The notch filter test method simulation for the intermodulationnoise of return path CATV amplifiers

CATV return path is mainly carrying QAM signals. The frequency spectrum of QAM digital signals is noise-like. This means, that a return path amplifier is loaded with wideband noise, and intermodulation products will be noise-like too. This article describes the numerical simulations of the notch filter test method for intermodulation noise distortion in return path CATV amplifiers. The calculation is based on the frequency dependent intermodulations coefficients of the second and third order as well as clipping effect. It is possible to calculate the return path distortion spectrum and the output level limit for any channel plan. The simulation proved to be in good accord with measurement     

Second-order analysis of the output of a discrete-time Volterra system driven by white noise

The second-order analysis of the output of a discrete-time nonlinear system described by a truncated Volterra series whose input consists of a sequence of independent random variables (white noise)is considered. The main result consists of an explicit formula for the mean value of the output process in terms of the cumulants of the input and of Volterra kernels. This formula, with suitable modifications, allows the calculation of the output correlation as well as of the continuous and discrete components of the spectral distribution. Several applications are considered, and in particular the Gaussian white noise case is worked out in detail. Finally, the computational aspects of the analysis are discussed with the aim of showing that in several situations closed-form results can be obtained.     

The Effect of a Nonlinearity upon Signals in the Presence of Noise

A general method is presented for determining not merely the output spectrum resulting from a nonlinear transformation of signals and noise but also the signal × signal distortion and intermodulation components, including their phases and their precise forms as functions of time. Recent work by Jain is thereby illuminated and generalized.     

Un outil pour la CAO des circuits microondes non linéaires attaqués par des générateurs non harmoniques

A new method for computing the spectrum of signals in nonlinear systems driven by non-harmonically related input generators is proposed. It is applicable to both periodic and non-periodic signals. A very efficient discrete Fourier transform is used which can be also included as an independant package in a time domain or an harmonic-balance software. The method is used in a improved harmonic-balance programme which works then as a spectral-balance analysis programme for use in non-linear mixing problems such as non-linear conversion in mixers, intermodulation in amplifiers, and noise conversion in oscillators. An illustrative example of a class-C amplifier is given.     

Calculating the CSO/CTB spectrum of CATV amplifiers and opticalreceivers

The discrete CSO/CTB intermodulation distortion has a big influence on the CATV net quality. This article describes a new method to calculate the composite second order (CSO) and composite triple beat (CTB) intermodulation distortion spectrum for the full frequency range of a coaxial cable CATV amplifier for any input frequency plan. The calculation takes into account the output level ripple and preemphasis, using frequency dependent intermodulation coefficients. These coefficients have been established through CSO/CTB measurements on multichannel test systems for standard frequency plans at 5-8 intermodulation frequencies or on distortion arrays for the two (three) oscillator measuring test system. The defined intermodulation coefficients are unrelated to the frequency plan and the input/output level ripple. It is also possible to calculate the CSO/CTB spectrum caused by analogue channels within digital QAM channels. The results equally apply to optical CATV receivers. Simulation results have been verified using extensive data from multichannel measurement systems     

Hard-Limiter Intermodulation Product Magnitudes for Three Signals in Random Noise

When two or more sinusoidal signals are passed through a hard limiter, intermodulation (IM) products are developed at the limiter output. The magnitudes of the IM products are a function of the relative levels of the input signals, as well as the input noise, if present. This paper considers the case of three input sinusoids plus random noise. Quantitative values for IM-product magnitudes are presented as a function of input signal-signal-to-noise ratio for two specific cases of relative input signal levels.     

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.     

An analytic expression for the magnitudes of the signal and intermodulation outputs of an ideal hard limiter,assuming n input signals plus gaussian noise

An expression is derived that gives the output fundamental and intermodulation product magnitudes for an ideal hard limiter, for the case of n input signals plus Gaussian noise. The expression is derived by building upon previous work by Shimbo⁴ to account for the Gaussian noise input. The expression is implemented in a computational tool. Results are generated and are compared with data generated by Jain⁵ for three-signal suppression, and by Blachman¹¹ for the functional relationship between the output and input SNR for a bandpass limiter. In all cases, the data generated agree extremely well with published results.     

A Stochastic Analysis of Signal Sharing in a Bandpass Nonlinearity

When constant-amplitude signals and noise constitute the input to a bandpass device exhibiting a nonlinear input-output power characteristic and AM/PM conversion, the relative signal levels may change and intermodulation (IM) products are produced. A new and totally general method of evaluating the complex Fourier coefficient of any desired output component is presented. The analysis is based on repeated extraction using expected values of output signals dependent on one or more of the input signals, and makes use of joint envelope-phase probability distributions of the input conditioned on given signal phases. Several analytical examples demonstrating the application of the method and its advantages are discussed. Numerical results are presented for 2, 4, and 100 equal carriers into several types of soft limiters with quadratic AM/PM conversion.     

New single-parameter models for electronic circuits with even symmetry nonlinearity

In this paper single-parameter models are presented for the instantaneous characteristics of electronic circuits/systems exhibiting even-symmetry nonlinearities. The models can easily provide closed-form expressions, in terms of the ordinary Bessel functions, for the amplitudes of the second-harmonic and second-order intermodulation components at the output of the nonlinear circuit/system excited by a multisinusoidal input signal. Moreover, by combining the proposed models with the previously published models for instantaneous characteristics exhibiting odd-symmetry nonlinearities, a new method and apparatus are proposed for characterizing nonlinear circuits/systems exhibiting both even- and odd-symmetry nonlinearities. The proposed method and apparatus use the amplitudes of the measured output second- and third-order intermodulation components resulting from a two-tone equal-amplitude input signal.     

Synthetic instruments extract masked signal parameters

We have reviewed the signal conditioning required to obtain high-quality spectral measurements with an FFT-based spectrum analyzer. The conditioning includes data windowing and extended length. Folded windows are required at the input to the transform, and significant ensemble averaging of power spectrum and cross power spectrum at the output of the FFT is needed. We also commented on the effect of cross coupling between signal and noise terms on the variance of the spectral output terms when the signal contains both spectral lines and additive noise. Finally, we presented techniques based on cross spectra. In particular, the normalized cross spectra known as the coherence function was shown as a technique to separate spectral components traceable to the input signal from those not traceable to the input signal.     

The Role of AM-to-PM Conversion in Memoryless Nonlinear Systems

A generalized proof is presented that AM-to-PM conversion can only degrade, never improve, the intermodulation-noise performance of memoryless nonlinear systems with random input signals having even probability density functions, and a measure of degradation is defined. It is also shown for such signals that AM-to-PM conversion causes a deterministic constant phase shift to be added to the argument of the signal component at the output but has no other effect on its phase. This class of inputs includes one or the sum of several PSK signals, as well as large ensembles that can be modeled as Gaussian noise. The latter are dealt with by using Bussgang's theorem on input-output cross correlation. In the proof, Bussgang's theorem is extended to the complex case, to include phase as well as amplitude nonlinearities, yielding a complex version of the theorem. For Gaussian inputs it is shown that the undistorted signal and the intermodulation noise at the output of such systems are uncorrelated.     

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.     

Third-Order Intermodulation Due to Quantization

When an input consisting of a strong signal and a weak signal is handled digitally, the resulting quantization introduces not only noise and distortion of the stronger signal (which have been thoroughly studied elsewhere) but also intermodulation between the two. Third-order intermodulation is the principal source of spurious inband signals, and it is important, therefore, to determine its strength in comparison with that of the true weak-signal output, which is of the same order of magnitude. The assumption that the weaker signal's amplitudeais very much smaller than the quantization step size permits a relatively simple analysis by means of two different approaches. Both of them lead to a finite series for the amplitudec_{2}aof the intermodulation. This series is easily evaluated numerically, but simple approximations obtained by truncation of Euler's summation formula show the behavior of c2more clearly as a function of the amplitude of the stronger input and will be found adequate for most applications.     

The spectrum of intermodulation generated in a semiconductor diode junction

In this paper exact formulas are found for the intermodulation generated in a semiconductor diode junction, and a method is developed to make the calculation of the intermodulation practicable. This method generates the intermodulation output spectrum by operating on the signal input spectrum with convolution. This method lends itself to tabular, graphical, or computer solutions, and the results can be easily interpreted. In the past the detailed calculation of intermodulation product amplitudes was a formidable task. With the techniques of this paper it should be possible to make these calculations routine. It will be feasible to determine RFI compatibility of new frequency allocations ahead of time, analyze existing RFI problems, and design receivers to work in severe interference environments. Equations are derived for the total intermodulation at a specific frequency, and for the spectrum of each order of intermodulation due to either CW or quasi-continuous input spectra. Examples are given of cross modulation, intermodulation, distortion, and third-order products.     

Power Division in Spread Spectrum Systems with Limiting

This paper finds power division through a bandpass nonlinearity when the input is two spread spectrum signals plus noise. This model applies to code division multiple access (CDMA) satellites or to multiple transmission of CDMA through a common Earth terminal transmitter. The solution requires finding a single attenuation constant for each input signal including the input noise. This approach provides the first exact power division solutions for spectrally overlapping, possibly coherently generated, spread spectrum signals plus noise through a bandpass limiter. Two examples illustrate the approach. Simultaneous transmission of coherently generated QPSK spread signals through a hard limiter without noise may cause whichever is the smaller of the two to suffer a sharp 6 dB suppression. This suppression is highly phase dependent and can be alleviated by proper phasing of the signals prior to hard limiting. In the second example, input/output SNR relations are found and compared with those given by Jones for two unmodulated sine waves and noise. A significant reduction in output SNR exists for spread signals compared to the two sine wave case examined by Jones.     

Accurate Time-Domain Simulation of Continuous-Time Sigma–Delta Modulators

In this paper, we present a methodology for the simulation of continuous-time (CT) sigma-delta converters. This method, based on a fixed-step algorithm, permits not only a time-domain simulation of the modulator output but also the simulation of intermediary signals. The method is based on the discretization of the CT models and the use of a discrete simulator such as Simulink, which is more efficient than an analog simulator. By using filters with a sampling frequency that is higher than the modulator output frequency, the model can simulate input signals with a bandwidth that is higher than half the modulator sampling frequency. The transformation is exact in terms of noise transfer function and asymptotically exact in terms of signal transfer function (the transfer function from the modulator input to each stage filter output rapidly tends to the CT-model transfer function when the number of steps increases).     

Quantization Error Analysis of Second Order Bandpass Delta-Sigma Modulator with Sinusoidal Inputs

The exact analysis of second order bandpassDelta-Sigma modulator with sinusoidal inputs isperformed. The results indicate that quantization erroris neither uniformly distributed nor white. Thequantization error spectrum is purely discrete andsymmetric with one forth of sampling frequency, and thelocations of these discrete frequency components arestrongly dependent on input amplitudes. Similar resultsare also observed for passband communication signals,such as quadrature amplitude modulation. From theanalysis, crosscorrelation between quantization error andsinusoidal input was shown to exist but can be cancelledout by proper design of the noise shaping function. Crosscorrelation can degrade the performance of thedelta-sigma system. Hence, the exact analysis is anothermethod to enable design for high performance.     

Frequency division multiplexed microwave and baseband digitaloptical fiber link for phased array antennas

A frequency-division multiplexed optical fiber link is described in which microwave (1-8 GHz) and baseband digital (1-10 Mb/s) signals are combined electrically and transmitted through a direct-modulation microwave optical link. The microwave signal does not affect bit error rate (BER) performance of the Manchester-coded baseband digital data link. The baseband digital signal affects microwave signal quality by generating second-order intermodulation noise. The intermodulation noise power density is found to be proportional to both the microwave input power and the digital input power, enabling the system to be modeled as a mixer (AM modulator). The conversion loss for the digital signal is approximately 68 dB for a 1-GHz microwave signal and is highly dependent on the microwave frequency, reaching a minimum value of 41 dB at 4.5 GHz corresponding to the laser diode relaxation oscillation frequency. It is shown that Manchester coding on the digital link places the intermodulation noise peak away from microwave signal, preventing degradation of close-carrier phase noise (<1 kHz offset). A direct trade-off between intermodulation noise and digital link margin is developed to project system performance     

Large signal analysis of optical directional coupler modulators

Expressions are obtained for the output harmonic and intermodulation products of optical electrical coupler modulators driven by multisinusoidal input signals. The special case of relatively small input amplitudes is considered. The results are verified by comparisons with previously published results