Stability Circles Research Articles

Design of Class F Power Amplifier for Sub 6 GHz

Class F power amplifiers increasingly have widespread use cases in the modern portable mobile communications and higher efficiency operation due to base station. This paper focuses on the design of sub 6 GHz class-F Power Amplifiers (PA) to ensure maximum output power and gain using Gallium nitride– High Electron Mobility Transistor (GaN HEMT). The work also aims to analyze stability and Power Added Efficiency (PAE) using Advanced Design System (ADS) software. Simulations for DC characteristics of the GaN HEMT transistor are performed, stability circles are simulated, and stability factor values have been noted, using ADS software. Stability analysis involves measurements to examine the conditions that may lead to unstable behavior of the PA. The load pull analysis followed by impedance matching is done to transfer maximum power from amplifier stage to load. The input and output network has been designed using transmission lines and incorporated in the final circuit of the PA design. Using the LineCalc tool, the values of electrical parameters are used in the respective MLIN and TLIN circuits, and the respective matching networks are designed at the input side and output side. The amplifier stability factor is 2.276 and the maximum PAE is 65.75%. The maximum output is 39.83 dBm. The layout for the PA network using ADS software has been obtained.

New Proofs of the Two-Port Networks Unconditional Stability Criteria Based on the Rollett K Parameter

The stability criteria based on the Rollett parameter (<inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula>) plus one auxiliary condition is yet the most popular method used by designers to evaluate the stability of a two-port network although other criteria are available. In this paper, novel analytical proofs of the criteria utilizing <inline-formula> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> and a new geometrical proof of the relationship between the stability of the ports of a circuit are proposed. They are obtained by making use of relationships between the reflection coefficients at the ports of the network and novel expressions that bind stability circles and unit mapping circles. The developed relations make the proposed proofs easier and more immediate than the traditional ones. Moreover, a new auxiliary condition having the same complexity and a greater geometrical insight with respect to the traditional ones is used.

The Use of S Parameters in Two-Port Analogue Networks Stability Analysis

If electrical systems are considered to consist of two-port linear analogue circuits (networks) in harmonic state, then S parameters can be used to establish the stable functioning states corresponding to such systems. This paper presents, on one hand, the practical use of S parameters to increase the efficiency of information transmission and propagation and of electromagnetic energy wireless transfer from the emitter-receiver point of view. On the other hand, the active power efficiency transfer from the wireless system input to the loads connected at its output, it’s taken into account. Starting from the correct formulation of S parameters, their generation is done automatically, based on modified nodal equations corresponding to the power transfer wireless systems. The magnetically coupled coils, used for wireless power transfer can be considered as a two-port circuit. To estimate the parameters of the magnetically coupled coils, advanced programs for electromagnetic field numerical computation is used: Cadence, ADS, Ansoft Extractor Q3D, COMSOL, Feko etc. In this paper there are also defined several parameters, function of S parameters, a series of constants which are further used to compute the stability factor. To generate: the reflection coefficient, the stationary waves ratio (SWR), the input and output impedances, the input and output active power transmission efficiencies, the power gains, various stability coefficients, the centres and the radius of the stability circles, the S , T , Z and Y matrices and the Smith diagrams, dedicated functions have been designed and implemented and the Microwave toolbox from MATLAB have been used. By comparing the simulated results with the experimental ones and with those presented in literature, the obtained error is acceptable.

On Locating and Counting Satellite Components Born along the Stability Circle in the Parameter Space for a Family of Jarratt-Like Iterative Methods

This paper is devoted to an analysis on locating and counting satellite components born along the stability circle in the parameter space for a family of Jarratt-like iterative methods. An elementary theory of plane geometric curves is pursued to locate bifurcation points of such satellite components. In addition, the theory of Farey sequence is adopted to count the number of the satellite components as well as to characterize relationships between the bifurcation points. A linear stability theory on local bifurcations is developed based upon a small perturbation about the fixed point of the iterative map with a control parameter. Some properties of fixed and critical points under the Möbius conjugacy map are investigated. Theories and examples on locating and counting bifurcation points of satellite components in the parameter space are presented to analyze the bifurcation behavior underlying the dynamics behind the iterative map.

ROBUST CONTROLLER DESIGN OF SINGULARLY PERTURBATION SYSTEMS WITH ACTUATOR SATURATION VIA DELTA OPERATOR APPROACH

The robust controller performances of singularly perturbation systemcould not satisfy the needs of industrial application, because of theperturbation parameters and the problem of crowding poles withinthe boundary of stability circle at high sampling frequency bytraditional shift operator.

Soliton excitations on a continuous-wave background in the modulational instability regime with fourth-order effects.

We study the correspondence between modulational instability and types of fundamental nonlinear excitation in a nonlinear fiber with both third-order and fourth-order effects. Some soliton excitations are obtained in the modulational instability regime which have not been found in nonlinear fibers with second-order effects and third-order effects. Explicit analysis suggests that the existence of solitons is related to the modulation stability circle in the modulation instability regime, and they just exist in the modulational instability regime outside of the modulational stability circle. It should be emphasized that the solitons exist only with two special profiles on a continuous-wave background at a certain frequency. The evolution stability of the solitons is tested numerically by adding some noise to initial states, which indicates that they are robust against perturbations even in the modulation instability regime. Further analysis indicates that solitons in the modulational instability regime are caused by fourth-order effects.

Low Cost RF Amplifier for Community TV

he capability of television to deliver audio video makes this media become the most effective method to spread information. This paper presents an experiment of RF amplifier design having low-cost design and providing sufficient RF power particularly for community television. The RF amplifier consists of two stages of amplifier. The first stage amplifier was used to leverage output of TV modulator from 11dBm to enable to drive next stage amplifier. CAD simulation and fabrication were run to reach optimum RF amplifier design circuit. The associated circuit was made by determining stability circle, stability gain, and matching impedance. Hence, the average power of first stage RF amplifier was 24.68dBm achieved. The second stage used RF modules which was ready match to 50 ohm for both input and output port. The experiment results show that the RF amplifier may operate at frequency ranging from 174 to 230MHz. The average output power of the 2nd stage amplifier was 33.38 Watt with the overall gain of 20.54dB. The proposed RF amplifier is a cheap way to have a stable RF amplifier for community TV. The total budget for the designed RF amplifier is only a 1/5 compared to local design of final TV amplifier.

Study of stability problems due to undesired coupling of a RF power amplifier using a distributed active transformer

In this study, we investigate the stability problems induced by undesired coupling between input feed lines and an output transformer for a linear CMOS power amplifier using a distributed active transformer (DAT) as an output balun. We extracted the losses of the input and output transformer, the undesired coupling, and the gains of the driver and the power stages to calculate the closed-loop gain. To determine the possibility of oscillation according to the location of the driver stage related to the undesired coupling and the closed-loop gain, we investigated the stability factor and stability circle. We show that the location of the driver stage of the power amplifier can be used to manage the value of the closed-loop gain. From the analyzed results, the driver stage of the linear power amplifier should be located outside the DAT to mitigate the stability issues.

X-parameters®-based closed-form expressions for evaluating power-dependent fundamental negative and positive real impedance boundaries in oscillator design

In this study, an analytical design tool, applicable under large-signal operation, based on X-parameters closed-form expressions, to determine the large-signal boundary between the negative (energy delivered) and positive (energy absorbing) real input impedance regions of the non-linear oscillator block, is presented to be used prior to and/or during non-linear oscillator circuit design. The consistency of the approach is demonstrated since in small-signal operation; the proposed expressions for the gamma equal to unity loci converges to the classic expression, generally referred to as the input or output stability circles. At large-signal levels, while we are not claiming that this formulation provides by itself similar general stability guidance, it can provide relevant information for oscillator design. The validity and usefulness of the proposed expressions as a real-time design aid, thus either minimising or avoiding the necessity for complex and time-consuming harmonic balance simulations, is demonstrated in the study.

Unconditional Stability Boundaries of a Three-Port Network

An analytical approach for acquiring the explicit expressions of the boundaries concerning the unconditional stability regions of a three-port network is presented. This approach begins with the expressions for the input reflection coefficients S 11 ' and S 22 ' at ports 1 and 2 of a three-port network having port 3 terminated with ?3 . |S 11 '| = 1 and |S 22 '| = 1 then give two stability circles in the ?3-plane. One can graphically determine that the tangent point of these two stability circles is on the boundary of the unconditional stability region for the terminating port. The explicit expressions of the boundary for port 3 are then acquired. This procedure may be followed for the other two ports in order to fully characterize the unconditional stability boundaries of a three-port network. In addition, issues pertaining to uniqueness and continuity in the plotting of unconditional stability boundaries are addressed. Using the agilent advanced design system software tool, the derived expressions of the unconditional stability boundary for the terminating port and related extreme phase values of reflection coefficients of the other two ports are implemented. These derived expressions can then enhance the computer-aided capability on the stability analysis of a three-port network and provide useful information for the microwave circuit designer.

Criteria for the evaluation of linear two-port stability using two geometrically derived parameters

Two geometrically derived stability parameters, µ′ (or µ) and ν′(or ν), are used to analyze the stability of a two-port network. The magnitudes of both µ′ (or µ) and ν′ (or ν) parameters determine geometrical relations between the stability circle and the unit Smith chart in the ΓS (or ΓL) plane. |µ′| (or |µ|) is defined as the minimum distance from the stability circle to the origin of the unit Smith chart in the ΓS (or ΓL) plane, while |ν′|(or |ν|) is defined as the maximum distance. Moreover, the signs of ν′ (or ν) and µ′ (or µ) parameters determine which region of the stability circle is stable (inside or outside) and whether the stable region includes the origin of the Smith chart, respectively. There are totally 12 situations between the stability circle and the unit Smith chart in the ΓS (or ΓL) plane by using µ′ (or µ) and ν′ (or ν) parameters. This paper classifies 12 situations in the ΓS plane and also presents the corresponding practical two-port networks.

Teaching Microwave Amplifier Design at the Undergraduate Level

Many textbooks on the subject of microwave amplifier design contain redundant material that may overload and confuse a student confronting microwave amplifiers for the first time. Some topics such as unilateral gain and unilateral design are often not necessary in this day of personal computing where exact gain and gain circle calculations can easily be used. Stability circles can be used to both identify allowable values of source and load reflection coefficients for the transistor and ascertain whether or not the transistor is unconditionally stable. By eliminating redundant topics and emphasizing the dual role of stability circles, instructors are able to effectively teach undergraduate students in a relatively short time design methods for narrow-band low-noise amplifiers, both single-stage and multistage, which employ either conditionally or unconditionally stable transistors.

Simple derivation and proof of geometrical stability criteria for linear two‐ports

AbstractThis paper presents a simple derivation of the single‐parameter geometrical stability criteria for linear two‐ports. The derivation is directly based on the classical constraints familiar to most circuit designers with regard to stability circles and stable regions. A straightforward proof of the mutual implications of various geometrical stability criteria involving dual or single parameters is also provided in a concise manner. © 2004 Wiley Periodicals, Inc. Microwave Opt Technol Lett 40: 81–83, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.11291

New simple proofs of the two-port stability criterium in terms of the single stability parameter μ/sub 1/ (μ/sub 2/)

The classical scattering-parameter stability criterium for a linear two-port makes use of two conditions involving the Rollet parameter K plus one additional parameter. A new stability criterium was developed by Edwards and Sinksky [1992] on the basis of a condition on a single parameter, i.e., /spl mu//sub 1/ or /spl mu//sub 2/. This paper presents a new, simpler, and more straightforward set of proofs of the single-parameter stability criterium for a linear two-port. The first proof is algebraic and shows the equivalence of the conditions K>1, b/sub 1/>1 with the condition /spl mu//sub i/>1 (i=1, 2). The second proof, which is geometrical, relies only on the classical stability circle concepts in an improved way with respect to the treatment by Edwards and Sinksky.

Port‐match optimization of microwave low‐noise amplifiers

The traditional approach to microwave low-noise amplifier design is to use graphical aids involving gain, noise, mismatch, and stability circles. In this paper, we propose a method, which avoids graphical methods, and uses a formula for the source reflection coefficient to minimize noise measure, and a robust numerical method for the load reflection coefficient to optimize the match at each port. The method is tested on a number of different transistors. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 27: 321–323, 2000.

Port-match optimization of microwave low-noise amplifiers

The traditional approach to microwave low-noise amplifier design is to use graphical aids involving gain, noise, mismatch, and stability circles. In this paper, we propose a method, which avoids graphical methods, and uses a formula for the source reflection coefficient to minimize noise measure, and a robust numerical method for the load reflection coefficient to optimize the match at each port. The method is tested on a number of different transistors. © 2000 John Wiley & Sons, Inc. Microwave Opt Technol Lett 27: 321–323, 2000.

Criteria for the evaluation of unconditional stability of microwave linear two-ports: a critical review and new proof

The problem of unconditional stability for active two-port networks has been widely discussed in literature. A geometrical condition involving the stability circles and the Smith circle is generally found. Then, depending on the authors, several criteria, involving the two-port S-parameters, and equivalent to the geometrical one, are derived. The equivalence among the different stability criteria has been clearly shown and some complete proof exists in the literature. In this paper, after a critical outlook on the material existing in the literature, a new proof of the unconditional stability criterion is presented. This proof has the advantage of being directly related to the concept of stability circles and to some geometrical conditions on the Smith chart. Moreover, a straightforward proof is given in which the unconditional stability at the input port implies that at the output port and vice versa.

Modified determinations of stability criteria for accurate designing the linear two-port amplifiers

An important consideration in designing linear two-port amplifiers is ensuring that the amplifiers are stable. The conventional treatments are graphic methods where the input/output stability circles are first given to assure the unconditionally stable area in the Smith chart. However, it is difficult to process the input-match and output-match simultaneously, since the source and load plane are made dependent on each other. Plots for working out the available matching area of linear two-ports have been presented here. From the study of the interaction among the input/output stability and the conjugate match conditions, the modified stability circles which are designated as matching circles are analytically developed. The available matching area is specified by using the modified determinations of the stability criteria.

Plots with matching circles for optimizing the performance of a low‐noise amplifier

AbstractPlots for optimizing the performance of LNA are presented here. From the study of the interaction between the input/output stability and the conjugate‐match conditions, four modified stability circles which are designated as matching circles are analytically developed for the input/ouptut networks. The available matching area is specified by using the modified determinations of the stability criteria. © 1993 John Wiley &amp; sons, Inc.

Equal-gain loci and stability of a microwave GaAs MESFET gate mixer

The performance of a microwave GaAs MESFET gate mixer is theoretically investigated to clarify the existence of a conditionally stable RF frequency range as well as an unconditionally stable frequency range in which maximum available conversion gain (MACG) can be defined. For the unconditionally stable range, the MACG and load and source impedances are calculated as functions of RF frequency. For the conditionally stable range, the stability circle and equal gain loci are shown for source RF and load IF impedances. The conditionally stable region of the GaAs MESFET mixer appears around F/sub T/ of the MESFET. Higher conversion gain is easily obtained by choosing a MESFET for which the F/sub T/ is close to the RF frequency. >