Large-signal Regime Research Articles

Transient‐based conversion matrix approach for nonlinear stability analysis

A new methodology aimed at assessing the large-signal stability of nonlinear driven circuits in the large-signal regime is presented. The procedure combines the conversion matrix approach with a transient envelope simulation and can be implemented with most commercial nonlinear microwave CAD tools. A method for the analysis of the onset of spurious oscillation in nonlinear circuits operating in large-signal conditions is also given and criteria for the evaluation and modification of the critical loads that give rise to spurious frequencies are provided. This approach has been successfully tested on a medium-power amplifier.

Theoretical Study of the Effect of Electron Beam Misalignment on Operation of the Gyrotron FU IV A

In this paper, the theory describing the processes in gyrotrons with misaligned electron beams is used for interpreting some experimental results obtained in the FU IV A, 335-GHz gyrotron operating at the fundamental cyclotron resonance. The theory describes the effect of the beam misalignment on the single-mode operation in the small-signal (start currents) and large-signal (efficiency) regimes. It also describes the effect of the beam misalignment on the interaction between two oppositely rotating modes. Comparison of theoretical and experimental results demonstrates good qualitative agreement; in particular, both of them show that 0.3-mm misalignment of the beam axis causes efficiency degradation by a factor of two.

Analysis and PIC simulation of a Gyrotron travelling wave tube amplifier

The analysis of a Ka-band gyrotron Travelling Wave Tube (gyro-TWT) amplifier using a uniform cylindrical waveguide as its interaction circuit has been presented for the TE01 mode of operation a self-consistent nonlinear analysis in the large signal regime. The analysis predicts that the saturated peak output power of ~ 134 kW with a power conversion efficiency of ~ 22.7 %. The saturated gain has been calculated as ~ 41.3 dB for the amplifier driven by 72 kV, 8.2 A electron beam of a pitch factor 1.05. The critical interaction length of smooth wall uniform metal guide is found 10.7 cm for the stable amplifier operation. The form factor and the norm factor have also been estimated with the large signal non-linear code. Further, for 5% spread the amplifier develops the peak power of ~ 128 kW with an electronic efficiency of ~ 21.7 % and the gain of ~ 41.07 dB. These results are found to be good harmony when the beam wave interaction is studied with a commercial 3-D electromagnetic particle in cell (PIC) code. The behaviour of the beam all over the length of the interaction circuit has been monitored by calculating its energy, momentum, phase, etc. with the help of a commercial PIC code and which also in good agreement with analytical results with 1% deviation.

Bimolecular recombination in molecularly doped polymers

We have investigated the bimolecular recombination of holes and electrons in a typical hole-conducting molecularly doped polymer (DEH-doped polycarbonate). The method used is a variant of the time-of-flight technique with the bulk generation of charge carriers. A small signal regime has been used to extract parameters of the multiple trapping model with an exponential as well as the Gaussian trap distributions. Then, using a large signal regime with the generation rate increasing sequentially in a power of 10, we compared model predictions with experiment. It was found that the best agreement is achieved once the Langevin recombination coefficient is used, this being defined by the microscopic mobility featuring in the models. The relevance of this fact to the published data has been addressed as well.

A nonlinear gain model for multiple quantum well transistor lasers

The gain spectra of single quantum well (SQW) heterojunction bipolar transistor laser (HBTL) is calculated with the gain coefficients and transparency carrier density as a function of the device structure factors by taking into account intraband relaxation. Inter-well coupling effects in a multiple quantum well (MQW) structure are considered as a correction factor in our approach. We introduce a six-order polynomial expression for a nonlinear carrier-dependent gain of MQW-HBTL considering ground, first excited and second excited states. We show that our gain model is notably more accurate than usual logarithmic equations, particularly in a large signal regime. Using computationally efficient numerical methods with a comprehensive rate-equation-based model, we obtain good agreement with experimental results for small signal, large signal and switching analysis of the SQW and MQW structures. We discuss the influence of different structure factors on the switching behaviour as well as on the optical bandwidth of the HBTL. Specifically, turn-on times (τon) of 160 and 540 ps are obtained for SQW and 4 QW structures, while τon considerably decreases below 100 ps for 6 QWs due to competing effects between tunneling and thermionic emission followed by carrier diffusion over the barriers. Finally, τon can be minimized independently of the QW number when a barrier width of ≈7 nm is used in the HBTL structure.

New Low-Frequency Dispersion Model for AlGaN/GaN HEMTs Using Integral Transform and State Description

A new concept for the low-frequency dispersion aspect of large-signal modeling of microwave III-V field-effect transistors is presented. The approach circumvents the integrability problem between the small-signal transconductance <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gm</i> RF and the output conductance <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dsRF</sub> by means of an integral formulation and simultaneously yields a proper description of the drain channel current in the small- and large-signal regime. In the theoretical description of the approach and in an extraction example of an AlGaN/GaN HEMT, it is shown that three independent 2-D nonlinear quantities determine the intrinsic drain channel current ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Gm</i> RF, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">G</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dsRF</sub> , and dc current). The concept is transferred to the modeling of the nonlinear charge control, where the integrability problem between the large-signal charge functions and the small-signal intrinsic capacitance matrix ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gs</sub> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">gd</sub> , and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ds</sub> ) is addressed consistently under consideration of the charge control delays. For the large-signal modeling under pulsed-dc/RF excitation, the dc continuous wave (dc-CW) modeling approach is combined with the state-modeling concept using a superposition formula for drain current and charges, respectively. The new model is implemented in ADS using a 12- and 14-port symbolically defined device for both the dc-CW and pulsed-RF case, respectively. The model has been verified by comparison to measured CW and pulsed-RF load-pull and waveform data at 10-GHz fundamental frequency.

Excitation of parasitic waves in forward-wave amplifiers with weak guiding fields

To produce high-power coherent electromagnetic radiation at frequencies from microwaves up to terahertz, the radiation sources should have interaction circuits of large cross sections, i.e., the sources should operate in high-order modes. In such devices, the excitation of higher-order parasitic modes near cutoff where the group velocity is small and, hence, start currents are low can be a serious problem. The problem is especially severe in the sources of coherent, phase-controlled radiation, i.e., the amplifiers or phase-locked oscillators. This problem was studied earlier [Nusinovich, Sinitsyn, and Antonsen, Phys. Rev. E 82, 046404 (2010)] for the case of electron focusing by strong guiding magnetic fields. For many applications it is desirable to minimize these focusing fields. Therefore in this paper we analyze the problem of excitation of parasitic modes near cutoff in forward-wave amplifiers with weak focusing fields. First, we study the large-signal operation of such a device with a signal wave only. Then, we analyze the self-excitation conditions of parasitic waves near cutoff in the presence of the signal wave. It is shown that the main effect is the suppression of the parasitic wave in large-signal regimes. At the same time, there is a region of device parameters where the presence of signal waves can enhance excitation of parasitic modes. The role of focusing fields in such effects is studied.

Analysis of Oscillation Modes in Free-Running Ring Oscillators

An in-depth investigation of oscillation modes in ring oscillators is presented. The small-signal stability is initially considered, demonstrating that the poles associated with the dc regime are uniformly distributed on a circle on the complex plane, with increasing density for a higher number of stages. The existence of multiple pairs of poles on the right-hand side of the complex plane gives rise to different oscillation modes, related here to the eigenvectors of the circulant active-device immitance matrix. This paper shows that the stability properties of detected modes depend on both the order of appearance from dc regime, in a sequence of Hopf bifurcations, and the bifurcations undergone by each steady-state mode until reaching the final operation point, when changing a bias voltage, for instance. Thus, the stability analysis must combine a bifurcation analysis from dc regime and a bifurcation analysis of each individual oscillation mode in large-signal regime. The large-signal stability analysis presented shows the possible stabilization mechanisms, which lead to the common physical observation of some of these modes. The stabilization of the desired mode, using concepts from bifurcation theory, is also presented. All techniques have been successfully applied to a ring oscillator at 12.6 GHz.

A Computationally Efficient Two-Dimensional Model of the Beam–Wave Interaction in a Coupled-Cavity TWT

A new computationally efficient 2-D model of the beam-wave interaction in coupled-cavity traveling-wave tubes (CC-TWTs) has been developed. The model provides self-consistent time-dependent solutions of Maxwell's equations together with a fully relativistic solution of the electron equations of motion. The model is based on different treatments of the RF fields in the region occupied by an electron beam and in the region of the coupled-cavity structure. The RF fields inside the beam tunnel are represented as a sum of eigenmodes of the local cross section of the beam tunnel. The fields outside the beam tunnel are represented as a superposition of modes of an equivalent circuit with lumped capacitors, inductors, and resistors. The model has been implemented in the TESLA-CC code. The results of the code predictions agree well with measured data for a wideband CC-TWT operating in the Ka-band. The code also shows good agreement with predictions of the 1-D code CHRISTINE-CC in regimes in which a 1-D approximation is applicable. A numerical study of CC-TWT operation shows that, in the small-signal regime, the code is able to predict a gain enhancement due to transverse motion at focusing magnetic fields comparable with Brillouin equilibrium values, which is the major 2-D effect. In the large-signal regime, the code is also capable of treating cases in which the transverse displacement of electrons becomes large and of determining the dependence of the spent beam energy distribution on radial position.

Theory of the ultrafast mode-locked GaN lasers in a large-signal regime

Analytical theory of the high-power passively mode-locked laser with a slow absorber is developed. In distinguishing from previous treatment, our model is valid at pulse energies well exceeding the saturation energy of absorber. This is achieved by solving the mode-locking master equation in the pulse energy-domain representation. The performances of monolithic sub-picosecond blue-violet GaN mode-locked diode laser in the high-power operation regime are analyzed using the developed approach.

Parameters for Quantitative Comparison of Two-, Three-, and Four-Level Laser Media, Operating Wavelengths, and Temperatures

Several parameters are proposed for describing the statistical thermodynamic component of the exchange of photons between a pump and a laser beam. They are based on the occupation probability of absorbing and emitting, pump and laser levels, and are complementary to the optical cross sections. The ldquooccupation factor,rdquo f 0 , is appropriate for describing an optical amplifier in the small signal regime. f 1 is appropriate for describing an amplifier in the large signal regime, e.g., a laser. They serve to facilitate a quantitative comparison of laser gain media, operating temperatures, and choice of pump and laser wavelengths. After a simple scaling, both occupation factors have a numerical value that coincides well, in most cases, with conventional usage of the terms two-, three-, and four-level laser. They can thus serve as an unambiguous, quantitative alternative to the quasi-two-, quasi-three-, and quasi-four-level terminology. The proposed definitions are general enough to apply to many types of gain media, but are particularly useful for comparing systems with discrete levels, pumped with a narrowband source, in near-resonance with the laser wavelength. Several low-quantum-defect combinations of pump and laser wavelengths are analyzed for Er3+ , Nd3+ , Yb3+ , and Ho3+ in YAG, as a function of temperature.

Nonstationary Nonlinear Discrete Model of a Coupled-Cavity Traveling-Wave-Tube Amplifier

A nonstationary nonlinear model for numerical simulation of a coupled-cavity traveling-wave tube is described. The model is based on the nonstationary discrete theory of excitation of a periodic waveguide structure, when it is supposed that the beam-wave interaction takes place only inside the cavity gaps separated by drift spaces. Such an approach allows one to consider properly the dispersion of the slow-wave structure (SWS) and to simulate processes at any point inside the SWS passband, including interaction near cutoff and even beyond the passband. Results of numerical simulations of amplification in small-signal and large-signal regimes are presented. Self-excitation processes near cutoff frequency are studied. In particular, drive-induced self-excitation that takes place only in the presence of a sufficiently strong driving signal is discussed.

Four-wave mixing and wavelength conversion in coupled-resonator optical waveguides

The four-wave mixing process in coupled-resonator optical waveguides is considered in detail and an approximate and simple approach allowing one to estimate the conversion efficiency is proposed. The analytical results are verified through a reliable and complete numerical technique taking into account nonlinear induced phase modulations, the large-signal regime, and the pulse shape evolution along the structure. The conversion efficiency is enhanced by the slow down factor to the fourth power and the impact of attenuation and phase mismatch are carefully investigated. The main aim of this study is to provide a technique to design efficient and compact wavelength converters. Two examples of devices operating on signals at 10 and 50 Gbits/s are presented and discussed. Pulse distortions induced by chromatic dispersion, frequency detuning, and slow down factor wavelength dependence are examined and the beneficial role of the nonlinear induced phase modulation on the phase mismatch is pointed out. Numerical examples show that with typical semiconductor characteristics, very high conversion efficiencies with pump powers of only a few tenths of milliwatts are achievable.

Large-Signal Vectorial Load–Pull Characterization of MEMS RF-Actuation

Electrostatic actuated radio frequency microelectromechanical systems (RF-MEMS) switches and variable capacitors are susceptible to issues related to RF actuation or even RF pull-in under large-signal regime. This phenomenon is strictly related to the average RF voltage more than power, and the impedance environment of the device should be fully accounted for. We perform for the first time large-signal time-domain measurements to characterize the RF actuation effect on the real-time capacitance value of a suspended membrane-based RF-MEMS varactor, while controlling the load impedance presented to the device with an active load-pull. The dependence of RF-actuation on both real impedance and inductive admittance is directly extracted, giving strong insights on how power handling should be carefully scrutinized against each specific circuit design.

Large and small signal distortion analysis using modified Volterra series

A new approach to the Volterra analysis of analog circuits is presented. Volterra analysis is widely used for the calculation of harmonic and intermodulation distortion products. However, the analysis is limited to circuits experiencing small signal excitations and becomes inaccurate when the input signal amplitude increases, especially when MOS transistors are involved. In this paper, we analyze the cause of this drawback, which is no other than the Taylor series' convergence properties. Moreover, we propose a solution, by calculating the nonlinearity coefficients using a different type of polynomial expansion, the Chebyshev series. This replacement improves significantly the capabilities of Volterra analysis. We also present results comparing Chebyshev series with other types of polynomial expansions. Finally, we apply the proposed method to analyze the intermodulation distortion (IMD) of a CMOS RF power amplifier, both in the small and the large signal regimes.

Experimental Study of Phase Pushing in a Fundamental-Mode Multiple-Beam Klystron

The authors present the results of experimental measurements of the radio frequency phase as a function of cathode voltage for an eight-beam four-cavity multiple-beam klystron (MBK) operated at a driven frequency of 3.25 GHz. The phase-pushing factor was measured in both the small- and large-signal regimes of amplifier operation and was found to be 0.0134deg/V and 0.0148deg/V, respectively. The experiment was also modeled with a simple analytic function and with telegraphist's equations solution for linear beam amplifiers, a multiple-beam 2.5-D nonlinear klystron code, with both methods yielding good agreement with the measured data. The low values for the phase-pushing factor are a benefit of the MBK's high-perveance operation that results in a shorter circuit length relative to single-beam devices of comparable power. These advantages contribute to the growing interest in the use of multiple-beam devices for high-power phase-sensitive applications such as advanced radar and high-data-rate digital communications

An Improved Representation of AC Space-Charge Fields in Steady-State Simulation Codes for Linear-Beam Tubes

Accurate evaluation of the ac space-charge electric field is required in order to obtain accurate predictions for linear-beam-tube performance using steady-state simulation codes. The space-charge field is commonly calculated under the assumption that the beam current density and space-charge fields are all periodic in time and locally periodic in axial distance. In this brief, it is shown by example that there are cases in which it is important, in both the small and large signal regimes, to include departures from this local spatial periodicity assumption. We find in the cases that we have studied that it is sufficient to keep a single additional term, proportional to the spatial derivative of the bunched beam current density, in the expression for the space-charge electric field. The resulting expression is much faster to evaluate numerically than a full convolution integral over all axial wavelengths. The improved representation is suitable for use in both small- and large-signal linear-beam simulation codes. It has been implemented and tested in the CHRISTINE large-signal TWT simulation code

Nonlinear Analyses of the Parasitic Backward-Wave Oscillation Power in the Magnetically Focused Pulsed Helix Traveling-Wave Tube Amplifier in the Absence of the Amplified Signal

This paper analyzes parasitic backward-wave oscillation power as a function of interaction length and focusing magnetic field parameters in a generic helix traveling-wave tube (TWT) amplifier in the absence of amplified signal. The permanent periodic magnetic (PPM) focusing of the electron beam, the relatively narrowband (less than one octave) TWT, the electron gun with no control grid, the pulsed full beam current cutoff operating mode of the TWT, and the accelerating voltage pulse wider than the amplified RF pulse are considered. Under such conditions, the parasitic backward-wave oscillation can build up at the leading and trailing edge and at the top of the accelerating pulse before and after the input RF signal is applied when the instantaneous accelerating voltage provides for the synchronism condition. The parasitic backward-wave oscillation, although nondesirable in general, can be tolerated if its power does not exceed some allowable level. In this paper, the nonlinear (large-signal) theory of beam-wave interaction in the TWT in the specified case is developed. The theory accounts for the interaction of the multiple harmonics of the backward wave of the slow-wave circuit with the electron beam that alternatively changes the direction of its rotation on each half period of the focusing magnetic field. A system of equations, which makes accessible the start oscillation length and the starting Pierce relative velocity parameter as a function of the electrical parameters of the TWT, the PPM focusing field period, and the magnetic flux density distribution in the large-signal regime, is obtained. A particular numerical example reveals the relation between interaction length, PPM focusing field period, and parasitic backward-wave oscillation power. The approach permits one to design a TWT having the maximum possible interaction length under the allowable parasitic backward-wave oscillation power. Also, the results demonstrate that the focusing magnetic field parameters have a significant effect on the interaction of the rotating electron beam with the backward wave in the nonlinear regime, as they have in the linear regime

Numerical model of wavelength conversion through cross-gain modulation in semiconductor optical amplifiers

A steady-state numerical model of wavelength conversion through cross-gain modulation in semiconductor optical amplifiers is described, which includes the spatial variations of the carrier density, gain coefficient, differential gain, and internal loss. Of particular interest is the analytic gain coefficient model, which is applied to the semiconductor optical amplifier converter problem for the first time to our knowledge. The model is used to compare performances of upconverters and downconverters for cases of long and short device lengths, and in large and small signal regimes. Comparisons with results of other studies are presented.

Semianalytic dynamic gain-clamping method for the fiber Raman amplifier

We present a physically meaningful semianalytic gain-clamping algorithm for multipump Raman fiber amplifier in large signal regime. By utilizing parameters from the steady state conditions, the suppression of gain excursion below 0.5 dB (up to 78/80 channel drop) can be achieved within microsecond/millisecond time scale, depending on the signal power level.