Vector Network Analyzer Calibration Research Articles

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.

A Multireflect-Thru Method of Vector Network Analyzer Calibration

We present a new method for two-port vector network analyzer (VNA) calibration, which uses multiple offset-reflect standards and a flush thru connection. Offset-reflect standards consist of sections of the same uniform transmission line with different lengths, which are terminated with the same highly reflective load. The unknown propagation constant of the transmission line and the load reflection coefficient are then determined simultaneously with the VNA calibration coefficients. We compare our method with the multiline thru-reflect-line (TRL) method and show that both methods yield similar results. Our new multireflect-thru method is solely based upon dimensional parameters of the calibration standards. Therefore, like the multiline TRL method, it can be used to establish a traceable VNA calibration. Thus, the multireflect-thru method constitutes an alternative to the multiline TRL calibration in environments in which the use of transmission lines is troublesome, such as in the case of VNAs with very small coaxial and waveguide connectors. The multireflect-thru method is also useful in on-wafer measurements since it allows us to keep a constant distance between the probes, which reduces the impact of crosstalk and speeds up automated testing.

Real-time microwave imaging of differential temperature for thermal therapy monitoring.

A microwave imaging system for real-time 3-D imaging of differential temperature has been developed for the monitoring and feedback of thermal therapy systems. Design parameters are constrained by features of a prototype-focused microwave thermal therapy system for the breast, operating at 915 MHz. Real-time imaging is accomplished with a precomputed linear inverse scattering solution combined with continuous vector network analyzer (VNA) measurements of a 36-antenna, HFSS-modeled, cylindrical cavity. Volumetric images of differential change of dielectric constant due to temperature are formed with a refresh rate as fast as 1 frame/s and 1 (°)C resolution. Procedures for data segmentation and postprocessed S-parameter error-correction are developed. Antenna pair VNA calibration is accelerated by using the cavity as the unknown thru standard. The device is tested on water targets and a simple breast phantom. Differentially heated targets are successfully imaged in cluttered environments. The rate of change of scattering contrast magnitude correlates 1:1 with target temperature.

Large-Signal RF Circuit Model for a High-Power Laser Diode Module

An electrical large-signal circuit model for a 30-W high-power laser diode module is presented. Such modules are designed primarily for continuous wave (cw) operation but can be pulsed in the sub- μs temporal range for special applications. Our model is thus valid up to 20 MHz in the electrical frequency domain. The elements of the circuit model have been derived from RF impedance measurements using a calibrated vector network analyzer and a high-current dc/RF bias-T. The impedance is dominated by the inductance of the high-current connecting leads from the laser driver to the laser chip. The skin effect has been found to influence considerably both resistive and inductive impedances at high frequencies. For large-signal circuit simulations in the time domain, the current-voltage characteristic of the diode p-n junction is included by an analytic equation. The model is verified by comparison of simulation results with measured currents, voltages, and laser powers in large-signal pulsed-mode operation. This model is well suited for the design of optimized pulsed-current driver circuits.

A simple and reliable technique to characterize amplitude to phase modulation distortion for high-frequency amplifiers and nonlinear devices

This paper presents a simple and reliable measurement system for characterizing the amplitude to phase modulation (AM-PM) characteristics of high frequency amplifiers and nonlinear devices. The AM-PM measurement system is based on a null detector implemented with a double balanced mixer, and requires a voltmeter and a calibrated phase shifter. A 12 W class A radio frequency power amplifier has been designed using a GaN transistor, and the AM-PM has been measured using both the method proposed in this work and the classical method with a calibrated vector network analyzer. A good correlation between both methods is observed, which validates the proposed method.

Multiport vector network analyzer calibration using the generalized 3-term error model

A generalized 3-term error model, where only three error matrixes are defined, is proposed for the calibration of n-port vector network analyzer (VNA) with n+1 measurement channels. In this model, the node is replaced by the complex vector, and correspondingly the branch gain is represented by the complex square matrix. According to this error model, which also obeys the fundamental rules of flow graph, the formula for actual scattering matrix of an n-port DUT can be deduced. Finally, the actual S-parameters of a four-port device can be corrected and they are compared with the measurement results by Agilent VNA E5071B. The good agreement attests the precision of the calibration algorithm.

Uncertainties of Multiport VNA S-Parameter Measurements Applying the GSOLT Calibration Method

For the general short-open-load-thru (SOLT) calibration of the n-port vector network analyzer with n + 1 measurement channels, the sensitivity coefficients for the S-parameters of the n-port device under test are developed as functions of the deviations of the scattering parameters for the SOLT calibration standards. Using the concept of general node equation, a generalized formula for the S-parameter deviations with respect to the error terms has been deduced. In addition, expressions representing the deviations of error terms with respect to the non-ideal calibration standards are given by a series of matrix operations. Finally, after calculation of sensitivity coefficients, they can be used for establishing the type-B uncertainty budget for S-parameter measurements.

A novel inconsistency condition for 2-port vector network analyzer calibration

An inconsistency condition for 2-port vector network analyzer (VNA) calibration is presented.This inconsistency condition discussed the use of Reciprocal device and Line or Thru for calibration of 2-port VNA. Mathematical analysis is carried out. The experimental results are compared with well known calibration algorithms like Thru-Short-Delay, Thru-Reflect-Line, Short-Open-Load- Reciprocal, and Thru-Short-Match. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2372–2375, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27072

Influence of Different Configurations of Nonideal Calibration Standards on Vector Network Analyzer Performance

To perform system error correction of a microwave vector network analyzer (VNA), several calibration procedures are applied, several of which are derived from the well-known short-open-load-through (SOLT) calibration method where lumped one-port circuits like short circuits, open circuits, and low-reflective loads are used as calibration standards. These derived calibration algorithms only use three calibration standard connections-instead of six for SOLT; hence, the calibration time is considerably reduced. Various configurations of high- and low-reflective standards at test ports 1 and 2 of the VNA are possible. Using inaccurate calibration standard modeling, the VNA calibration is incorrect, and hence, inaccurate -parameters of a device under test (DUT) are measured. In this paper, it is theoretically and experimentally shown how, due to non-ideal calibration standard modeling, the deviations of measured -parameters of the DUT from their hardware-defined true values depend on the inaccurate calibration standard modeling, on the configurations of the calibration standards at the test ports, on the reflection values of the calibration standards, and on the -parameter values of the DUTs themselves.

Multimode TRL Calibration Technique for Characterization of Differential Devices

In this paper, a new comprehensive analytical derivation and discussion of the multimode thru-relfect-line (TRL) calibration based on the new generalized reverse cascade matrices is presented. The advantage of the presented formulation is that it can account for certain symmetries in the measurement setup and reflect them in the symmetry of the derived relationships. The focus is on the two-mode case since this covers the majority of the practical applications. To demonstrate the effectiveness of the new formulation, the practical use of the multimode TRL calibration technique for de-embedding purposes is discussed. The common de-embedding assumptions such as reciprocity and symmetry are analyzed and their consequences on the multimode TRL calibration are discussed. It is shown that these assumptions applied to the embedding networks can reduce the requirements on the reflect standard. The use of the multimode TRL calibration technique for un-terminating purposes is discussed. It is demonstrated that in the special de-embedding case it is possible to completely characterize the partially leaky embedding networks. The problems of interpretation and re-normalization of the measured scattering parameters are also discussed. Finally, the on-wafer measurement results are presented that verify the multimode TRL approach for four-port vector network analyzer calibration and de-embedding of differential devices.

Smart and Quick Dk, Df Extraction Flow of Halogen-free and Lead-free Materials under Different Temperatures

Halogen-free and lead-free materials are eco-friendly and the main trend in the long run. Recently, a lot of electronic gadgets including not only mobile phones but relevant accessories have been gradually made of this kind of material in place of traditional formulas to comply with the compliance by European Union. However, there are many drawbacks about halogen-free and lead-free materials such as mechanical reliability and thermal issues which will cause the failure in use. Besides, electrical property is another inevitably critical problem. Not a few of electronic devices are needed to operate under different environmental temperatures stemming from different locations or the heat generated itself. Different ambient temperatures can affect the normality of each material used within the device and further influence the whole function. Therefore, correct and quick extraction of electrical parameters of the material is desirable in the development of high speed application easily influenced by the variation of temperature to conform to the requirement of higher precision of parameters and lower-cost expectation. Based on this reason, the main purpose of this paper is to set up a procedure which can provide an easy and reliable calibration and measurement of vector network analyzer (VNA) accompanies with thermal cycle oven to satisfy the users who want to get these electrical parameters in short time. Dielectric constant (Dk) and dissipation factor (Df), the most two important electrical parameters, have been quickly analyzed in planar-circuit methods and processed by the programs designed by ourselves under ambient temperatures ranging from −40 to 85 degree Celsius. The results of measurement reveal that Dk and Df of the halogen-free and lead-free material among these interest temperatures are 4.5–4.85 and 0.01–0.035, respectively.

Evaluation of a concept for density measurement of solid particle flows in pneumatic conveying systems with microwaves (8–12 GHz)

Abstract. This paper presents a novel density measuring concept for gas/coal particle compositions in pneumatic conveying systems. The proposed monitoring system uses horn antennas to perform complex electromagnetic transmittance measurements through the cross section of the conveying tube. The phase of the complex transmittance gives information about the effective permittivity, which is related to the mean volume fraction of the coal. Electromagnetic field simulations have been performed for the evaluation of the concept and the performance of the designed setup. A test stand for measurements on coal dust under reproducible conditions and with well-defined particle concentrations has been developed and implemented. The test tube has a diameter of 200 mm and a length of 400 mm. Coal particles with a diameter between 20 μm and 100 μm have been dispersed by injecting nitrogen gas inside the test tube. Complex transmission measurements are performed in the implemented setup with a calibrated vector network analyzer within a frequency range of 8–12 GHz. Results of the conceptual evaluation by measurements with different concentrations of coal particles are presented and discussed.

CAT-7 Cable Evaluation for Square Kilometre Array Analogue Signal Transport

Data-cable systems are essential for an evolving Square Kilometre Array (SKA) phased- array demonstrator project. Loss, dispersion and channel coupling are the characteristics of interest. We evaluate a Category 7 (CAT-7) cable system, which incorporates a 20 m CAT-7 cable, balun transformers, and ARJ45 connectors. Measurements from 30 MHz - 1.5 GHz are made using a calibrated Vector Network Analyzer (VNA). Through, Reflect, Line (TRL) as well as Short, Open, matched Load, Through (SOLT) calibration techniques were performed, which separately test the cables and the entire system performance respectively. A further measurement isolates the baluns. The connectors and baluns are mounted on customised printed circuit boards. We investigated phase dispersion, return loss, attenuation, near-end crosstalk (NEXT) and far-end crosstalk (FEXT). The best system was found to have a linear phase response in the 30 MHz to 1.4 GHz band, with NEXT and FEXT levels below -50 dB and -63 dB respectively. Such performance makes this cable class a candidate for high-volume data streams anticipated for the SKA.

Combination of Advanced Inversion Techniques for an Accurate Target Localization via GPR for Demining Applications

We used advanced ground-penetrating radar (GPR) inversion techniques for detecting landmines in laboratory conditions. The radar data were acquired with a calibrated vector network analyzer combined with an off-ground monostatic horn antenna, thereby setting up a stepped-frequency continuous-wave radar. Major antenna effects and interactions with the soil and targets were filtered out using frequency-dependent complex antenna transfer functions. The proposed strategy first exploits inversion approaches that are able to give an accurate characterization of the antenna-soil interaction and a reliable estimate of the soil permittivity. The outcomes of this first phase are at the basis of the application of a microwave tomographic approach based on the Born approximation to achieve the imaging of the subsurface. The algorithms were applied for imaging three landmines of different sizes and buried at different depths in sand. Although the radar system was off the ground, the results showed that it was possible to reconstruct all mines, including a shallow plastic mine as small as 5.6 cm in diameter. This last mine was invisible in the raw radar data, and the use of common GPR imaging techniques did not lead to satisfactory results. The proposed integrated method shows great promise for shallow subsurface imaging in a demining context, particularly because it automatically provides accurate information on the shallow soil dielectric permittivity.

Extended Through-Short-Delay Technique for the Calibration of Vector Network Analyzers With Nonmating Waveguide Ports

The extension of the through-short-delay (TSD) technique to the calibration of two-port vector network analyzers (VNAs) with nonmating waveguide ports is reported. The method retains the well-known high accuracy of the basic TSD technique while it enables to calibrate VNAs using two waveguide ports with different cross sections. Comparisons with the reciprocal-short-open-load technique commonly adopted to calibrate VNAs with nonconnectable ports and with theoretical data are reported. The present method can be adopted as either a one- or a two-tier calibration technique.

Calibration of the Three-Port VNA using the General 6-Term Error Model

A general 6-term error model is presented for the calibration of the three-port vector network analyzer (VNA). In the general two-port 6-term error model where port i (i ≤ 3) is the signal source, and other unexcited ports are regarded as a general port. The nodes and coefficients related with the general port are replaced by the complex vectors and square matrixes. With every port connected to the power source, the actual S-parameters of the three-port device can be finally solved from the general 6-term error model. Experiment results of a three-port device attest the good performance of the general 6-term error model.

Propagation Constant of a Coaxial Transmission Line With Rough Surfaces

This paper describes the accurate calculation of the propagation constant of a precision coaxial transmission line with rough plated conductors. The results are compared with previous publications and with traceable measurements of 2.4- and 1.85-mm air lines. In contrast to all tested existing procedures the present algorithm's results agree simultaneously with the real and imaginary part of the measured propagation constant. In the new algorithm, the effects of roughness and plating are represented by perturbed material parameters of a smooth coaxial line problem. A highly accurate multiple multipole field solver is used for the computation of the perturbed material parameters. The differences between the predicted and the measured propagation constant of 1.85-mm air lines are less than 0.01% at 67 GHz. Such high-precision computations are needed for the specification of offset short standards for vector network analyzer calibration.

Electronic vector-network-analyzer verification [Application Notes

The National Institute of Standards and Technology (NIST) recently introduced a new electronic approach for verifying microwave vector- network-analyzer (VNA) calibrations with a single computer-controlled electronic verification artifact. The verification results are captured in easy-to-understand performance metrics that, unlike those derived from measurements of mechanical verification artifacts, are independent of the actual artifacts employed. The approach also verifies VNA calibrations more completely than was previously possible. Finally NIST's VeridiCal software automates the entire process and allows you to log results directly to NIST servers over the Internet or generate verification reports on site, greatly simplifying record keeping.

Determination of the Complex Residual Error Parameters of a Calibrated One-Port Vector Network Analyzer

A novel approach for the determination of the complex residual error parameters of a calibrated one-port vector network analyzer (VNA) is proposed. The method is based on a single-reflection measurement employing a high-precision airline terminated by a short. The complex-valued residual directivity and source match are extracted over the entire measured frequency range by applying a sophisticated data analysis scheme utilizing low-pass filtering and linear prediction. By including an additional reflection measurement of the utilized short, the method allows the residual reflection tracking to be evaluated. Based on numerical simulations, advisable settings of method parameters are determined. In addition to the verification of the VNA calibration, the complex residual error parameters can be used for a second-order correction of the measured data. The significant enhancement of accuracy, which can be achieved this way, is demonstrated for standard calibrations by comparing the second-order corrected reflection data with results obtained from the well-established cross-ratio (quarter-wave) method.

Improved Characterization Methology for MOSFETs up to 220 GHz

Measurement and modeling procedures to accurately extract a small-signal equivalent circuit of advanced MOSFETs up to 220 GHz are proposed. The methodology carried out goes from the vector network analyzer calibration to the simulation results using complex deembedding. Good comparisons between the measurement and the simulation data obtained using this procedure are shown up to 220 GHz.