Buildup behaviour of IMPATT oscillators in linear and nonlinear ranges

The growth rate, frequency shift and starting amplitude of oscillations in IMPATT-diode oscillators are calculated in the linear and nonlinear range. It turns out that, with increasing r.f. amplitude, the frequency in such oscillators always decreases, and that this frequency shift cannot be compensated for by proper tuning of the load. The r.f. amplitude remains below the measurable level for a certain time depending on the oscillator tuning. This accounts for the observed delay of the onset of the r.f. pulse.     

Amplitude Behavior of Injection-Locked Oscillators

Subject to a reasonable constraint on the frequency of the amplitude modulation of the injected signal, the reduced amplitude equation for an injection-locked oscillator, a nonlinear differential equation, is reduced to a nonlinear algebraic equation which is solved numerically. AM limiting, power limiting, and output-power increment are calculated as functions of injected-signal amplitude for several types of negative-conductance nonlinearities. A method of characterizing the conductance nonlinearity from the measured output-power increment is given and is used to characterize avalanche- and tunnel-diode oscillators. Excellent agreement between calculated and measured limiting is shown. In addition to clarifying the amplitude behavior of the locked oscillator, the results show what types of nonlinearities are desirable for limiter applications, that avalanche-diode oscillators have the potential for excellent limiting, and that the output-power increment is indicative of the oscillator impedance match.     

General equation for quasisinusoidal oscillators

A nonlinear differential equation has been obtained to describe the behaviour of any quasisinusoidal oscillator, Simple relationships are also proposed whereby the frequency and amplitude of an oscillation can be calculated and its stability verified. Application examples involving some typical circuits are then given.     

Distortion and noise-induced DC offset in operational amplifiers

Experimental measurements on many different commercial operational amplifiers indicate that a sizable d.c. offset voltage occurs which is a function of input signal amplitude and frequency. This offset is shown to be the result of nonlinear distortion in the input stage. A simple nonlinear model is used to analyze the effect, and calculated and experimental results are in good agreement.     

Nonlinearities of multicavity klystron amplifiers

The nonlinearities of a five-cavity klystron for wide-band operation are investigated by making use of the large signal analysis and experiments. The variations of frequency-response characteristics with respect to the input signal level, and the amplitude and phase nonlinearities are presented in detail for two typical tunings. It is shown that the nonlinearities are affected by the tuning of the intermediate cavity. The amplitude nonlinearity at saturation is about -3 to -6 dB within a frequency range of 80 MHz at the 14-GHz band. There exists some discrepancy between the calculated and measured phase nonlinearities. The nonlinear mechanisms are discussed to explain the results obtained by categorizing them into four parts. In the discussions, an emphasis is placed upon the velocity modulation of the beam by the intermediate cavity which introduces the frequency dependence into the nonlinearities.     

Nonlinear Gain in Semiconductor Ring Lasers

Nonlinear gain in semiconductor ring lasers has been investigated theoretically based on density-matrix equations, including the effects of carrier density pulsations, carrier heating, spectral hole burning, and carrier diffusion. Expressions for nonlinear susceptibilities are derived analytically and compared with previous theoretical results. It is found that carrier diffusion have strong effects on both the amplitude and beat frequency dependency of the nonlinear susceptibilities. Various nonlinear parameters are also calculated based on the expressions obtained, and are consistent with published experimental results by other groups.      

用沃尔泰拉级数对非线性器件建模的探讨

本文提出使用沃尔泰拉级数去分析具有非线性器件的振荡系统。文中用实例论证了沃尔泰拉级数适用于设计微波FET振荡器。肯定了这个理论是有效的,在其所估算的振荡幅度值和频率值与实际测量值之间的差值不大于1O％。     

Noise Analysis of Nonlinear Feedback Oscillator with AM-PM Conversion Coefficient

The noise of a microwave nonlinear feedback oscillator with AM-PM conversion coefficient is analyzed. The oscillation wave is divided into a carrier and noise sidebands. It is assumed that the noise sideband is the first-order perturbation to the carrier wave and can be superposed with each other. The amplitude and frequency of the carrier are graphically determined by the "device-load line" method, considering the nonlinearity of the amplifier. In order to take the AM-PM conversion effect of a nonlinear amplifier into account, the "transfer matrix" for the small AM and PM sideband components which has amplitude-dependent diagonal and off-diagonal terms is introduced as an extension of the incremental describing function. The spectra of the oscillator noise and their dependence on operating conditions can be easily calculated by using these transfer matrices. The AM and PM noise spectra are measured when a traveling-wave tube is used as an amplifier. The measured values well agree with the calculated ones.     

恒压源驱动下的扬声器低频跳跃

通过能量法求解扬声器非线性振动系统的非线性微分方程的一阶近似解，得出幅频关系方程和幅频关系曲线，并着重分析讨论磁场的非线性对扬声器低频跳跃的影响，得出一些结论。     

Up-conversion of subpicosecond light pulses

Harmonic generation and frequency mixing in nonlinear media pumped by subpicosecond pulses are studied. The propagation and interaction of subpicosecond pulses in a dispersive medium is influenced by group velocity "walk through" and spreading of the light pulses. The amplitude and spectrum of theNth harmonic are calculated taking into account both the group velocity and group velocity dispersion. Conditions for group velocity matching in crystals and mixtures of metal vapors and gases are considered, together with their relation to the phase velocity matching. An example of using four-wave mixing to generate ultrashort pulses with tunable duration over a wide range by proper group velocity matching is discussed.     

A method of analysis of periodic processes in nonautonomous discrete-time systems with quantization

A method of analysis of stationary processes in systems with an arbitrary number of quantization levels in the presence of periodic external signals is proposed. The method is based on the representation of stationary oscillations in the form of an invariant set of nonlinear discrete point mappings. The spectral composition of the response of a system with an arbitrary period coupled with the discretization period through a rational relationship is calculated with the use of the discrete Fourier transform. The discrete Fourier transform is applied also to calculate nonlinear distortions. It is suggested to use the dependence of the ratio of the first-harmonic amplitude of the system’s steady-state response to the amplitude of the input-signal harmonic on the frequency of the input harmonic signal as the amplitude-frequency characteristic of a nonlinear system. In addition, it is suggested to use the dependence of the difference between the argument of the first harmonic of the system’s response and the initial phase of the input signal on the frequency of the input harmonic signal as the phase-frequency characteristic of the system. The usage of the method is illustrated by its application for the analysis of processes in first-and second-order circuits.     

超宽带信道的频率色散特性对脉冲波形的影响

采用幂形式衰减模型和建立的抛物线型非线性相位模型分别研究了超宽带脉冲信号在频域中发生的幅度失真和相位失真,分析了超宽带信道的频率色散特性对脉冲信号波形产生的影响。仿真结果表明,传播信道中物体的边缘折射产生的频率依赖特性较强,引起的脉冲幅度失真较大;收发天线较小的非线性相位响应,也会导致较大的波形畸变。因此,在实际的超宽带信道建模时应根据实际环境考虑超宽带信道的频率色散特性。     

Optimization of SNDR for amplitude-limited nonlinearities

Many components used in communication systems are nonlinear and have a peak power or peak amplitude constraint. Nonlinearity generates distortions and thus signal-to-noise-and-distortion ratio (SNDR) is an appropriate performance measure. In this paper, we are interested in finding the nonlinear mapping that maximizes the SNDR subject to the peak amplitude constraint. The answer is a soft limiter with gain calculated based on the noise power and the probability density function of the input amplitude. We also investigate a bounding relationship between the SNDR and capacity of the nonlinear channel. The results of this paper can be applied for efficient transmission of high peak-to-average power ratio signals or for optimal linearization of nonlinear devices.     

Perturbation solution of self-pulsing in semiconductor lasers witha saturable absorber

We solve the three-component rate equations for semiconductor lasers with a saturable absorber or for multi-section semiconductor lasers by using a singular perturbation method. The effects of nonlinear gain and spontaneous emission are included in the rate equations. By transforming the rate equations to the generalized coordinates, we eliminate the most rapidly varying term adiabatically for the fast saturable absorber. Then, we solve the two-component nonlinear equations to obtain analytic expressions for parametric dependence of self-pulsing amplitude and self-pulsing frequency. the self-pulsing frequency shifts from the small-signal oscillation frequency to the lower-frequency side as we increase the self-pulsing amplitude. The square of the self-pulsing frequency does not linearly depend on the injection current, in agreement with experimental observations. We also derive an optimum saturable absorber recovery time for the shortest optical pulse generation     

超声手术手柄振动系统的有限元与实验分析

给出了有限元法求解压电耦合振动的原理，利用有限元软件ANSYS对手柄振动系统进行了模态分析和谐响应分析，得到了精确的纵振动振型以及刀头的振幅、系统振幅放大系数等结果。并分析了施加的电压、压电片数和阻尼对刀头振幅的影响。利用动态信号分析仪对手柄的谐振频率进行了测试，结果与有限元计算的谐振频率非常接近。     

一种分析非线性振荡器频率及振幅灵敏度的新方法

本文提出了一种基于Volterra函数分析非线性振荡器频率及振幅灵敏度的新方法,该方法不仅克服了传统分析方法所受到的非线性元件应为弱非线性,非线性振荡幅度应足够小这两方面的限制,而且还可以用来分析高阶非线性振荡电路.本文对该方法进行了理论上的探讨.     

载流梁的热磁弹性3次超谐共振

在磁弹性动力学理论的基础上,应用动力学方法建立电磁场和温度场联合作用下的载流梁的非线性热磁弹性振动方程。应用非线性振动的多尺度法,求得了系统受Lorentz力和温度影响共同作用的3次超谐共振幅频响应方程,并对其进行了数值计算,研究电磁场、温度变化、电流、几何参数等参数对载流梁3次超谐共振响应曲线的影响。结果表明：当温度、磁场强度、长度、横截面积达到特定值时,系统振幅会大幅增加。     

Optimal PWM based on real-time solution of harmonic eliminationequations

Pulse-width modulation of DC/AC power converters (PWM) based on the elimination of low-order harmonics necessitates solving systems of nonlinear equations. Conventional implementations of this technique based on storing off-line calculated solutions have the common problem that the system flexibility is very limited, especially for applications that require both amplitude and frequency control. A new implementation scheme based on real-time solution of nonlinear harmonic elimination equations using a digital signal processor DSP56001 is reported in this paper. With this digital signal processor (DSP), optimal pulse patterns having 15 switching angles in each quarter fundamental period can be determined within 2.15 ms. Details of the system hardware and software are described. New theoretical results concerning the solvability of harmonic elimination equations are also presented     

A relatively short cylindrical broadband antenna with tapered resistive loading for picosecond pulse measurements

A relatively short cylindrical antenna with continuously tapered resistive loading has been studied for the purpose of picosecond pulse measurements. The antenna considered is a nonconducting cylinder with continuously deposited varying-conductivity resistive loading. The current distributions on the antenna were numerically calculated using the method of moments. Using these current distributions, other quantities such as input admittance, near-field and farfield radiation patterns, and radiation efficiency, were also numerically calculated and compared with the results using the Wu-King's approximate current distribution. Agreement is relatively good except at high frequencieskh > pi/2where the method of moments appears to give better results. To verify the theoretical results, several resistively loaded antennas were fabricated, and their picosecond pulse receiving characteristics were analyzed for the frequency range between 5 kHz and 5 GHz. The experimental results indicate excellent linear amplitude and phase response over the frequency range. This provides the unique capability of this antenna to measure fast time-varying electromagnetic fields with minimal pulse-shape distortion due to nonlinear amplitude or phase characteristics.     

The effect of capacitive mixing and detection in Schottky-barrier diodes at high, intermediate, or modulation frequencies

At high IF or modulation frequencies a Schottky-barrier diode not only operates as a conductance mixer or detector due to its nonlinear conductance but also as a capacitance mixer or detector due to its nonlinear capacitance. The effect is calculated for a heavily doped Schottky-barrier diode in which the pump amplitude and the signal amplitude are relatively small so that short Taylor expansions of the current and charge characteristics can be used. Beyond an upper corner frequency f1the effect gives rise to a considerable increase in the output signal and to a considerable increase in signal-to-noise ratio. Due to the electronic feedback between input and output, the output conductance g_{out} can be negative foromega_{i} = omega_{P} - omega_{0}when capacitive mixing predominates. At the limit of stability (g_{out} = 0) the noise figureF = 1 + n_{1}omega_{i}/omega_{0}, where n1lies between ½ and 1.