Computer-aided distortion analysis of switched capacitor filters in the frequency domain

A Volterra series-based distortion analysis technique for switched capacitor circuits is presented. The algorithm has been implemented in the DIANA-SC program and is completely compatible with other DIANA simulation modes. The efficiency of the method is based on the use of direct z-domain and compaction methods, while only one extra circuit analysis is needed for each higher order distortion fraction of interest. Nonlinear operational amplifiers and capacitors can be handled using polynomial models. Both harmonic and intermodulation distortion analysis modes are available. The method is demonstrated using a practical design example.     

Nonlinear Transient and Distortion Analysis via Frequency Domain Volterra Series

This paper presents a novel approach for transient and distortion analyses for time-invariant and periodically time-varying mildly nonlinear analog circuits. Our method is based on a frequency domain Volterra series representation of nonlinear circuits. It computes the nonlinear responses using a nonlinear current method that recursively solves a series of linear Volterra circuits to obtain linear and higher-order responses of a nonlinear circuit. Unlike existing approaches, where Volterra circuits are solved mainly in the time domain, the new method solves the linear Volterra circuits directly in the frequency domain via an efficient graph-based technique, which can derive transfer functions for any large linear network efficiently. As a result, both frequency domain characteristics, like harmonic and intermodulation distortion, and time domain waveforms can be computed efficiently. The new algorithm takes advantage of identical Volterra circuits for second- and higher-order responses, which results in significant savings in driving the transfer functions. Experimental results for two circuits—a low-noise amplifier and a switching mixer—are obtained and compared with SPICE3 to validate the effectiveness of this method.     

Analysis of intermodulation distortion in GaAs m.e.s.f.e.t. amplifiers

Intermodulation distortion generated in a m.e.s.f.e.t. amplifier is analysed using a Volterra series representation. The transistor model used enables direct analytical determination of the nonlinear elements from small signal measurements. Experimental verification comparing predicted and measured second-and third-order intermodulation products in the amplifer is presented.     

Distortion in variable-capacitance diodes

Distortion in variable-capacitance diodes is analyzed using the Volterra series approach. Closed-form expressions for intermodulation distortion produced by variable-capacitance diodes in series- and parallel-tuned circuits are derived and verified by experiment at frequencies up to 200 MHz. The choice of the diode capacitance law exponent for minimum distortion is investigated. Distortion in multiple-diode connections is analyzed and the advantages of the back-to-back connection is shown. Calculation shows the elimination of third-order distortion for n=0.5 in this connection.     

微波功率放大器非线性失真分析

功率放大器非线性失真产生的交调失真、邻道干扰等直接影响通信系统的性能，在放大器模型的基础上，如何定量地描述和分析其非线性具有重要意义。文中讨论了放大器非线性失真的泰勒级数分析法、Volterra级数分析法和谐波平衡分析法，给出相应的仿真和实验结果。结果表明：根据非线性的强弱采用不同的分析方法，结果具有较大的参考意义。     

Intermodulation Distortion Analysis of Reflection-Type IMPATT Amplifiers Using Volterra Series Representation

Intermodulation distortion generated in a stable IMPATT amplifier is analyzed using Volterra series representation. An IMPATT amplifier model, which takes into account the interaction between the nonlinearities of the diode and its embedding circuitry, is described. The Volterra transfer functions are derived for this model. Nonlinear terms up to and including the fifth order are considered. Intermodulation distortion products are calculated for a low-level input signal consisting of two tones. The results of this analysis are extrapolated into the direction of increasing output power in order to obtain the third-order intercept point. Further, closed form expressions for the third-order intermodulation IM/sub 3/ and intercept point P/sub I/ are derived. The distortion of a specific 6-GHz IMPATT amplifier is evaluated for illustrative purposes; the predicted distortion behavior compares favorably with experimental results.     

应用Volterra级数分析AlGaAs/GaAsHBT的三阶互调失真

分析了AlGaAs／GaAsHBT的非线性失真产生的机理,应用Volterra级数理论计算了AlGaAs／GaAsHBT的三阶互调失真,理论值与实测值吻合较好,获得了AlGaAs／GaAsHBT的非线性失真量比较弱的结果,其值并不像人们认为的那样强,并解释了HBT高线性度的原因,这证明了AlGaAs／GaAsHBT在抗干扰方面的潜在能力。     

Comparison of ordinary and time-varying Volterra analysis for finding distortion contributions

Volterra analysis can be used to perform distortion contribution analysis. It is shown here that an ordinary time-invariant (TI) Volterra analysis with fitted polynomial models can be used in such a non-linear application as mixers and switching power amplifiers, where time-varying (TV) Volterra analysis has often been used. TI and TV Volterra analyses are compared behaviorally, and the use of TI Volterra with fitted polynomial coefficients is illustrated by analyzing two highly non-linear example circuits using a recently developed Volterra-on-Harmonic-Balance (VoHB) analysis tool.     

Perturbation Analysis of Nonlinear Distortion in Analog Integrated Circuits

A method for predicting the distortion in weakly nonlinear analog circuits is presented, which relies on the classical theory of regular perturbation. Accordingly, a nonlinear circuit is described and analyzed as a perturbation of its linearized model, and the response to a periodic signal is analytically calculated through frequency-domain recurrent formulas. The method is simple and quite straightforward to apply, as it involves the calculation of frequency-domain transfer functions and of Fourier coefficients only, making it easily adaptable to any circuit topology. The method can be a valid alternative to the Volterra series method. A relationship between the proposed method and the Volterra series method is established, showing that they lead to very similar approximants to the solution. The method has been numerically tested in practical circuits wherein the devices are modeled by polynomial and exponential nonlinearities.     

Intermodulation distortion of cascaded transistors

Intermodulation distortion performance of cascaded transistors is analyzed using a nonlinear frequency-dependent model for the transistor and with Volterra series as an analysis tool. The objective of this study is to determine the optimum cascade that has high gain and good modulation performance especially for higher frequencies. A particular application is in long-haul, analog, solid-state coaxial systems where intermodulation distortion is a critical problem. Both experimental as well as computer results are used in this analysis. It is shown, for example, that certain low distortion configurations can exhibit high distortion when cascaded. A few optimum cascade configurations are discussed in detail.     

Inter modulation distortion analysis of cascaded MESFET amplifiers using Volterra series representation

The third-order intermodulation distortion generated in a two-stage cascaded amplifier is derived analytically by means of the Volterra series expansion, for non-linear systems with memory. A unilateral transistor model is used, which takes into account the three major non-linearities, the gate capacitance, the trans-conductance and the output conductance, in each stage of the amplifier. The Volterra transfer functions are determined for this transistor model and closed-form expressions for the intermodulation distortion ratio are given, where the terms with a contribution less than 1% have been neglected. The equations identify the principal sources of the distortion in the amplifier circuit and the influence of the transistor parameters and load impedance is investigated. The analysis of the two-stage cascaded amplifier gives a new insight into the intermodulation distortion behaviour and is discussed in detail at the end of the paper. The results obtained here are compared with those received for single-stage amplifiers.     

Accurate Nonlinear Volterra Series Analysis for Vertical-Cavity Surface-Emitting Lasers

In this letter, an accurate nonlinear Volterra series analysis for vertical-cavity surface-emitting lasers (VCSELs) is presented. Closed-form expressions for the modulation response, harmonic distortions, and second- and third-order intermodulation distortions are derived. Moreover, the suggested nonlinear model avoids the numerical solution of laser rate equations and provides in-depth insight of a distortion analysis of VCSEL.     

Analysis of envelope signal injection for improvement of RF amplifier intermodulation distortion

Adaptive bias techniques based on envelope signal power detection have been proposed for linearity enhancement and dc current reduction in RF amplifiers. Experimental results show an improvement in amplifier linearity, although asymmetric intermodulation distortion (IMD) was observed. This work rigorously studies the effects of the envelope signal injection on amplifier distortion using the Volterra series formulations. The results intuitively explain the spectral regrowth asymmetry, and point to a design technique in which third-order IMD can be optimally cancelled. The theory was verified through comparison to measurement and simulation results.     

Integral function method for determination of nonlinear harmonic distortion

The analysis of harmonic distortion is of prime importance for the analog and mixed integrated circuits. Recently we presented a new integral function method (IFM), based on a completely new principle, which allows the calculation of harmonic distortion using the DC output characteristic of devices or circuits. In this work we complement the integral function method to provide direct calculation of the following distortion figures: total harmonic distortion (THD), second harmonic distortion (HD2) and third harmonic distortion (HD3), voltage intercept points (VIP) and the intermodulation distortion (IMD). The comparison with the same distortion figures calculated by the Fourier coefficients (FC), by direct AC measurements and from FFT in simulators, indicates that results obtained by IFM give an excellent agreement in the full range of the analyzed active regions. The IFM combines simplicity and computer efficiency with accuracy and with the possibility to easily analyze the distortion when varying any of the circuit or device parameters.     

Detailed distortion analysis technique based on simulated large-signal voltage and current spectra

This paper presents an analysis technique implemented on top of normal harmonic-balance simulation, where the simulated nonlinear voltage and current spectra is used for fitting a polynomial device model around the large-signal bias point. Further, using the fitted model and spectra of the controlling voltages, the detailed structure of the third-order intermodulation distortion is calculated using a simplified form of Volterra analysis. This detailed information can be used to find the dominant causes of distortion and possible cancellation mechanisms, to study the bandwidth-dependent memory effects caused by up- or down-converted mixing results, or to find harmonic matching impedances that minimize the overall distortion.     

Distortion cancellation by polyphase multipath circuits

It is well known that in balanced (or differential) circuits, all even harmonics are canceled. This cancellation is achieved by using two paths and exploiting phase differences of 180/spl deg/ between the paths. The question addressed in this paper is: what distortion products (harmonics and intermodulation products) are canceled if more than two paths (and phases) are used? These circuits are called polyphase multipath circuits. It turns out that the more paths (and phases) are used, the more distortion products are canceled. Unfortunately, some intermodulation products cannot be canceled without also canceling the desired signal. An analysis of the impact of mismatch between the paths shows that the suppression of distortion products will be larger if more paths are used. As an application example, the design of an upconversion mixer with a clean output spectrum is presented.     

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.     

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.     

Intermodulation Distortion Analysis of MESFET Amplifiers Using the Volterra Series Representation

Third-order intermodulation distortion generated in a MESFET amplifer is analyzed by means of the Volterra series representation. A transistor model is used which enables direct analytical determination of the nonlinear elements from small-signal measurements. The four nonlinearities considered are the gate capacitance, transconductance, drain feedback capacitance, and output conductance. Volterra transfer functions are derived for a simplified model and closed-form expressions for the third-order intermodulation ratio and intercept point are determined. The equations show the dependence of distortion on frequency, terminating impedances, and transistor parameters. Principal sources of distortion are identified and the influence of device parameters and network terminations is investigated. Experimental verification on specific MESFET amplifiers, with 2-mu m and 1-mu m gate devices, comparing predicted and measured intermodulation products for various load conditions is presented.