Nonlinear Vector Network Analyzer Research Articles

RF linearity trade-offs for varying T-gate geometries of GaN HEMTs on Si

AbstractShort-channel Gallium Nitride (GaN) high-electron-mobility transistors (HEMTs) often utilize T-shape gates due to their large gate-line cross-sectional area and subsequent fMAX increase. In this paper, we report the linearity trade-offs associated with varying the T-gate geometries of AlGaN/GaN HEMTs on Si, specifically the gate extensions which serve as field plates and their impact on the large-signal performance. Small-signal characterization and modeling, in addition to TCAD, provide initial guidelines for the optimal dimensions for the gate field plates using the ratio of fT and the product of the gate resistance and the gate-to-drain capacitance. We utilize various characterization methods, including 6 GHz non-linear vector network analyzer characterization in addition to load-pull, to quantify the amplitude and phase distortion and their subsequent impact on the large-signal metrics of the devices under differing matching conditions and bias points. We deduce that the influence of the gate field plates on the amplitude and phase distortion is non-negligible, particularly under matched conditions.

Characterization of Millimeter-Wave Wideband FMCW Signals Based on a Precisely Synchronized NVNA for Automotive Radar Applications

In this article, a nonlinear vector network analyzer (NVNA) measurement setup is developed to characterize frequency modulated continuous wave (FMCW) signals in the frequency domain. Thanks to the use of precisely synchronized multisine phase reference and pulsed-RF phase calibration standards, such NVNA setup is validated for high-accuracy measurement of wideband FMCW signals at the millimeter-wave test bands. According to the method validation at 24 and 60 GHz with a maximum FMCW bandwidth of 2 GHz, the proposed NVNA setup has lower measurement errors and uncertainties than the commercial real-time oscilloscope (RTO) and vector signal analyzer (VSA), offering a reference standard of test and calibration for automotive radar applications.

Evaluation of admittance domain behavioural model complexity requirements for Power Amplifier design

In the framework of Power Amplifier (PA) design for communications, frequency domain non-linear behavioural models have shown their potential as efficient complementary modelling tools when Field Effect Transistor compact models are not available or sufficiently accurate. The Admittance behavioural model, formulated in the V-I domain, is especially suitable for device size and fundamental frequency scaling. It is important to note that the direct extraction of this model, from the Nonlinear Vector Network Analyser (NVNA) load-pull (LP) measurements, requires some extra processing since it necessitates a Look-up-Table indexed to |V11| rather than |A11|. When using such models in PA design, there is the need for the user to select the necessary model complexity. To address this requirement, in this paper, a systematic analysis methodology, to guide the user, is presented and validated in different PA design scenarios. The methodology was tested using NVNA LP measurements of GaN Heterostructure FETs. A fifth order Admittance model formulation showed good accuracy in the studied PA design scenarios.

Advances in Microwave Large-Signal Metrology: From Vector-Receiver Load-Pull to Vector Signal Network Analyzer and Time-Domain Load-Pull Implementations (Invited Paper)

Radiofrequency (RF) power amplifiers (PAs) are important elements of modern communication systems. The most important components in PAs are the transistors, which are operated under large-signal regimes in such applications. Designing and optimizing PAs are challenging tasks that demand the highest accuracy on large-signal measurements at both device and circuit levels. Large-signal power transistor characterization demands the development and utilization of high-frequency and low-frequency load-pull systems. Furthermore, the static and dynamic characterization of two-input PAs requires the development of new measurement systems that consist of an nonlinear vector network analyzer (NVNA) and an arbitrary waveform generators (AWG). This paper reviews the research activities, achievements, and current research goals at CICESE Research Center in Mexico in the large-signal microwave metrology field.

NVNA Test Bench for Characterizing In-Band Full-Duplex Performance of Millimeter-Wave Antennas

In this article, we present a novel nonlinear vector network analyzer (NVNA) setup for charactering the in-band full-duplex (IBFD) performance of millimeter-wave antenna systems. To achieve millimeter-wave modulated measurements on dense spectral grids, this NVNA setup utilizes user-defined: 1) digitally-modulated test stimuli; 2) multisine phase reference; and 3) pulsed-radio frequency (RF) phase calibration standards for test bench establishment and calibration. To create the IBFD test scenario, a special design of test stimuli is developed for antenna characterization, where the spectral components of two periodical transmitting signals (digitally modulated within the same frequency band) do not overlap with each other. In this way, the desired magnitude and phase information of transmitted and received signals can be easily separated and extracted from the NVNA measurements, to support various frequency-, time-, and digital-domain analysis. The validity of the proposed NVNA setup is experimentally verified at 28 GHz, where the error vector magnitude (EVM) results of 100 MSymbol/s 64-QAM test signals are from 2.0% to 2.3%. From the application perspective, this measurement setup and test method can be widely used for fifth-generation (5G)-oriented over-the-air test of IBFD antenna systems.

비선형 벡터 회로망분석기를 이용한 파형 측정과 불확도 평가

This paper presents the measured waveform and its uncertainty using a nonlinear vector network analyzer (NVNA). For traceable measurement, calibration standards such as a coaxial calibration kit, comb generator, and power sensor are used, and the associated uncertainties are evaluated. We manufactured mTRL calibration standards on the PCB and evaluated its uncertainty using StatistiCAL. In particular, a comb generator and calibration kit were evaluated considering the correlation between frequencies. This evaluation enables the uncertainty of the inverse Fourier transformed waveform to have an increasing value at the transient in the time domain. The uncertainties of the power sensor and mTRL calibration standards assume that their correlations between frequencies are small. Finally, the effects of each uncertainty factor were compared and analyzed in the time domain.

Analysis of Time and Frequency Response for Single/Multi-Tone Stimulus Harmonic Phase-Reference Based on Prime Number Algorithm

We present a spectrally-dense phase-reference and its calibration for nonlinear vector network analyzers (NVNAs) using a step recovery diode (SRD) comb-generator with a multi-tone stimulus. Frequency selection for multi-tone stimulus based on prime number algorithms was used with the Digital Real-Time Oscilloscope (DRTO) to avoid the sub-Nyquist spurs components and to increase the effective sampling rate so that the waveform can be observed in greater detail. The measured results were calibrated to minimize drift and jitter and achieved excellent agreement between the prime number and the exact frequency strategies except at the sub-Nyquist frequencies. The analysis indicates that the prime number selected frequencies show significantly improved performance by avoiding the DRTO distortion components. We have verified the validity of the method described in this paper by experimental measurement results.

Precisely Synchronized NVNA Setup for Digitally Modulated Signal Generation and Measurement at 5G-Oriented Millimeter-Wave Test Bands

In this article, we present a novel nonlinear vector network analyzer (NVNA) setup for generating and measuring digitally modulated signals at millimeter-wave test bands. The first difference between this setup and commercial NVNAs is the use of a user-defined multisine signal as the phase reference, in order to enable more precise synchronization and denser spectral grid. To achieve this, a single 12.5-GHz microwave source is used for generating both the digitally modulated test signal and the phase reference, which not only offers the clock to the arbitrary waveform generator for user-defined intermediate frequency (IF) waveform generation but also provides the local oscillator drive after frequency multiplication. The second novelty of this work is the use of pulsed-radio frequency (RF) signals for NVNA phase calibration. By replacing the digitally modulated IF waveform with pulsed-RF signals, tone-by-tone phase calibration on dense spectral grids can be easily achieved under the same synchronization scheme. The validity of the proposed NVNA setup (as well as its simplified modification) and the phase calibration method is verified at the fifth-generation (5G)-oriented millimeter-wave bands of 28, 39, 43, and 70 GHz in this work, where the EVM measurements of 64-QAM test signals with a wide range of symbol rates from 0.1 to 1.5625 GSymbol/s are demonstrated reachable in practice.

X-Parameters Based Characterization and Compact Modeling of SiGe HBT Linearity

Linearity is an important SiGe HBT RF characteristics that has received a great deal of research for decades. For relatively small signal RF circuits such as LNAs, linearity is often characterized by measuring 3rd order intercept points, IP3, using a spectrum analyzer, or better, a Nonlinear Vector Network Analyzer (NVNA). For highly linear common-base SiGe HBTs, however, we find that the distortions generated within the RF source, which itself is also a transistor circuit, can be amplified by the HBT under test, which then interfere with the HBT’s distortions, making experimental validation of distortion in compact modeling difficult, or even impossible, for biases of high IP3. The devices used are the high voltage SiGe HBTs from NXP’s QUBIC4Xi technology. We overcome this problem with X-parameter (an invention of Keysight) measurements that are uniquely capable of removing the unwanted RF source harmonics as well as correcting for source mismatch [1], leading to more accurate transistor IP3 measurement. Fig. 1 shows the fundamental and 3rd order Pout versus Pin measured on an on-wafer through structure, with and without using X-parameters. Using X-parameters, the 3rd order harmonic output power is significantly reduced, increasing measurement system’s OIP3 to about 50 dBm.X-parameters approximate the generally nonlinear relationship between reflected waves and incident waves at the fundamental and harmonic frequencies, by a linear expansion around the system response excited by a relatively large fundamental stimulus at port 1, a situation of practical interest for amplifiers and mixers, as shown in Fig. 2. Nonlinear effects are relatively weak so that harmonic components can be superposed. The reflected wave at port p and harmonic index k, Bpk , relates to the large incident wave A11 , and all the small signal incident waves aql (port k, harmonic index l) by Eqs. (1) and (2) embedded in Fig. 2. The term P is the phase of the large signal fundamental incident wave. The superscript “*” means taking complex conjugate. N is number of ports, and K is number of harmonics. In our measurements, N=2, K=3.Fig. 3 shows output IP3 (OIP3) versus VCB for IE=1, 10, 20 and 30 mA, calculated from two FB type X-parameters, XFB23 and XFB21. Fundamental frequency is 2GHz. The Mextram 505.1 model does an excellent job in modeling IP3. While IP3 is an important linearity figures-of-merit, just like fT and fmax are for current and power gains, IP3 is not a complete representation of transistor linearity, just like fT and fmax represent only current and power gain for specific circuit terminations. At a given bias and fundamental frequency, there are for instance 78 X-parameters, for up to order 3 harmonics, including FB, S and T types, while only two FB type X-parameters are used for IP3. A logic question is if our compact model, in this case, Mextram, is capable of accurately modeling the complete X-parameter set, which represent distortion behavior much more completely. A systematic comparison of measured and modeled X-parameters is thus called for. Unfortunately, X-parameters are not supported yet by ICCAP, an industry standard device modeling tool also from Keysight, due to the complexity of X-parameter simulation. Out of necessity, here we use ADS to simulate X-parameters and then manually overlay simulation results with measurement by post-processing, a tedious process, particularly when model parameters are tuned. To a large extent, Mextram 505.1 [2], the latest version, is found to accurately model nearly all the X-parameters for a quite large range of emitter current and collector voltage biasing conditions.As an example, we show in Fig. 4 the FB and S type X-parameters as a function of VCB, for an IE of 30mA. A11 corresponds to an input power of -5dBm. The T type X-parameters for this current are small and below noise floor of measurement, and thus not shown. In the full paper we will also discuss the importance of modeling avalanche, particularly its biasing current dependence as it relates to Kirk’s effect, in modeling X-parameters, as well as how to use behavior of specific X-parameters to identify the dominant distortion mechanism, e.g. CB capacitance nonlinearity, avalanche nonlinearity, or transport current nonlinearity.[1] D. Root, J. Verspecht, J. Horn, and M. Marcu, X-Parameters, Characterization, Modeling and Design of Nonlinear RF and Microwave Components, Cambridge Press, 2013.[2] G. Niu et al., The Mextram Bipolar Transistor Model, version 505.1.0, Auburn University, 2019. Figure 1

Using Pulsed-RF Signals as Phase Standards for Millimeter-Wave Modulated Measurement and Calibration in Frequency Domain

This article presents the evaluation of using pulsed-radio frequency (RF) signals as multitone phase standards for modulated measurements at millimeter-wave (mm-Wave) bands, offering an alternative phase calibration choice for nonlinear vector network analyzers (NVNAs). Based on the NVNA measurements of two pulsed-RF signals generated by square-wave-driven mixers, a high correlation between magnitude and phase errors of unideal pulsed-RF signals is discovered, and an empirical method is developed to accurately estimate the phase errors according to magnitude-only measurements. To confirm its robustness and key preconditions for wide-range applications, theoretical support and explanation to the empirical method is revealed, in which the dominant waveform distortion of an applicable pulsed-RF signal can be decomposed into modulated perturbations with Sinc-like envelopes. The validity of the proposed empirical method, as well as its application for mm-Wave NVNA phase calibration, is verified by both experimental measurements and simulation results, where an estimation error (or phase calibration error) less than ±2° is demonstrated that is reachable in practice.

Phase calibration and uncertainty evaluation for a RF comb generator

In this paper, we present calibration and uncertainty evaluation methods for the phase of a radio-frequency comb generator using a calibrated sampling oscilloscope. In addition, we present many solutions that are indispensable for the precise calibration of phase up to 50 GHz. First, we correct the sampling time error, which is the systematic error of the equivalent time sampling system. Second, the frequency response of the oscilloscope is de-convoluted from the measured pulse, and the impedance mismatch between the radio-frequency comb generator and the oscilloscope is calibrated. Finally, we present the calibrated phase of the radio-frequency comb generator and the measurement uncertainty, which demonstrated 95% confidence intervals within ±4.4° up to 50 GHz. The calibrated radio-frequency comb generator, which is traceable to SI units, is used to calibrate a nonlinear vector network analyzer, vector signal analyzer, and oscilloscope. Uncertainties are easily propagated to the measurement uncertainty of other apparatus since it is obtained in the form of covariance.

Injection Locking at Fractional Frequencies of Magnetic-Tunnel-Junction-Based Read Sensors’ Ferromagnetic Resonance Modes

Being nonlinear dynamic systems, magnetic read sensors should respond to an excitation signal of a frequency considerably different from their natural ferromagnetic resonance (FMR) frequencies. Because of the magnetization dynamics' inherent nonlinear nature, the sensors' response should be measured at the DC, excitation frequency, and its multiples (harmonics). In this paper, we present results of such measurements, accomplished using a one-port nonlinear vector network analyzer (NVNA), which show distinct resonances at fractional frequencies of the free layer (FL) FMR mode. Identification of these resonances, resulting from the nonlinear nature of the spin-torque (ST)-induced magnetization dynamics, was performed using micromagnetic modeling. In particular, we show that the measured DC response at the above-mentioned fractional frequencies can be explained by a low-order nonlinearity and strong magnetodipolar feedback between magnetic layers adjacent to an MgO barrier. Additionally, we determined that the simulated harmonic response is strongly enhanced by the mutual ST effect between these layers. Finally, we demonstrate that the read sensors' nonlinear magnetization dynamics and, by extension, their harmonic response are highly sensitive to various magnetic and ST parameters. Thus, this study shows that using NVNA measurements in conjunction with micromagnetic modeling can clarify the uncertainty in the definition of these parameters.

Direct ${E}$ -Field Measurement and Imaging of Oscillations Within Power Amplifiers

We present, for the first time, a measurement system that is capable of directly detecting and identifying the physical location of an oscillation within radio frequency (RF) and microwave power amplifiers (PAs). The method uses a combined external electrooptic, nonlinear vector network analyzer, and vector load-pull measurement system, which allows the measurement of cross-frequency phase-coherent multiharmonic vector electric fields ( ${E}$ -fields) above the transistor with an 8- $\mu \text{m}$ spatial resolution and 20 MHz–40 GHz bandwidth. Raster scans above the amplifier allow the time-domain ${E}$ -fields to be animated and superimposed on top of the amplifier image, enabling immediate identification of any oscillations by direct inspection. The method is first demonstrated on a low-power PA composed of two parallel 0.1-W pseudomorphic high electron mobility transistors that is intentionally designed to have an odd-mode oscillation. The applicability of the method is further demonstrated by measuring and animating in-package parametric odd-mode oscillations within a 260-W laterally diffused metal–oxide–semiconductor transistor operating at 2.2 GHz under pulsed RF conditions with 10- $\mu \text{s}$ pulses and 10% duty cycle. The measurement and identification technique are applicable to all semiconductor devices as the external ${E}$ -field is noninvasively measured above the amplifier.

Automation of S-parameters measurements of high-power microwave transistors in a contact device with tunable strip matching circuits

In the practice by microwave power transistor amplifiers developing, the variable load method is usually used to determine the impedances of matching circuits in the complex conjugate matching mode. This solution involves the use of expensive equipment - coaxial impedance tuners and contact devices for mounting transistors in low impedance strip lines. An even more complicated and expensive way is the concept of X- parameters, based on the use of unique measuring equipment - a non-linear vector network analyzer, and a simulator for non-linear circuits design. The article proposes an alternative solution adapted to the operation of the transistor in real conditions and allowing to design the output stages of microwave power amplifiers using analysis and optimization of linear electrical circuits. The essence of the proposed solution is to automate the measurement of non-linear S-parameters of high-power microwave transistors in a contact device with tunable strip matching circuits for various DC supply voltage, frequency and input power mode in case of continuous or pulse input signal. The nonlinear S-parameters of the contact device are measured using the method of spatially remote variable load in the frequency range, in which the line conditioning and the maximum output power are achieved. The minimum of the reflected wave amplitude and the maximum gain are reached using movable strip matching transformers. The S-parameters measured in the coaxial line are automatically recalculated to the physical boundaries of the transistor by registering the positions of the input and output strip transformers.

Phase Repeatable Synthesizers as a New Harmonic Phase Standard for Nonlinear Network Analysis

In this paper, the synthesized phase reference standard is introduced as a new viable alternative to comb generator-based phase references for nonlinear vector network analyzer measurements. Emphasis is put on the achievable higher specific output power of a frequency picket of interest for a denser spacing in the reference frequency grid. Supporting calculations on network analyzer IF filter bandwidths and limits for a denser grid spacing for comb-based phase references are presented. The concept is evaluated with a reference prototype covering the frequency range of 54 MHz to 6.8 GHz requiring only a 10-MHz reference signal and no network analyzer generators for stimulus, thus enabling even 2-port network analyzers without direct receiver and generator access to perform nonlinear reflection measurements. Furthermore, a method for generating a low-jitter trigger signal for the oscilloscope in absence of the comb generator pulse is shown. The synthesized phase standard implementation and the characterization setup are described in high detail to facilitate reproducibility of the results. Characterization of the new phase standard is performed in a frequency hopping pattern for amplitude and phase values of the reference pickets with a sampling oscilloscope-based setup. Startup and steady state measurements are provided. A steady-state relative phase repeatability better than 2° over power cycles and drift of 0.089 °/h at 4 GHz referenced to a synthesized 1-GHz fundamental is achieved.

Application of rough set theory for NVNA phase reference uncertainty analysis in hybrid information system

The representation and processing of uncertainty knowledge are among the most commonly investigated problems in the rough set theory. In this paper, we apply the rough set theory to analyze the phase uncertainty of multi-tone stimulus scheme for nonlinear vector network analyzer (NVNA) phase reference frequency response in hybrid information system (HIS). Matlab was used to process the oscilloscope-based measured data for time and frequency response. The phase uncertainty experimental results revealed a significant correlation between the standard uncertainty and the response amplitude. Additionally, the lower amplitude in spectrum corresponded to higher phase uncertainty and vice versa. The proposed multi-tone stimulus scheme provides high resolution and rich intermodulation components around each harmonic for NVNA phase reference standard in HIS. The measured results were in good agreement with the theoretical formula-based results, and therefore, confirmed the validity of the proposed work.

Extension of NVNA Baseband Measurement for PA Characterization Under Complex Modulation

We investigated the measurement techniques of the nonlinear vector network analyzer (NVNA) test bench, to fully characterize the nonlinear behavior of radio frequency (RF) power amplifiers (PAs) driven by complex modulated signals. In order to extend the baseband measurements, two kinds of NVNA phase reference approaches are developed as alternative solutions, so that the baseband phase measurements can be achieved with those of modulated components at multiharmonic RF bands. In the first approach, a modulated baseband signal is combined with another modulated RF one to become the desired NVNA phase reference. While as an alternative solution, the second phase reference design is based on a “stepped” multisine, which is stepped through the baseband and each harmonic following the NVNA swept measurements, to achieve stable phase measurements. To validate these proposed NVNA test bench designs, an RF PA, driven by a large-signal long-term evolution-like multisine, was tested and compared with digital real-time oscilloscope measurements.

Design of Multisine Phase References/Standards for Modulated Measurements

AbstractThis paper presents a design methodology of multisine signals, so that they can be used as phase references or standards convenient for modulated measurements. To achieve an extendable measurement bandwidth, the spectrum of each multisine is designed with three successive segments, where the left (lower‐frequency) and right (higher‐frequency) ending ones have the same phase spectra. In this way several multisines, one by one overlapped at the ending segments, can jointly serve as an integrated phase reference/standard signal, which, in theory, has an arbitrarily extendable bandwidth. By the example of “Schroeder” phase relationship, the proposed method is experimentally verified for wideband‐modulated measurements, where the designed multisines are used as the phase references and standards, respectively, of a Nonlinear Vector Network Analyzer test bed. In this work, a phase measurement error less than ±1° is experimentally confirmed for 1,601 t measurements with 160 MHz modulation bandwidth around 2 GHz.

A Two-Port Nonlinear Dynamic Behavioral Model of RF PAs Subject to Wideband Load Modulation

This work presents a full two-port, i.e., double input-double output, behavioral modeling approach suitable for radio frequency power amplifiers (PAs) in the presence of dynamic load modulation (DLM). The formulation of the model, based on a first-order approximation of a modified Volterra series, accounts for the nonlinear distortion determined by large-signal operation under mismatched conditions, and also for the memory effects stimulated by a modulated PA input signal, or by the dynamic variations of the PA load. By following an exhaustive procedure defined in the frequency domain, the model of a general purpose commercial PA is extracted over 160 MHz of modulation bandwidth (BW) with nonlinear vector network analyzer measurements. Validation results under 20-MHz BW multisine excitation and injected 80-MHz BW multisine load modulation show improved prediction capabilities with respect to quasi-static or single-input descriptions, allowing for reliable system-level simulations in the presence of DLM.

Design and Evaluation of Nonlinear Verification Device for Nonlinear Vector Network Analyzers

A simple diode-based nonlinear verification device (NVD) design for nonlinear vector network analyzers is presented together with an improved figure of merit (FOM) parameter that is insensitive to impedance match and isolates variation of the device’s nonlinear parameters. The stability over 84 h and load–pull performance of this new design have been evaluated.