A Large Signal Analysis Leading to Intermodulation Distortion Prediction in Abrupt Junction Varactor Upconverters

Even though the abrupt junction varactor parametric upconverter is a "square-law" device, it exhibits gain saturation. This nonlinearity of the transfer characteristic is responsible for the nonlinear distortion present at the output of the device. Of the several methods used to measure nonlinear distortion, the two tone test has been widely used. It is the accepted test method of both SMPTE and CCIR. This paper discusses the relationship between the nonlinear distortion measured by the two tone test and the nonlinear gain characteristic. It shows that if one is known the other is uniquely determined. The analysis is broken into two parts. The first is a large signal analysis of the "square-law" parametric frequency converter. The results show that the gain is a function of the input signal level. It is this nonlinear relationship that is responsible for gain saturation. The second part is a study of the series representation of this nonlinear equation with respect to the terms containing the intermodulation frequencies. The final result is an equation which predicts the amplitude of the intermodulation distortion at any of the intermodulation frequencies. The analysis presented is closely related to the circuit and diode parameters and therefore not only predicts the amount of intermodulation distortion but also shows how it may be reduced. Experimental verification of the theory is also included.     

基于傅立叶级数法的互调产物一般特性分析

分析和讨论了非线性器件互调产物的一般行为特性.在已知传递函数的情况下,采用傅立叶级数法,推导了二载波情况下互调产物的幅度及其随阶数变化的一般表达式.针对两种典型的传递函数(分段线性软限幅器和光滑软限幅器),对二载波输入时的互调产物的幅度进行了数值计算.分析和数值结果表明:互调产物的幅度一般来说随阶数的增加而下降;高阶互调产物的下降行为本质上与传递函数的类型有关.     

Large/small carrier performance of non-linear devices

The intermodulation properties of a memoryless non-linear amplifier with two carriers having large level difference are in the limit determined by the properties of the amplitude characteristic of the amplifier at a single point, i.e. at the operating point determined by the stronger carrier. The paper derives the mathematical expression for the level of the dominating third-order intermodulation product, and also shows how this level can be determined graphically from a given amplitude characteristic.     

Analysis and Compensation of Bandpass Nonlinearities for Communications

There are many instances in communication systems where bandpass signals are passed through nonlinear devices, such as traveling wave tubes, which exhibit both amplitude and phase nonlinearities. When the input signal is narrow band, the device may be characterized by measurements of its single-carrier amplitude and phase transfer functions. A sufficient model for such a device is a quadrature structure that includes two nonlinearities each of which, acting on its own, would exhibit only amplitude distortion. The outputs of the two halves of this model are linearly independent for arbitrary narrow-band input signals so that their power spectra add. Consequently, almost all previously published results for amplitude nonlinearities can be readily applied to the analysis of the general device. Emphasis is laid on practical procedures for analysis based directly on measured device characteristics rather than analytic approximations and accuracy is checked by comparison of certain intermodulation results with previous results and with measurements. A new result is the performance of an Intelsat IV tube for a large number of independent equal-power-density signals. A heuristically optimal saturating nonlinearity is introduced and analyzed and two methods of compensating an arbitrary saturating device to obtain this optimal characteristic are presented. Two methods of inverting the Chebyshev transform are used in this paper and the choice of basis functions for obtaining series representations of the measured device characteristics is discussed.     

Nonlinear models for the intermodulation analysis of FET mixers

An accurate, detailed analysis program has been developed for intermodulation distortion (IMD) simulation of FET mixers. This program is very efficient at calculating the IMD from multiple RF inputs. We have proposed a simplified nonlinear model for IMD analysis of FET gate mixers. The accuracy of the simplified model has been verified experimentally using two different MESFET mixers and one HEMT mixer at X band. All the tests show good agreement between measured results and the calculated results for second- and third-order IMD. The simplified model is based on modeling the derivative of the device transconductance by a sum of a Gaussian function and a linear function of the gate voltage. Drain bias dependence is ignored. The advantage of this model is that it can be used for both MESFET and HEMT mixers, and its fitting parameters can be easily determined from a nonlinear characterization of the devices at low frequencies     

Harmonic gain and noise in a frequency-doubling gyro-amplifier

Nonlinear gain in a 34-GHz three-stage frequency-doubling gyro-traveling wave tube (gyro-TWT) has been experimentally studied. The device consists of a thermionic electron gun, TE/sub 01//spl rarr/TE/sub 02/ fundamental gyro-TWT input section, second harmonic TE/sub 03/ intermediate buncher section, and a second harmonic TE/sub 02//spl rarr/TE/sub 04/ complex output circuit. Nonlinear bunching in the electron orbital phase generates harmonics of the input signal in the beam current, which excite the subsequent circuits at the second harmonic frequency. Since the gain is nonlinear, noise or applied sideband signals intermodulate with the carrier generating high-order products in the output. Therefore, it has been suggested that the noise figure of these devices may be unreasonably high. In this study, the complex harmonic transfer characteristics were experimentally measured and compared with calculations based on the assumption that the gyro-amplifier gain can be described, in the narrowband sense, as a classical frequency-doubling circuit. The results show that narrowband intermodulation gain is 6 dB higher than the carrier as predicted in the small signal limit, but as the device reaches saturation the nonlinear products become suppressed with respect to the carrier. Tests on the broadband gain characteristics show that output noise consists of second harmonic shot noise spontaneously excited in the output circuits along with the products of the intermodulation between external noise and the carrier. Good agreement between the experimental results and the calculations is demonstrated.     

Intelligible Crosstalk in Nonlinear Amplifiers: Calculation of AM-PM Transfer

This concise paper analyzes the transfer of amplitude modulation from one sinusoidal carrier to phase modulation of other carriers passing through the same memoryless nonlinear device. It gives exact expressions for the AM-PM transfer coefficient, which is one part of the mechanism that leads to intelligible crosstalk, and the expressions are valid for sinusoidal carriers in the presence of Gaussian noise through devices with known amplitude and phase characteristic. Two particular input signal combinations (two carriers with a given level difference, and a large number of small carriers) are considered in more detail, and the expressions are applied to a typical TWT characteristic.     

Analysis and design of microwave linearized amplifiers using activefeedback

Intermodulations distortion of active feedback amplifier systems has been analyzed using a simple method. Starting from the amplitude characteristic of both amplifiers-the main and the auxiliary-it is possible to calculate the intermodulation distortion of the complete system. Analytical results show that third-order intermodulation products can be considerably reduced when active feedback with correct amplitude and phase is used. Experimental measurements that confirm the theoretical analysis have been made on a one-stage bipolar transistor amplifier     

Systematic DC/small-signal/large-signal analysis of heterojunctionbipolar transistors using a new consistent nonlinear model

In this paper, a new systematic approach to heterojunction bipolar transistors (HBT's) characterization and modeling is presented. The proposed approach is based on a new compact HBT nonlinear circuit model which accounts for both self-heating and the temperature dependence effects. The model's parameters are extracted from measured dc-IV characteristics and S-parameters. The power characteristics of the device are then predicted using the extracted model without any further optimizations. The same model is also used for intermodulation distortion analysis. The model has been implemented in a number of commercial nonlinear simulators and in an in-house computer code. Results are presented for two different size devices showing good agreement with measurements     

基于正态分布宽带信号的无源互调特征行为分析

在现代无线通信中,无源互调是影响通信信号传输质量的重要因素。双音互调测试能够有效衡量无源器件的非线性特性,却无法准确预测出器件在宽带信号激励下的非线性失真。因此本文提出了一种基于正态分布的宽带信号激励下的射频连接器无源互调特性分析方法。通过双音互调测试,建立射频连接器无源非线性传输数学模型,并将基于正态分布的等效宽带信号作为非线性传输模型的激励源进行模拟仿真。结果表明,宽带无源互调功率分布与宽带信号功率分布相同,n阶宽带无源互调带宽为原宽带信号带宽的n倍,宽带信号的无源互调产物相较于双音测试信号有所增强,且信号的信噪比下降,说明宽带信号在传输过程中受到的干扰更加严重。电路仿真和数值计算呈现出良好的一致性,证明了本分析方法的有效性。     

波导法兰连接的无源互调分析与测量

在卫星通信系统中,非铁磁性微波无源器件的无源互调(PIM)问题非常严重,产生PIM的根源在于天线、波导法兰等无源器件的非线性效应,例如场发射、量子隧穿、热电子发射、电致伸缩、微放电等[1]。文中通过对波导法兰无源互调模型的分析和测量,得出波导间接触压力越大,各阶PIM越小;PIM阶数越高,载波功率之比对其影响越大。     

Prediction of Gain Expansion and Intermodulation Performance of Nonlinear Amplifiers

A mathematical model for the input‐output characteristic of an amplifier exhibiting gain expansion and weak and strong nonlinearities is presented. The model, basically a Fourier‐series function, can yield closed‐form series expressions for the amplitudes of the output components resulting from multisinusoidal input signals to the amplifier. The special case of an equal‐amplitude two‐tone input signal is considered in detail. The results show that unless the input signal can drive the amplifier into its nonlinear region, no gain expansion or minimum intermodulation performance can be achieved. For sufficiently large input amplitudes that can drive the amplifier into its nonlinear region, gain expansion and minimum intermodulation performance can be achieved. The input amplitudes at which these phenomena are observed are strongly dependent on the amplifier characteristics.     

Dynamic range and other fundamentals of the complex Bessel functionseries approximation model for memoryless nonlinear devices

An explanation is given of the application of the complex Bessel function series approximation model of the memoryless amplitude and phase characteristics of nonlinear devices. Confusion had arisen because of the choice of a value of a parameter in the approximating expression. The practice had been to choose this simply as though it was just an arbitrary constant which scales the input, or as an optimizing parameter in the effort to get a best fit of the approximation to the measured data. By examining the derivation of the particular approximation, a determining and important link between this parameter and the desired operating dynamic range of the nonlinear characteristic being approximated is shown. How values for this parameter are calculated in terms of input overdrive relative to device saturation is also shown. In examining the origin of the approximating expressions, an alternative and simpler derivation to that given by J.C. Fuenzalida et al. (1973) is presented that is based on the work of M.J. Eric et al. (1972)     

Improved Intermodulation Rejection in Mixers

Intermodulation is one of the most pernicious forms of spurious response in superheterodyne receivers. This type of interference cannot be completely eliminated by narrowband filters. Improvements in receiver performance can be made only by improving and making more effective use of the mixing element. Intermodulation results from terms of higher order than two in the v-i power series expansion about the dc operating point of the mixing element. The magnitude of these higher order terms must be reduced in order to improve intermodulation rejection. In the work described in this paper, it has been observed that such a reduction in higher order terms can be obtained by proper design of the mixing element and by a proper choice of dc operating point. More than 80 dB intermodulation rejection was obtained with a single ended hot carrier diode mixer. Best performance is obtained by operating two hot carrier diodes at different operating points in a balanced mixer arrangement. Intermodulation ratios greater than 100 dB have been measured for this operating mode. Optimization of performance for IM rejection has little effect on sensitivity or rejection of other spurious responses. A new mixing element, the space-charge-limited resistor (SCLR), was designed to minimize the higher order terms in the current function. A balanced mixer provided the best performance with these mixing elements also. Intermodulation from +5 dBm inputs can be rejected below the mixer noise level. Early models of this device are not as sensitive as hot carrier mixers, but improvement appears to be possible.     

A Nevv Method of Third-Order Intermodulation Reduction in Nonlinear Microwave Systems

Third-order intermodulation distortion (IMD (3)) of some microwave systems has been analyzed using Vollterra series. In this paper, theoretical results which have been calculated with a nonlinear FET model show that third-order intermodulation prodgcts of two input signals at f/sub 1/ and f/sub 2/ can be reduced by several orders of magnitude (in fact, theoretically, IMD (3) should be reduced to zero), with a low-frequency feedback at f/sub 1/- f/sub 2/, when the amplitude and the phase of this feedback are correctly chosen. To verify this prediction, a circuit has been realized and measurements have been made on a one-stage FET amplifier. First results confirm our analysis. Experimental measurements show a 12-dB decrease of intermodulation products with our method.     

前馈系统中辅助放大器非线性分析

前馈系统中由于信号对消环路失配,导致在辅助功放输入端载波信号无法完全对消,辅助放大器的再次非线性失真会影响整个系统的失真。本文研究了残余载波信号再次产生的互调失真对整个系统线性化指标的影响,并给出了系统性能与电路参数和幅度、相位失配的关系式,通过这个关系式可以计算出要达到特定载波互调比时所需器件的最低指标要求。     

A Fast Algorithm for Sorting and Counting Third-Order Intermodulation Products

This paper presents a fast algorithm that performs a selective counting of the third-order intermodulation products generated when several carriers of various types are transmitted through a common nonlinear device. In deriving the algorithm, the carrier configuration and the frequency distribution of intermodulation products are both described by polynomials which are related to each other. The frequency distributions of third-order intermodulation products of the various kinds are then obtained with the aid of an FFT algorithm and a numerical method for solving a set of linear equations. When compared to a direct counting procedure, the proposed algorithm has presented a drastic reduction on the required Computational effort. This advantage is particularly important when the number of carriers sharing the nonlinearity is large. In an example with 1366 carriers of three different types sharing the nonlinearity, the CPU time was reduced from 7 h 46 min. down to 52 s.     

Third-order intermodulation reduction by harmonic injection in aTWT amplifier

A method for reducing the two-tone third-order intermodulation products arising from two carrier frequencies at 1.95 and 2.00 GHz is demonstrated in a traveling wave tube-distributed amplifier. The optimum amplitude and phase of an injected second harmonic and the resulting intermodulation suppression of up to 24.2 dB are examined for fundamental drive levels approaching saturation     

The static and dynamic characteristics of single and multiplephase-shifted DFB laser structures

The influence of longitudinal mode spatial hole burning (LMSHB) on the performance of distributed feedback (DFB) laser structures is examined in detail. A comprehensive model has been used to interpret the experimental results and to construct a theoretical framework that was utilized to develop more advanced device designs. An increasing side mode intensity with output power, movement of the lasing mode relative to the stopband, and curvature of the light-current characteristic at low power can all be manifestations of the influence of LMSHB on the static device performance. The dynamic behavior can also be affected, with extended wavelength chirp and amplitude patterning effects on the timescale of the effective carrier recombination time being particularly important     

Optimization of Third-Order Intermodulation Product and Output Power from an X-Band MESFET Amplifier Using Volterra Series Analysis

A third-order analysis for accurately predicting large-signal power and intermodulation distortion performance for GaAs MESFET amplifiers is presented. The analysis is carried out for both single- and two-tone input signals using the Volterra series representation and is based only on small-signal measurements. Simple expressions for the nonlinear power gain frequency response, the output power, the gain compression factor, and the third-order intermodulation (IM/sub 3/) power are presented. The major sources of gain compression and intermodulation distortion are identified. Based on the developed nonlinear analysis in conjunction with the device nonlinear model, a systematic procedure for designing a MESFET amplifier under large-signal conditions for optimum output power and IM/sub 3/ performance is proposed. The method utilizes out of band computed matching compensation through a nonlinear model of the amplifier. The accuracy of the device large-signal and IM/sub 3/ distortion characterization and the practicability of the proposed method are illustrated through comparison between measured and predicted results.