Symmetric-Reciprocal-Match Method for Vector Network Analyzer Calibration

This paper proposes a new approach, the symmetric-reciprocal-match (SRM) method, for calibrating vector network analyzers (VNAs). The method involves using multiple symmetric one-port loads, a two-port reciprocal device, and a matched load. The load standards consist of two-port symmetric one-port devices, and at least three unique loads are used. However, the specific impedances of the loads are not specified. The reciprocal device can be any transmissive device, although a non-reciprocal device can also be used if only the one-port error boxes are of interest. The matched load is fully defined and can be asymmetric. We numerically demonstrated the proposed method's accuracy with synthetic data and with measurements of coaxial standards using a commercial short-open-load-reciprocal (SOLR) calibration kit with verification standards. An advantage of the proposed method is that only the match standard is defined, whereas the remaining standards are partially defined, either through symmetry or reciprocity.Comment: GitHub: https://github.com/ZiadHatab/srm-calibratio

Indirect Measurement of Switch Terms of a Vector Network Analyzer with Reciprocal Devices

This paper presents an indirect method for measuring the switch terms of a vector network analyzer (VNA) using at least three reciprocal devices, which do not need to be characterized beforehand. This method is particularly suitable for VNAs that use a three-sampler architecture, which allows for applying first-tier calibration methods based on the error box model. The proposed method was experimentally verified by comparing directly and indirectly measured switch terms and performing a multiline thru-reflect-line (TRL) calibration.Comment: GitHub: https://github.com/ZiadHatab/vna-switch-term

Propagation of Linear Uncertainties through Multiline Thru-Reflect-Line Calibration

This study proposes a linear approach for propagating uncertainties in the multiline thru-reflect-line (TRL) calibration method for vector network analyzers. The multiline TRL formulation we are proposing applies the law of uncertainty propagation as outlined in the ISO Guide to the Expression of Uncertainty in Measurement (GUM) to both measurement and model uncertainties. In addition, we conducted a Monte Carlo analysis using a combination of measured and synthetic data to model various uncertainties, such as additive noise, reflect asymmetry, line mismatch, and line length offset. The results of our linear uncertainty formulation demonstrate agreement with the Monte Carlo method and provide a more efficient means of assessing the uncertainty budget of the multiline TRL calibration.Comment: GitHub: https://github.com/ZiadHatab/uncertainty-multiline-trl-calibratio

An Impedance Transition Method to Verify the Reference Impedance of Multiline TRL Calibration

In this paper, we present a new technique for assessing the validity of the reference impedance in multiline thru-reflect-line (mTRL) calibration. When performing an mTRL calibration, it is assumed that all transmission line standards exhibit the same characteristic impedance. As a result, the reference impedance after calibration is set to the characteristic impedance of the transmission line standards used in the calibration. However, because of imperfections, these assumptions are prone to errors. The purpose of this paper is to assess the validity of the reference impedance after an mTRL calibration. The method we propose uses the reflection coefficient of an impedance transition segment as a verification metric. The verification is achieved by performing two mTRL calibrations. The first mTRL calibration is the one we desire to validate, while the second mTRL calibration is based on step impedance lines that create the impedance transition. We conclude that the mTRL calibration is valid if the resulting reflection coefficient falls within the expected 95% confidence interval. We demonstrate our proposed method with printed circuit board (PCB) measurements of microstrip lines up to 150 GHz. The advantage of our approach is that the reflection coefficient of an impedance transition is almost constant with respect to frequency for many types of transmission line, which makes this validation metric easy to interpret when errors are present.Comment: Code on github: https://github.com/ZiadHatab/verification-multiline-trl-calibratio

A Review of Broadband Low-Cost and High-Gain Low-Terahertz Antennas for Wireless Communications Applications

Low-terahertz (Low-THz, 100 GHz-1.0 THz) technology is expected to provide unprecedented data rates in future generations of wireless system such as the 6th generation (6G) mobile communication system. Increasing the carrier frequencies from millimeter wave to THz is a potential solution to guarantee the transmission rate and channel capacity. Due to the large transmission loss of Low-THz wave in free space, it is particularly urgent to design high-gain antennas to compensate the additional path loss, and to overcome the power limitation of Low-THz source. Recently, with the continuous updating and progress of additive manufacturing (AM) and 3D printing (3DP) technology, antennas with complicated structures can now be easily manufactured with high precision and low cost. In the first part, this paper demonstrates different approaches of recent development on wideband and high gain sub-millimeter-wave and Low-THz antennas as well as their fabrication technologies. In addition, the performances of the state-of-the-art wideband and high-gain antennas are presented. A comparison among these reported antennas is summarized and discussed. In the second part, one case study of a broadband high-gain antenna at 300 GHz is introduced, which is an all-metal model based on the Fabry-Perot cavity (FPC) theory. The proposed FPC antenna is very suitable for manufacturing using AM technology, which provides a low-cost, reliable solution for emerging THz applications

Modeling and compensation of direct conversion transmitters and receivers

Zsfassung in dt. SpracheModerne Mobilfunksysteme sind einer ständigen Weiterentwicklung unterworfen, um den steigenden Datenraten Rechnung zu tragen. Eine Vielzahl unterschiedlicher Sende- und Empfangsstrukturen wurde entwickelt, um eine möglichst effiziente Implementierung dieser Systeme in Hardware zu ermöglichen.Direkt umsetzenden Architekturen kommt hierbei eine große Bedeutung zu.Sie bieten zahlreiche Vorteile im Vergleich zu dem traditionellen superheterodynen Konzept. Durch die Vermeidung bzw. Reduktion von Filtern im Hoch- und Zwischenfrequenzbereich ist die Realisierung dieser Architekturen als integrierte Schaltungen deutlich vereinfacht. Diese Vorteile stehen einer Reihe von Störmechanismen gegenüber, die sich begrenzend auf die Leistungsfähigkeit des Übertragungssystems auswirken.Zu den wichtigsten Störquellen gehören ungleiche Verstärkung der beiden Basisbandsignale sowie die Erzeugung von Intermodulationsstörungen und harmonischen Störprodukten der Hüllkurve.Im Rahmen dieser Dissertation wurden ein umfassendes Modell und ein Linearisierungskonzept für das Verhalten von direkt umsetzenden Architekturen für den Sender und den Empfänger entwickelt. Die entwickelten Modelle wurden in einem ersten Schritt mit dem simulierten Verhalten der betrachteten Architekturen verglichen. Daraufhin wurden Algorithmen zur Extraktion der Modellparameter anhand von Messungen des Sende- und Empfangszweigs entwickelt. Die gewonnenen Koeffizienten müssen nicht direkt mit den Parametern des eigentlichen Modells übereinstimmen, da sie nur einen isolierten Teilbereich des Verhaltens beschreiben. In einem nächsten Schritt wurden dann die gewonnenen Parameter zu einem Blockmodell zusammengesetzt und von diesem das vollständige Modell parametrisiert.Die Entwicklung der Linearisierungskonzepte wurde ausgehend von den Koeffizienten der Modelle des Sende- und Empfangszweiges durchgeführt.Daher können die Parameter der vollständigen Modelle direkt zur Reduktion der erzeugten Störung herangezogen werden.Modern mobile communication systems are continuously evolved to account for the increasing data transmission rates. A large variety of transmitter and receiver concepts was proposed to allow an efficient hardware implementation of these systems.The direct conversion transmitter and receiver architectures are important concepts for mobile communication systems. They offer several advantages over the traditional superheterodyne topology. By reducing or avoiding filters at the RF or the IF band these architectures are well suited for integration. The advantages are, however, confronted by the presence of several distortion mechanisms limiting the achievable performance. The most important distortion sources are the gain imbalance between the two baseband branches as well as the generation of intermodulation and harmonic distortion of the envelope signal.In this doctoral thesis a comprehensive model and a linearizer for direct conversion transmitter and receiver topologies were developed.The derived models were compared under different operating conditions to the simulated response of the architectures. Thereupon parameter extraction algorithms were developed on the basis of measurements of the transmit and receive branch. The extracted coefficients needn't coincide with the parameters of the complete model as they only represent an isolated part of the behavior of the branches.In a next step the gathered information was used to compose a block model from which the complete model parameters were derived. The development of the linearizers was based on the parameters of the complete model for the transmit and receive branch. Thus, the same set of coefficients is used to describe the system behavior as well as to reduce the generated distortion.23

A Thru-free Multiline Calibration

This paper proposes a modification to the traditional multiline thru-reflect-line (TRL) or line-reflect-line (LRL) calibration method used for vector network analyzers (VNAs). Our proposed method eliminates the need for a thru (or line) standard by using an arbitrary transmissive two-port device in combination with an additional reflect standard. This combination of standards allows us to arbitrarily set the location of the calibration plane using physical artifacts. In contrast to the standard multiline TRL method, the suggested approach avoids a post-processing step to shift the calibration plane if a line standard is used. We demonstrate our proposed method with measurements on a printed circuit board (PCB) and compare it to the multiline TRL method with a perfectly defined thru.Comment: GitHub: https://github.com/ZiadHatab/thru-free-multiline-calibratio