Output Power Spectral Density Research Articles

A low-cost technique for broadband gain and noise figure characterization of optical amplifiers using a broadband source and a filter

We report a unique low-cost technique for broadband gain and noise figure characterization of erbium-doped fiber amplifiers using an amplified-spontaneous-emission source and a wavelength filter with multiple steep slopes. Gain and noise figure of the amplifier can be obtained by extracting the slope and intercept of output versus input power spectral density at filter slopes. Based on this technique, we present two methods of gain and noise figure measurements: one by using a fixed filter with multiple steep slopes at the measured wavelengths, and the other using a tunable filter with one or more steep slopes. The required filter depth is about 35 dB. The results obtained over a 20 dB total input power range using both methods are in good agreement with those obtained using conventional spectral-interpolation technique employing multiple DFB lasers at 100 GHz spacing. The discrepancy is within ±0.3 dB in the C-band. This technique can also be used to characterize other types of broadband optical amplifiers, as its accuracy is in principle not affected by the response time of the amplifying medium.

Spectral Analysis of Polynomial Nonlinearity with Applications to RF Power Amplifiers

The majority of the nonlinearity in a communication system is attributed to the power amplifier (PA) present at the final stage of the transmitter chain. In this paper, we consider Gaussian distributed input signals (such as OFDM), and PAs that can be modeled by memoryless or memory polynomials. We derive closed-form expressions of the PA output power spectral density, for an arbitrary nonlinear order, based on the so-called Leonov-Shiryaev formula. We then apply these results to answer practical questions such as the contribution of AM/PM conversion to spectral regrowth and the relationship between memory effects and spectral asymmetry.

Measuring Gain and Noise Figure of Erbium-Doped Fiber Amplifiers Using a Broad-Band Source and a Transmission Filter

We report a unique low-cost technique for measuring gain and noise figure (NF) in erbium-doped fiber amplifiers using a broad-band amplified spontaneous emission source and a transmission filter, by extracting the slope and intercept of output power spectral density versus input power spectral density at filter edges. The required filter depth is 30 dB. Discrepancies of /spl les/0.3 dB are found between gain or NF obtained from this technique and those measured using conventional spectral-interpolation technique employing multiple lasers at 100-GHz spacing across the C-band.

Power Spectral Analysis of Networked Control Systems With Data Dropouts

This note derives a closed-form expression for a control system's output power spectral density (PSD) as a function of the data dropout probability. We use the PSD to determine a dropout compensator that minimizes the regulator's output power. We show, by example, that the optimal dropout compensator does not always correspond to a filter that minimizes the mean square error between the predicted and dropped feedback measurement.

Broadband radiation sources based on quantum-well superluminescent diodes emitting at 1550 nm

The emission spectra of superluminescent diodes (SLDs) based on a multilayer quantum-well (InGa)PAs heterostructure are studied in the wavelength range from 1450 to 1650 nm. The FWHM of these spectra exceeds 120 nm in certain operating regimes. The experimental samples of light-emitting modules with output single-mode fibres are fabricated based on the SLDs studied, which produce the output power spectral density above -45 dBm nm-1 within the band over 200 nm. The spectrum of such an emitter covers the main bands (S, C, and L) of WDM telecommunication systems. The possibilities of a further broadening and flattening of the emission band of these SLDs are considered.

Predicting spectral regrowth of nonlinear power amplifiers

Power amplifiers (PAs) are important elements in communications systems and they are inherently nonlinear. Nonlinearity generates spectral regrowth (i.e., spectral broadening) in digitally modulated signals which causes adjacent channel interference. In this paper, we present a closed-form expression for the auto-covariance function of the PA output, whose Fourier transform yields the output power spectral density (PSD). The PA input does not need to be Gaussian and the PSD calculation can be carried out using common PA descriptions such as the AM/AM and AM/PM characteristics. We assume that the input is narrow-band, thus PA memory effects, on the order of a symbol period, are not present. The analytical results allow us to predict spectral regrowth without running expensive or time-consuming time-domain simulations; they also lead to a variety of optimization possibilities in transmitter design that includes the PAs.

A BiCMOS Wideband Amplifier for the Extraction of Base Spreading Resistance with Noise Measurement Techniques

This paper presents a BiCMOS wide band amplifier optimized for maximum sensitivity to noise introduced in the base spreading resistance. It was used to characterize the base spreading resistance of bipolar devices found in Orbit’s low-noise, n-well BiCMOS process available through MOSIS. The base spreading resistance is extracted by measuring the output power spectral density of the aforementioned amplifier and isolating the amount caused by thermal noise in the base. The results give insight as to what noise sources are significant in this technology.

Higher order stochastic resonance in a level-crossing detector

We investigate stochastic resonance in a simple level-crossing detector at the base frequency, as well as the higher harmonics, of a periodic stimulus. Using quadratic approximations, we observe a stochastic resonance phenomenon with two maxima (in the presence of white Gaussian background noise) in the first harmonic at the output power spectral density of the system. That means that there is an optimal strength of the input noise, where the signal transfer is the most linear, as the first harmonic is concerned. This unique feature of this system cannot be found at the fundamental harmonic in the output. The theoretical results are confirmed by numerical simulations. This system is a good candidate for use in simple models of neurons, and other (nonlinear) signal detection systems.

Noise analysis of a class of oscillators

This paper presents noise analysis of a class of oscillators, which can be modeled by a positive feedback system with a frequency-selective Mth-order filter, an ideal comparator, and a white noise source. An explicit analytical expression for the output power spectral density is derived. A simplified expression is obtained for a special case when the Mth-order filter is replaced by a second-order bandpass filter. The general expression is shown to reduce to a well-known result if a high and-factor filter is further assumed. Theoretical results presented here are verified by experiment.

Higher-order resonant behavior in asymmetric nonlinear stochastic systems

We study periodically modulated bistable dynamic elements subject to Gaussian noise and a symmetrybreaking dc signal. The skewing of the bistable potential function by the dc signal leads to the appearance of even multiples of the drive frequency in the output power spectral density. The spectral amplitudes of all the harmonics are found to exhibit maxima as functions of the noise statistics and the dc signal; the maxima can be shown to depend on matchings of characteristic deterministic and stochastic time scales. A phenomenological description based on a generic bistable system is followed by actual perturbation calculations of the first two spectral amplitudes for a real system, a Josephson junction shorted by a superconducting loop ~the mainstay of the rf superconducting quantum interference device!. This behavior underlies a recently proposed ‘‘frequency-shifting’’ technique for circumventing detector noise limitations which would otherwise constrain the detection of very low-amplitude signals. @S1063-651X~97!05604-3#

State estimation of road surface and vehi cle system using a Kalman filter.

In this paper, an approach to estimating the state variables of a vehicle system and the absolute displacement of a road surface is presented. The Kalman filter theory is applied to an augmented system which consists of the vehicle system and the shaping filter. The shaping filter is taken so that the power spectral density of output is equal to that of the displacement of the road surface, while white noise is taken as input. The Pade approximation is used in the augmented system to take account of the time delay between the input values of the front and rear wheels. The results obtained using the Pade approximation are compared with the results obtained by assuming that the inputs of the four wheels are independen of each other. A method for identifying the shaping filter in the augmented system, which may be effective in constructing the augmented system adaptively in actual driving case, is also presented. Some simulation models are examined to validate the presented methods.

State estimation of a road surface and vehicle system using a Kalman filter.

In this paper, an approach to estimating the state variables of a vehicle system and the absolute displacement of a road surface is presented. The Kalman filter theory is applied to an augmented system which consists of the vehicle system and the shaping filter. The shaping filter is taken so that the power spectral density of output is equal to that of the displacement of the road surface, while the white noise is taken as input. The Pade approximation is used in the augmented system to take account of the time delay between the input values of the front and rear wheels. The results obtained by using the Pade approximation are compared with the results obtained when assuming that the inputs of the four wheels are independent each other. A method for identifying the shaping filter in the augmented system, which may be effective to constructing the augmented system adaptively in an actual driving case, is also presented. some simulation models are examined to validate the presented methods.

Spectral performance characterizations of some generalized median filters

Output correlations and power spectral densities are obtained for two types of generalized median filters: the L- and M-filters, for a sequence of independent, identically distributed inputs and also for a simple first-order Markov input sequence. The results show the ability of generalized median filters to flexibly achieve performance compromises between edge preservation and impulsive noise rejection, and Gaussian noise suppression.

Influence of Some Excitations on Rotary Motion Perturbations of Electric Locomotive Drive System

SUMMARY The influence of some excitations acting on the drive system (i.e. vertical and lateral track roughness, motor torque changes, random changes of the coefficient of friction and internal parametrical excitations caused by the kinematic properties of the tension couplings) on the rotary motion perturbations have been studied in the paper. On the basis of the physical model of the drive system, a mathematical model has been determined. The method of determining the output power spectral density function has been described and the results obtained have been discussed.

The Gaussian Nonlinearity's Output Power Spectral Density Due to a Sinusoid Plus Band-Limited Noise

A sinusoid accompanied by stationary, additive, nonzero-mean, band-limited, white Gaussian noise is passed through a Gaussian nonlinear characteristic, and the output power spectral density is evaluated by using known results due to Rice and Atherton. Several characteristics of the Gaussian nonlinearity are revealed in the process, and input tuning is shown to contribute to output noise reduction. The results are applicable in the analysis of tracking systems employing sinusoidal dithers.

Resolution bias errors in spectral density, frequency response and coherence function measurements, III: Application to second-order systems (white noise excitation)

A general theory of spectral estimation given in a previous paper is applied to second-order systems such as a simple spring-mass system where either the displacement, velocity or acceleration of the vibrating mass may be considered as the output signals. By means of approximate formulas, an extensive bias error discussion of frequency response, output power spectral density and coherence estimates is given, which clarifies characteristic differences between spectral estimators obtained with the rectangular window on the one hand and the Hanning window (or another continuous window) on the other hand. In particular, characteristic coherence notches in the measurement of resonance systems, as reported in the literature, are explained from first principles. All of the theoretical predictions are verified experimentally to great accuracy by using electrical LRC-resonance circuits which are equivalent to the respective mechanical systems.

Performance of Baseband Digital Data Transmission in Nonlinear Channels with Memory

This paper considers the performance of digital data transmission in nonlinear channels with memory. The analysis is based on the application of a particular form of Volterra series representation for the nonlinear system describing the transmission channel. First, expressions are derived for the output mean and power spectral density under certain conditions. Next, the paper presents a computationally convenient expression for the error rate involved in such transmission.

Optimisation and synthesis of low phase-noise microwave-feedback oscillators

A procedure is presented for the improved design of low phase-noise microwave-feedback oscillators. The measured circuit parameters of the individual circuit elements are used in a nonlinear model which, in conjunction with a parametric computer-aided-design technique, allows one to predict the operating point of the circuit, namely the oscillation frequency and output power level. From this, together with the amplifier noise figure and Q-factor of the feedback element, the phase-noise spectral density of the oscillator output signal is derived. Theoretical and experimental results are compared and found to be in good agreement. The computer-aided design technique is also used to study the effects of various S-parameter variations upon the output power and phase spectral density. From perturbation studies it is shown how optimum sets of S-parameters can be derived to obtain either maximum output power or minimum phase noise, as desired. A correcting network for a first amplification stage is synthesised and the reduction of phase noise is experimentally verified.

Lifting Surface Approach . . to the Estimation of Gust Response of Finite Wings

Unsteady response of finite wings flying though turbulence is investigated using linearized lifting surface theory. The NLR method, extended to the unsteady case, is employed for the numerical calculation of the lift force arising from oscillatory gusts for a wide range of frequencies. An efficient numerical procedure is presented for the estimation of the response to random turbulence. It takes into consideration the instantaneous variation of the vertical velocity of turbulence along the span as well as the spanwise distribution of the aerodynamic influence function. This procedure uses the relation between the output power spectral density and the spanwise cross-spectrum of turbulence, defined in terms of the spanwise correlated frequency response function, which in turn is derived from the aerodynamic transfer matrix for the modified upwash field. The results computed by means of this method with a model of turbulence uniform in span, and with a model of isotropic turbulence, exhibit considerable differences.

Addendum to "Volterra Systems with Random Inputs: A Formalized Approach"

A newly derived expression for the higher order crosscorrelation function of two jointly stationary Gaussian random processes is used to determine the output autocorrelation function of a Volterra system driven by a Gaussian input and to simplify a previously published expression for the output power spectral density and its derivation.