Vector Network Analyzer Calibration Research Articles

A calibration method for vector network analyzers using a line and three or more offset-reflect standards

Abstract This article proposes a method for two-port vector network analyzer (VNA) calibration that uses a line standard and three or more offset-reflect standards (LnΓ, where n is the number of offset-reflect standards and n ≥ 3). The reflection coefficient of the highly reflecting offset-reflect standards and the propagation constant of the transmission line are unknown for this calibration method, but they can be obtained in the process of calculating the VNA calibration error coefficients. In the LnΓ calibration method, the calibration fixtures are all equal in mechanical length. Therefore, compared with the thru-reflect-line (TRL) method, this calibration method is convenient when the test fixtures of both sides of the VNA are fixed or difficult to move during the measurement. To further simplify the experimental operation, a corrugated reflector is also designed. In this calibration method, only one corrugated reflector used as the offset-reflect standard is needed. Different offset-reflect standards are realized easily by changing the position on the microstrip line. The proposed LnΓ calibration method is accurate, which is proven by theoretical analysis, simulations, and measurements.

Connector effects and reference plane influence in the N-Type connector

In this paper we outline the impact of mixing slotted N-type and slotless N-type connectors during a vector network analyzer calibration. We want to point out that making precise measurements of typical transfer standards, while using both N-type jack connectors is very difficult, because of the reference plane shift. We performed simulations of the two connector jack geometries to estimate the impact on measurements of devices under test with either plug or jack interface. The influence of mixing slotted and slotless connectors is then validated through simple measurements, which can be easily repeated in many labs. The results show that mixing of slotted and slotless jacks adds errors in the same order of magnitude sometimes reported as measurement uncertainties by national metrology institutes.

Applicability of the Meniscus-Removal Method for Q-Band Liquid Characterization in Semi-Open Waveguide Cell

We present the broadband transmission-reflection meniscus-removal method for liquid characterization in a semi-open rectangular waveguide. The algorithm utilizes 2-port scattering parameters measured with a calibrated vector network analyzer for three states of the measurement cell: empty and filled with two liquid levels. The method enables the mathematical de-embedding of a symmetrical sample of a liquid, not distorted with a meniscus, and provision of its permittivity and permeability, as well as its height. We validate the method for propan-2-ol (IPA), a 50% aqueous solution of IPA, and distilled water in the Q-band (33–50 GHz). We investigate typical problems for in-waveguide measurements, such as phase ambiguity.

Propagation Constant Measurement Based on a Single Transmission Line Standard Using a Two-Port VNA.

This study presents a new method for measuring the propagation constant of transmission lines using a single line standard and without prior calibration of a two-port vector network analyzer (VNA). The method provides accurate results by emulating multiple line standards of the multiline calibration method. Each line standard was realized by sweeping an unknown network along a transmission line. The network need not be symmetric or reciprocal, but must exhibit both transmission and reflection. We performed measurements using a slab coaxial airline and repeated the measurements on three different VNAs. The measured propagation constant of the slab coaxial airline from all VNAs was nearly identical. By avoiding disconnecting or moving the cables, the proposed method eliminates errors related to the repeatability of connectors, resulting in improved broadband traceability to SI units.

Sensitivity of FET parasitic elements extraction due to uncertainty on TRM calibration structures

In order to develop equivalent circuit models of microwave transistors, electrical measurements performed on the device to be modeled are mapped to a network of circuit components that mimic the device's physical structure. To accomplish this, S-parameters measurements using a calibrated vector network analyzer are required. This article presents a comprehensive analysis of the sensitivity of field-effect transistors (FETs) parasitic elements extraction due to uncertainty on the thru-reflect-match (TRM) calibration structures. This analysis assesses straightforwardly the importance of knowing the impedance of the load used as TRM match structure on the extraction of the FETs' parasitic elements. Analytical equations that allow an in-depth understanding of the uncertainty propagation from TRM calibration to parasitic elements extraction are presented. The simplicity of the obtained equations allows to identify the origins of some discrepancies typically observed in FET parasitic elements extraction.

Characterization Techniques of Millimeter-Wave Orthomode Transducers (OMTs)

We report on advanced techniques for the accurate characterization of millimeter-wave Orthomode Transducers (OMTs) enabling the derivation of the fundamental parameters of such devices, i.e., the insertion loss, the return loss, the cross-polarization, and the isolation. These techniques include standard frequency-domain and time-domain VNA (Vector Network Analyzer) measurement methods, which can be applied to remove the effects of the waveguide transitions necessary to access the OMT ports and excite the desired modes. After reviewing the definition of the OMT parameters, we discuss the test equipment, the VNA calibration procedures as well as the VNA time-domain time-gating method for application in OMT characterization. We present simplified equations that relate the calibrated VNA measured quantities with the OMT S-parameters, illustrate various characterization methods, and examine various OMT experimental test setups. The advantages and disadvantages of each of the OMT characterization procedures are presented and compared among them. We provide a list of waveguide components required in the OMT test setups (adapters, loads, quarter-wave and longer waveguide sections, feed-horn, etc.), discuss the error terms introduced by such components and examine their impact on the measured values. Furthermore, we identify strategies to mitigate or remove the effects of the measured errors, to derive the desired OMT parameters. Different OMT configurations, with a distinct orientation of the waveguide input and outputs, are discussed. Although the presented techniques refer to the characterization of a specific configuration of a W-band OMT, the described methods can be applied to other OMT configurations and frequency ranges (from microwave to THz frequencies), therefore having a general validity.

Single Step 2-Port Device De-Embedding Algorithm for Fixture-DUT-Fixture Network Assembly

The de-embedding of measurement fixtures is relevant for an accurate experimental characterization of radio frequency and digital electronic devices. The standard technique consists in removing the effects of the measurement fixtures by the calculation of the transfer scattering parameters (T-parameters) from the available measured (or simulated) global scattering parameters (S-parameters). The standard de-embedding is achieved by a multiple steps process, involving the S-to-T and subsequent T-to-S parameter conversion. In a typical measurement setup, two fixtures are usually placed before and after the device under test (DUT) allowing the connection of the device to the calibrated vector network analyzer coaxial ports. An alternative method is proposed in this paper: it is based on the newly developed multi-network cascading algorithm. The matrices involved in the fixture-DUT-fixture cascading gives rise to a non-linear set of equations that is in one step analytically solved in closed form, obtaining a unique solution. The method is shown to be effective and at least as accurate as the standard multi-step de-embedding one.

Methods and models of calibration of vector network analyzers

Currently, measurement devices and instruments operating in the microwave range are widespread. Therefore, the problem arises of periodic checks, verifications and calibrations of such devices and instruments. The task of minimizing the systematic measurement error is a key task when performing verification of measuring instruments, measuring systems and devices operating in the microwave range using vector network analyzers. Various methods and models for performing calibrations of a vector network analyzer for determining the scattering parameters of passive microwave devices are described. The analysis of calibration methods is carried out, recommendations for its applications are given.

A Novel Calibration Method for Active Interferometer-Based VNAs

The addition of RF interferometers to vector network analyzer (VNA) test benches has allowed for realization of low-noise high-frequency measurements of extreme impedance devices. However, when employing correction techniques such as the short-open-load method, the RF response of the interferometer hardware introduces measurement inaccuracies due to unwanted load-dependent inconsistencies. This letter presents a novel VNA calibration method that enables both low-noise and accurate small-signal characterization of highly mismatched devices. The proposed solution is experimentally validated in the 10–18-GHz band, confirming a 23-fold improvement in measurement resolution with absolute accuracy across the entire $\Gamma $ range of the VNA. The accuracy of the new calibration process is verified via comparison with traceable reference standards supported by state-of-the-art uncertainties.

Calibration of Vector Network Analyzer for Measurements in Radio Frequency Propagation Channels

Calibration of Vector Network Analyzer for Measurements in Radio Frequency Propagation Channels

Calibration of Vector Network Analyzer for Measurements in Radio Frequency Propagation Channels.

In situ measurements of radio frequency (RF) spectrum activity provide insight into the physics of radio frequency wave propagation and validate existing and new spectrum propagation models. Both of these parameters are essential to supporting and preserving interference-free spectrum sharing, as spectrum use continues to increase. It is vital that such propagation measurements are accurate, reproducible, and free of artifacts and bias. Characterizing the gains and losses of components used in these measurements is vital to their accuracy. A vector network analyzer (VNA) is a well-established, highly accurate, and versatile piece of equipment that measures both magnitude and phase of signals, if properly calibrated. This article details the best practices for calibrating a VNA. Once calibrated, it can be used to accurately measure components of a correctly configured propagation measurement (or channel sounding) system or can be used as a measurement system itself.

A substitution method for nanoscale capacitance calibration using scanning microwave microscopy

This paper presents a calibration method and an uncertainty budget for capacitance measurements performed on micrometric size capacitors at microwave frequencies and nanometric resolution using a scanning microwave microscopy (SMM). The method applies the classical one-port vector network analyzer calibration for SMM using three known capacitance standards. These standards are established from a commercial calibration kit placed close to the microcapacitors in order to be calibrated. The calibration kit is composed of a large number of Metal-Oxide-Semiconductor (MOS) microcapacitors with capacitance values C ranging from 0.1 fF to 8.6 fF. Diligent selection criteria were established for the choice of the three capacitors. Their capacitance values were calculated from the AFM measured values of the area of the top electrodes and the dielectric thickness and considering the contribution of fringing fields. The combined type uncertainty on these calculated values amounts between 5% and 14% in relative value (uncertainty given at one standard deviation). The comparison between the capacitance values measured on calibration kit capacitors using the calibrated SMM and the calculated values show a good agreement for capacitances higher than 0.8 fF within uncertainties varying between 6% and 9%. For smaller capacitances, most of the observed deviations are not significant at two standard deviations. The uncertainties are mostly dominated by dimensional measurements and less importantly by unwanted capacitance effects. Based on these results, capacitances of two sets of microcapacitors were calibrated. The combined uncertainties vary from 14% to 7% for capacitances ranging from 0.1 fF to 3.1 fF respectively. The permittivity values of the dielectric layer of the two samples have been determined. They are found equal to 4.0 and 4.1 with a standard uncertainty of 0.6 and correlate with the expected value of 3.9.

Transmission Line Impedance Characterization Using an Uncalibrated Vector Network Analyzer

For determining the line characteristic impedance ${Z}_{1}$ of uniform transmission lines, it is typically necessary to use a calibrated vector network analyzer (VNA), whose calibration reference impedance ${Z}_{2}$ is known. Using the eight-error term model for modeling a VNA and based on the fact that the values of the error terms are unique and independent of the calibration structures used to determine them, a new method for determining the line characteristic impedance of uniform transmission lines is presented. The main feature of the new method is that it only uses $S$ -parameter measurements of a thru-line and a thru-load combination measured with an uncalibrated VNA.

An Alternative Experimental Determination of a Two-Port Dipolar Antenna Model

It has been shown previously that a symmetric antenna such as a dipole driven via a balun from a coaxial transmission line can be represented as a 3-terminal, 2-port network and that for vertically-polarized antennas operated near ground this network is asymmetric. An experimental approach for the determination of the values of the elements in this network representation has also previously been given. Although reasonably good agreement between simulation and experiment was obtained, the experimental procedure required three 1-port measurements and could not accommodate full error correction in the vector network analyzer (VNA) calibration. Therefore, we consider an alternative experimental approach for determining the network components of the 2-port antenna model. The new approach involves connecting both ports of the antenna simultaneously to the 2-port VNA via a dual coaxial cable and fully exploits the capabilities of a VNA including calibration and adapter removal. Both approaches are presented in detail and compared. Finally, the effect of ferrite choke beads on the coaxial feed transmission line on the equivalent network is investigated.

Complete Meniscus Removal Method for Broadband Liquid Characterization in a Semi-Open Coaxial Test Cell.

We present a new technique for broadband liquid characterization using a semi-open, vertically oriented test cell that is measured with a calibrated vector network analyzer in three states: the empty one and filled with two different volumes of the liquid under test. Using the measurements, we de-embed a transfer matrix representing a volume increment of the liquid sample and determine its column height with a novel closed-form formula. Thanks to the de-embedding, the method enables one, for the first time, to completely remove effects caused by a reproducible meniscus forming the top surface of a liquid tested in the cell and determine not only the propagation constant, but also characteristic impedance of the liquid sample, from which its permittivity and permeability are calculated. The results are highly consistent, because all the measurements are performed without disassembling the cell. We validate experimental results of the meniscus removal method by comparing them with reference data and outcomes of the Nicolson–Ross–Weir method.

First-Order Modeling of Errors Due to Coaxial Connector Interface

We present an approach for first-order modeling of errors in vector-network-analyzer (VNA) measurements caused by the coaxial-connector interface. These errors result primarily from the presence of a gap in the inner conductor. Our approach relies on an approximate model of the connector interface that comprises an analytical equivalent-circuit for the inner conductor gap section and a behavioral scattering-parameter model for the socket-contact section. We verify this model using full-wave electromagnetic simulations for the 1.85, 2.4, 3.5 mm, and Type-N coaxial-connector interface for different inner conductor-gap widths. We further apply this model to asses first-order errors in VNA calibration introduced by the tolerance on the inner conductor-gap width. We show that the inner conductor-gap effect can be accounted for with a series inductance inserted at the inner conductor mating-plane while the effect of the socket contact can be lumped into the VNA calibration coefficients. We verify this error model experimentally by measuring a Type-N offset load with an adjustable inner conductor gap. We also demonstrate that including our error model in coaxial offset-short definitions leads to improved consistency of a one-port VNA calibration with 3.5-mm coaxial offset-short standards. Our results can be used in the uncertainty analysis and accuracy enhancement of VNA scattering-parameter measurements.

Establishing a New Form of Primary Impedance Standard at Millimeter-Wave Frequencies

This paper investigates the possibility of using layers of graphene to form primary impedance standards for millimeter-wave rectangular metallic waveguide. It is shown that standards with values of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Y_{0}$ </tex-math></inline-formula> , <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2Y_{0,}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3Y_{0}$ </tex-math></inline-formula> can be produced by a monolayer, bilayer, or trilayer of graphene, respectively, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Y_{0}$ </tex-math></inline-formula> is the characteristic admittance of the waveguide. These standards could then be used in the calibration of vector network analyzers.

Scanning microwave microscope algorithm offers robust calibration method for doped semiconductors

One-port algorithm draws on classical vector network analyzer calibration to extract quantitative carrier densities from a semiconducting n-doped GaAs multilayer sample.

Scanning microwave microscopy applied to semiconducting GaAs structures.

A calibration algorithm based on one-port vector network analyzer (VNA) calibration for scanning microwave microscopes (SMMs) is presented and used to extract quantitative carrier densities from a semiconducting n-doped GaAs multilayer sample. This robust and versatile algorithm is instrument and frequency independent, as we demonstrate by analyzing experimental data from two different, cantilever- and tuning fork-based, microscope setups operating in a wide frequency range up to 27.5 GHz. To benchmark the SMM results, comparison with secondary ion mass spectrometry is undertaken. Furthermore, we show SMM data on a GaAs p-n junction distinguishing p- and n-doped layers.

A Unified Approach for Reformulations of LRM/LRMM/LRRM Calibration Algorithms Based on the T-Matrix Representation

This paper investigates a unified theory to derive vector network analyzer calibration algorithms based on the T-matrix representation, by which means the line-reflect-match (LRM), line-reflect-match-match (LRMM), and the line-reflect-reflect-match (LRRM) calibrations are formulated. The proposed calibration theory is more general than other versions of LRM, LRMM, and LRRM in that an arbitrary known two-port device can be used as the line standard L, rather than a perfect thru or transmission line. Experimental verifications of the proposed theory using on-wafer calibrations from 0.5 GHz to 110 GHz are given.