas Schramm, Frauke Gellersen, Florian Rausche, Karsten Kuhlmann Physikalisch-Technische Bundesanstalt (PTB), Germany {andreas.schramm, frauke.gellersen, florian.rausche, karsten.kuhlmann}@ptb.de 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 over determined 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. Keywords — S-parameter, coaxial, calibration, VNA. I. INTRODUCTION Current coaxial precision connectors (PC), such as the PC 1.0 mm, are limited to frequencies of up to 110 GHz [1]. A logical progression is represented by PC 0.8 mm, which was first introduced by Anritsu nearly 10 years ago and is standardized in [1] since 2021. As there is no traceability to the Système international d’unités (SI, International System of Units) for PC 0.8 mm yet, 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 of PC 0.8 mm to the SI is established using seven offset short standards to solve an over determined system of equations. The characterization of their dimensions and estimates of material parameters like DC conductivity and surface roughness enables the calculation of their reflection coefficient s s s11. A least-squares (LSQ) method according to [2] is used to optimize the estimates of the unknown material parameters of the standards by minimizing their residuals. This approach is used for the SI-traceable calibration of PC 1.35 mm [3] and PC 1.0 mm [4] already. All calculations regarding the definition of the standards presented in Sec. II as well as the calibrations themselves described in Sec. 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, because the modeling of the connector interface is less complex and therefore more precise, as exemplified in [4, see Fig. 4 and 7]. Fig. 1. Primary offset shorts (standing) and verification flush short (lying). Figure 1 shows the seven offset shorts used for calibration and an additional flush short for verification. The offset lengths of ideal standards (smooth perfect electric conductor) are optimized for a bandwidth of 10 GHz to 165 GHz using [8] and summarized in Table 1. The dimensional characterization involves measuring the inner and outer conduct diameter as well as their physical lengths. The standards are then each divided into three parts: the connector S S SCis simulated using a 3D-full-wave simulation tool, and the offset line S S SLand short plane s s ssare calculated analytically based on [9]. Cascading of S S SC,S S SL, and s s ssyields s s s11 of each offset short. Table 1. Nominal offset short line lengths for 0.8 mm calibration. offset short 1 2 3 4 5 6 7 length / mm 1.153 3.036 3.890 4.554 5.179 7.634 10.000 Material parameters including DC conductivity and surface roughness are utilized to calculate the frequency-dependent, effective conductivity using [10]. Recent improvements allow the consideration of multiple layers of different materials [11]. The influences of dimensional and material parameters as well as their uncertainties on s s s11 are discussed in [12]. The geometry of the interface - most importantly the inner and outer chamfer as depicted in [4, Fig. 4] - are challenging to characterize and calculate analytically. The interface including the measured pin as well as estimates for inner and outer chamfer is characterized using a 3D-full-wave simulation. 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 s s s11 is observed for pin gap values smaller than 4 µm and pin depths smaller than 2 µm. All offset shorts used in this work have a pin depth of 10 µm to 15 µm. No observable problems occurred during measurement. This paper was presented during the 2025 International Microwave Symposium (IMS), San Francisco, CA, USA, on 19 June 2025, Session Th2D: Advances in RF to THz Instrumentation and Device Measurements. The paper was selected for publication in the Special Issue of the IEEE Microwave and Wireless Technology Letters, doi: 10.1109/LMWT.2025.3562419. Table 2. Frequency bands and calibration schemes of the 0.8 mm calibration. frequency range and boundary / GHz primary experiment transfer experiment PC 1.85 0.01 - 68 < 15.5 Copy OSM1UOSM > 14.5 Copy LSQ UOSM WR 10 67 - 115 < 85.5 Copy LSQ UOSM > 84.5 Copy LSQ SSS WR 6 110 - 165 Copy LSQ SSS 1poly-fitted values for OSM standards below ≈15 GHz III. S-PARAMETER CALIBRATION S-parameter measurements are separated into three frequency bands to achieve small measurement uncertainties, because no comparable broadband-system exists yet. Table 2 summarizes the calibration setups used. In the first band, the setup is directly connected to the VNA using PC 1.85 mm. The second and third frequency bands use WR 10 and WR 6 frequency extensions, respectively. Thermal coupling of VNA extenders is minimized by introducing cooling plates similar to [4] to reduce phase shift during repeated measurements. 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 6 −0.8) →DUT. 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. A specific averaging method is used in overlapping frequency ranges (e.g. 67 GHz to 68 GHz and 110 GHz to 115 GHz) to ensure that both the result and the weights w1≃cos2and w2≃sin2are continuous and free of discontinuities. Traceability of PC 0.8 mm to the SI is established using calculable offset short standards on Port 1 and an ideal 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 like the Thru as detailed in [13], are prevented in both experiments, because no additional 2-port DUTs are measured. A. Repeatability of the 0.8 mm Interface For small connectors in particular, the connection repeatability significantly influences the achievable measurement uncertainty. 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 ∆z z zκis calculated similar to [7, G.5] for each DUT κ. The combined repeatability of both experiments is determined by the mean ∆z z zκand the standard deviation σ(∆z z zκ). Figure 2 summarizes the values ∆z z zκ+2·σ(∆z z zκ), so that approximately 95 % of all DUTs lie within that interval. 0.01 20 40 60 80 100 120 140 160 −80 −60 −40 frequency f/ GHz repeatability / dB PC 0.8 PC 0.8⋆ PC 1.85 WR 10⋆ WR 10 WR 6 Fig. 2. Repeatability of PC 0.8 mm. Measurements in the WR 10 band marked with ⋆were performed under fluctuating room temperatures. According to [7, G.5] an envelope represented by the solid and dashed, unmarked black lines is defined. The second frequency band ranging from 67 GHz to 110 GHz was measured a second time, because the room temperature fluctuated by 2 °C in about 20 min during the first set of measurements. In comparison, the PC 1.85 measurements were conducted under stable conditions with fluctuations of 0.3 °C over several hours. This directly translates into worse repeatability of 4 dB to 6 dB in the WR 10 band as shown in Figure 2. A suitable envelope for both scenarios is determined and used accordingly 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 in the primary experiment. The experiment itself involves the calibration of Port 1 using plug standards and measuring plug DUTs. An LSQ method described in [2] is utilized from 14.5 GHz to 165 GHz to optimize the estimates of the material parameters. To calibrate the range below 15.5 GHz, a broadband match and an open termination from the calibration kit are poly-fitted and extrapolated to 10 MHz. The polynomial coefficients of the open are obtained using METAS VNA Tools II [6]. By choosing a primary offset short matching the open’s electrical length, a one port open-short-match (OSM) calibration is performed. In both cases Port 2 is characterized using the error terms of Port 1 and an ideal Thru connection comparable to [14]. The Thru definition T T Tand its measurement M M Mallow to transfer the error terms from Port 1 (e e e1) to Port 2 (e e e2) following e e e2= (e e e1⊕T T T)⊖1⊕M M M. (1) The operation ⊖1denotes matrix inversion of a 2-port and ⊕ describes the cascading of 2-ports. The calibration result of a plug flush short is depicted in Fig. 3, which follows the expected behavior described in the CG-12 [7]. A phase angle discontinuity around 68 GHz in the WR 10 band is observed, which is caused by temperature fluctuations described in Sec. III-A. Expanded uncertainties (k= 2) in reflection magnitude U(|s s s11|)of 0.002 to 0.019 and expanded uncertainties in phase angle U(6(s s s11)) of 0.1° to 1.5° are achieved for high reflect DUTs. The highest 0.01 20 40 60 80 100 120 140 160 −184 −182 −180 0.98 1 1.02 frequency f/ GHz |s s s11| 6(s s s11)/◦ Fig. 3. Primary calibration results of a flush short (plug). uncertainty is present in the WR 10 band because of degraded repeatability during the measurement caused by temperature fluctuations. Expanded uncertainties of U(|s s s11|) = 0.013 instead of 0.019 are achievable by repeating the experiment under stable temperature conditions mentioned in Sec. III-A. Three conclusions can be drawn from the uncertainty budgets for magnitude in Fig. 4 and 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. Additionally, 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 During the primary experiment an OSM transfer kit is calibrated, which is in turn used to calibrate other calibration kits. From 10 MHz to 85.5 GHz the transfer kit together with an ideal Thru is used for an Unknown Thru OSM (UOSM) calibration [15]. Above 84.5 GHz up to 165 GHz triple-offset short (SSS) calibrations as described in [16] are performed for each port, because no 2-port DUTs are measured additionally. 0.01 20 40 60 80 100 120 140 160 0 0.001 0 0.001 0.005 0.01 frequency f/GHz unc. component uκ(|s s s11|) Connector Repeatability Calibration Standard VNA Linearity VNA Noise VNA Drift Fig. 4. Uncertainty budget of the reflection magnitude of the flush short. 0.01 20 40 60 80 100 120 140 160 0 0.1 0 0.1 0.2 0.6 frequency f/GHz unc. component uκ(6(s s s11)) /◦ Connector Repeatability Calibration Standard VNA Linearity VNA Noise VNA Drift Fig. 5. Uncertainty budget of the reflection phase of the flush short. 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 GHz and 156 GHz resonance effects because of beads in the DUT are observed. Expanded uncertainties (k= 2) in reflection magnitude U(|s s s22|)of 0.006 to 0.031 and expanded uncertainties in phase angle U(6(s s s11)) of 8° to 97° are achieved for low reflect DUTs. High uncertainty in phase results from small values in magnitude. Four conclusions can be drawn from the uncertainty budgets for reflection magnitude in Fig. 7 and phase angle in Fig. 8: 1) The main influence on the magnitude uncertainty is the connection repeatability caused by temperature fluctuations. 2) Magnitude uncertainty is influenced by repeatability and calibration standards. 3) VNA linearity is non-negligible for low reflect DUTs, when mainly high reflects are used during calibration. 4) At low frequencies the phase uncertainty increases because the magnitude approaches zero. IV. CONCLUSION This paper details the successful establishment of SI-traceable S-parameter measurements within the coaxial 0.8 mm precision connector system up to 165 GHz. Seven offset short terminations of different offset length and an ideal Thru connection are used for primary calibration. 0.01 20 40 60 80 100 120 140 160 −100 0 100 −60 −40 −20 frequency f/ GHz |s s s22| 6(s s s22)/◦ Fig. 6. Transfer calibration result of a match (jack). 0.01 20 40 60 80 100 120 140 160 0 0.001 0 0.001 0.005 0.01 frequency f/GHz unc. component uκ(|s s s22|) Connector Repeatability Calibration Standard VNA Linearity VNA Noise VNA Drift Fig. 7. Uncertainty budget to the reflection magnitude of the match. 0.01 20 40 60 80 100 120 140 160 0 1 0 20 40 frequency f/GHz unc. component uκ(6s s s22)/◦ Connector Repeatability Calibration Standard VNA Linearity VNA Noise VNA Drift Fig. 8. Uncertainty budget to the reflection phase of the match. Careful characterization of the offset short dimensions enables the calculation of their reflection coefficient s s s11. An over determined 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(|s s s11|)of 0.002 to 0.019 and U(6(s s s11)) of 0.1° to 1.5° are achieved with k= 2. In contrast, a match with jack connector and reflection |s s s11|<−20 dB is examined as a low reflect standard up to 150 GHz. Expanded uncertainties U(|s s s11|)of 0.003 to 0.031 and U(6(s s s11)) of 8° to 97° with k= 2 are observed. The main uncertainty contribution in both cases is the connection repeatability, which shows high sensitivity to room temperature fluctuations. During the experiments a repeatability definition was established comparable to the procedure of the CG-12 [7, G.5]. Overall, the capability to calibrate one-port DUTs up to 165 GHz traceable to the SI is shown with potential room for improvement up to 168 GHz. 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