A Nonlinear Filter for Independent Gain and Phase (With Applications)

1966 ◽  
Vol 88 (2) ◽  
pp. 457-462 ◽  
Author(s):  
W. C. Foster ◽  
D. L. Gieseking ◽  
W. K. Waymeyer
Keyword(s):  
Signal Amplitude ◽  
Analog Computer ◽  
Paper Analysis ◽  
Nonlinear Filter ◽  
Phase Lag ◽  
Linear Filters ◽  
Stability Margins ◽  
Response Data ◽  
Analytical Work ◽  
Input Signal Amplitude

Compensation of control systems by means of linear filters is a basic and well-known art. However, the limitations of linear compensation are also well known. In particular, the interdependence of the phase and gain characteristics of linear filters is always in conflict with the desires of the control-system designer. For example, it is impossible to introduce attenuation into a system without introducing undesirable phase lag as well. The development of a split-path nonlinear filter (SPAN filter) concept promises to yield a practical device which has independent phase and gain characteristics. These characteristics are independent of input signal amplitude. This filter can, therefore, have desirable characteristics which are unattainable with conventional linear filters. The design of the nonlinear filter to meet a desired gain-phase, describing-function specification is simplified by results given in the paper. Analysis and simulation of three sample problems has shown that a great deal of flexibility is available with this nonlinear filter. It is possible to obtain phase lead and amplitude attenuation by a proper choice of linear filtering in the two channels. Analog-computer simulation has verified the analytical work with respect to stability margins, and provided transient-response data, in the absence of analytical methods.

Mechanical Contact Frequency Response Measurements

2000 ◽  
Vol 122 (4) ◽  
pp. 828-833 ◽  
Author(s):  
S. S. Kupchenko ◽  
D. P. Hess
Keyword(s):  
Frequency Response ◽  
Phase Lag ◽  
Lithium Grease ◽  
Mineral Oils ◽  
Vibration Data ◽  
Response Data ◽  
Lubricated Contacts ◽  
Wide Range ◽  
Contact Frequency ◽  
Dry Conditions

This paper presents friction frequency response measurements taken from a planar steel contact subjected to controlled random broadband normal vibration. Data are included from both dry and various lubricated contact conditions under different vibration input levels and different sliding velocities. Frequency response data for dry contacts are found to have nearly steady magnitude and negligible phase lag over a relatively wide range of frequencies. This suggests a coefficient of friction, independent of frequency but dependent on levels of normal acceleration and sliding velocity, may adequately define the dry contact frequency response. The frequency response data for lubricated contacts are mixed. For example, with MoS2 grease the frequency response may adequately be defined by a constant, as with dry conditions. However, frequency response data for contacts with pure mineral oils, mineral oils with additives, and lithium grease are found to be dependent on frequency. [S0742-4787(11)00101-9]

Study of Dominant Performance Characteristics in Robot Transmissions

1993 ◽  
Vol 115 (3) ◽  
pp. 472-482 ◽  
Author(s):  
H. Schempf ◽  
D. R. Yoerger
Keyword(s):  
Force Control ◽  
Closed Loop ◽  
Stability Margin ◽  
Viscous Friction ◽  
Open Loop ◽  
Phase Lag ◽  
Stability Margins ◽  
Loop Bandwidth ◽  
Hard Contact ◽  
Following Error

Six different transmission types suitable for robotic manipulators were compared in an experimental and theoretical study. Single-degree-of-freedom mechanisms based on the different transmissions were evaluated in terms of force control performance, achievable bandwidth, and stability properties in hard contact tasks. Transmission types considered were (1) cable reducer, (2) harmonic drive, (3) cycloidal disk reducer, (4) cycloidal cam reducer, (5) ball reducer, and (6) planetary/cycloidal gear head. Open loop torque following error, attenuation and phase lag, and closed loop bandwidth and stability margin were found to be severely dominated by levels of inertia, stiffness distribution and variability, stiction, coulomb and viscous friction, and ripple torque. These aspects were quantified and shown to vary widely among all transmissions tested. The degree of nonlinearity inherent in each transmission affected its open and closed loop behavior directly, and limited the effectiveness of controller compensation schemes. Simple transmission models based on carefully measured transmission characteristics are shown to predict stability margins and achievable force-control bandwidths in hard contact to within a 5 to 15 percent error margin.

STOCHASTIC RESONANCE IN NONLINEAR TRANSMISSION OF SPIKE SIGNALS: AN EXACT MODEL AND AN APPLICATION TO THE NEURON

1996 ◽  
Vol 06 (11) ◽  
pp. 2069-2076 ◽  
Author(s):  
FRANÇOIS CHAPEAU-BLONDEAU ◽  
XAVIER GODIVIER
Keyword(s):  
Stochastic Resonance ◽  
Signal Amplitude ◽  
Nonlinear Transmission ◽  
Enhanced Transmission ◽  
Exact Model ◽  
Neural Information ◽  
Neural Information Processing ◽  
Satisfactory Approximation ◽  
Input Signal Amplitude ◽  
Spike Signals

Nonlinear transmission of trains of pulses enhanced by noise addition through stochastic resonance is studied. First, an exact model is presented which describes stochastic resonance in the transmission of a periodic train of pulses by a threshold system in the presence of arbitrarily distributed white noise. Second, a simulation demonstrates a novel possibility of stochastic resonance in the neuron, in the nonlinear transmission of spike trains assisted by noise. Third, it is shown that the exact model can provide a satisfactory approximation of stochastic resonance in the neuron, as the reported effect is mainly sensitive to correlations at a dominant time scale formed by the coherent period, and to the overall input signal amplitude relative to the threshold of the nonlinearity. The present results enlarge the scope of the effect of noise-enhanced transmission of signals through stochastic resonance, and also of the possible mechanisms for neural information processing.

scholarly journals Reliability Analysis of 0.5μm CMOS Operational Amplifiers under TID Effects

2014 ◽  
Vol 9 (1) ◽  
pp. 70-79
Author(s):  
Guilherme S. Cardoso ◽  
Tiago R. Balen ◽  
Marcelo S. Lubaszewski ◽  
Odair L. Gonçalez
Keyword(s):  
Integrated Circuits ◽  
Harmonic Distortion ◽  
Signal Amplitude ◽  
Building Blocks ◽  
Programmable Analog ◽  
Input Signal Amplitude ◽  
Performance Results ◽  
Cmos Operational Amplifiers ◽  
Previous Irradiation ◽  
Accumulated Dose

Analog integrated circuits operating in radiation environments. In previous irradiation experiments performed on a switched-capacitor filter, implemented in a programmable analog array, it was observed a sudden recovery of the device performance during the irradiation, while increasing the accumulated dose. In some cases the considered performance parameters (such as the total harmonic distortion) may even be enhanced if compared to the pre-irradiation measurements, in specific accumulated dose intervals. This behavior is associated to partial inactivity windows in the internal components of the device. Spice simulations considering two complementary architectures of a simple CMOS Operational Amplifier (OpAmp) are performed, aiming to understand the origins of this effect. Results indicate that shifts on the operating point of the amplifier building blocks are responsible for the degradation and recovery of the OpAmp performance. Results also show that specific architectures, as well as, application constraints (such as the external feedback and the input signal amplitude and frequency) may result in different robustness levels related to the linear applications of the OpAmps in radiation environments.

Analysis of structure importance of compensation capacitor in jointless track circuit

2016 ◽  
Vol 231 (3) ◽  
pp. 329-344 ◽  
Author(s):  
Linhai Zhao ◽  
Yi Maggie Guo ◽  
Barbara D Klein
Keyword(s):  
Input Signal ◽  
Signal Amplitude ◽  
Relative Impact ◽  
Maintenance Strategy ◽  
Close Attention ◽  
Work Mechanism ◽  
Main Track ◽  
Input Signal Amplitude ◽  
Track Circuit ◽  
Ballast Resistance

This paper models the input signal amplitude of the main track and the small track of the adjacent jointless track circuit (JTC) when JTC is idle and the track circuit reader(TCR) received signal amplitude when JTC is occupied, based on the work mechanism of JTC and TCR. Based on the models, the relative impact of compensation capacitor on signal amplitude is obtained by simulation. The paper further proposes a calculation method for structure importance of compensation capacitors. Experimental results indicate that the rankings of structure importance are not affected by ballast resistance of JTC in this method. The results also show that the compensation capacitors closer to the receiving end are more important than those closer to the sending end. In addition, C2, C6, and C3 closer to receiving end are the most important and should be paid close attention during maintenance. The second, the first and the fifth capacitor from the sending end, have less impact on the JTC and TCR signal. This paper is helpful to determine the maintenance priority of each capacitor, optimize the maintenance strategy, and make better use of JTC.

On the Dynamics of Steam Liquid Heat Exchangers

1961 ◽  
Vol 83 (2) ◽  
pp. 244-251 ◽  
Author(s):  
Arvid Hempel
Keyword(s):  
Frequency Response ◽  
Heat Exchangers ◽  
Transfer Functions ◽  
Liquid Velocity ◽  
Amplitude Ratio ◽  
Analog Computer ◽  
Phase Lag ◽  
Liquid Temperature ◽  
Response Measurement ◽  
Liquid Heat

The aim of the present work has been to present relatively simple transfer functions for steam/liquid heat exchangers, relating outlet liquid temperature to variations in, respectively, the steam temperature, the liquid velocity, and the inlet liquid temperature. The transfer functions are first obtained from the partial differential equations of the system and then simplified. From the simplified expressions the transient response can readily be obtained and, in addition, they are of a form easily simulated on an analog computer. Experimental frequency response data are provided. An analog computer proved useful in analyzing phase lag and amplitude ratio in the frequency response measurement.

Non-analytic at the origin, behavioral models for active or passive non-linearity

2013 ◽  
Vol 5 (2) ◽  
pp. 133-140 ◽  
Author(s):  
Jacques Sombrin
Keyword(s):  
Input Signal ◽  
Theoretical Foundation ◽  
Signal Amplitude ◽  
Behavioral Models ◽  
Hyperbolic Tangent ◽  
Harmonic Response ◽  
Linear Behavior ◽  
Non Linear ◽  
Series Development ◽  
Input Signal Amplitude

Most non-linear behavioral models of amplifiers are based on functions that are analytic at the origin and thus can be replaced by their Taylor series development around this point, e.g. polynomials of the input signal. Chebyshev Transforms can be used to compute the harmonic response of the model to a sine input signal. These responses are polynomials of the input signal amplitude. A second application of the Chebyshev transform to the first harmonic response or radio frequency (RF) characteristic will lend the carriers and intermodulation (IM) products for a two-carrier input signal, again polynomials. An important class of non-analytic non-linear behavior encountered in practice, such as hard limiters and detectors are either empirically treated or only approximated by an analytic function such as the hyperbolic tangent. This work proposes to generalize the polynomial non-linearity theory by adding non-analytic at the origin functions that, like polynomials, are invariant elements of the Chebyshev Transform. Devices modeled with these non-analytic at the origin functions exhibit intermodulation behavior significantly different from that of classical polynomial models, giving theoretical foundation to a number of important unexplained practical measurement observations.

scholarly journals Understanding the Input Signal Frequency Effects on the Resistive Window of Memristors

2020 ◽  
Author(s):  
Marcos Maestro Izquierdo ◽  
Mireia B. Gonzalez ◽  
Francesca campabadal ◽  
Enrique Miranda ◽  
Jordi Suñé
Keyword(s):  
Input Signal ◽  
Signal Amplitude ◽  
Electrical Stimulus ◽  
Balance Model ◽  
Signal Frequency ◽  
Electrical Behavior ◽  
Memory State ◽  
Input Signal Frequency ◽  
Input Signal Amplitude ◽  
The Difference

As theoretically predicted by Prof. Chua, the input signal frequency has a major impact on the electrical behavior of memristors. According with one of the so-called fingerprints of such devices, the resistive window, <i>i.e.</i> the difference between the low and high resistance states, shrinks as the frequency increases for a given input signal amplitude. Physically, this effect stems from the incapability of ions/vacancies to follow the external electrical stimulus. In terms of the electrical behavior, the collapse of the resistive window can be ascribed to the shift of the set/reset voltages toward higher values. Moreover, for a given frequency, the resistance window increases with the signal amplitude. In this letter, we show that both phenomena are the two sides of the same coin and that can be consistently explained after considering the snapback effect and a balance model equation for the device memory state.

A frequency and time domain study of the horizontal and vertical vestibuloocular reflex in the pigeon

1988 ◽  
Vol 59 (4) ◽  
pp. 1143-1161 ◽  
Author(s):  
T. J. Anastasio ◽  
M. J. Correia
Keyword(s):  
Time Delay ◽  
Frequency Response ◽  
Time Constant ◽  
Mean Value ◽  
Step Response ◽  
Phase Lag ◽  
Vestibuloocular Reflex ◽  
Stimulus Magnitude ◽  
Response Data ◽  
The Mean

1. The horizontal and vertical vestibuloocular reflex (HVOR and VVOR, respectively) was studied in four chronically instrumented pigeons. Eye movements were measured using the magnetic search-coil technique and were produced by rotation in the dark. During the rotation paradigms, the pigeons were either pharmacologically aroused (using amphetamine) or drug free (normal). The pigeon HVOR and VVOR were tested using step and sinusoidal rotational stimulation. The range of frequencies (0.03-6.0 Hz) and the magnitude of the sinusoidal stimuli were chosen to match those used in a previous study of the responses of semicircular canal primary afferents (SCPAs) in unanesthetized (i.e., normal) pigeons. 2. The gain of the HVOR and VVOR in both normal and aroused pigeons was independent of stimulus magnitude (6-30 degrees/s) over the frequency range tested. In aroused pigeons, the frequency independent gain (G) of the HVOR (G = 0.6) and VVOR (G = 0.9) was roughly twice that for normal pigeons. Pigeon VOR phase under all combinations of orientation and arousal level was independent of stimulus magnitude except at the lowest frequency tested (0.03 Hz). At this frequency, phase lead decreased as stimulus magnitude increased for the HVOR and VVOR in both normal and aroused pigeons. 3. The step and sinusoidal gains were greater for the VVOR than for the HVOR under the same level of arousal. Neither the gain nor the dominant time constant of the VOR (tau vor) differed for rotation direction (clockwise or counterclockwise) for the HVOR or VVOR in normal or aroused pigeons. 4. The mean value of tau vor was 4.0 +/- 0.5 (SE) s as estimated from frequency response data and 4.3 +/- 0.4 s as estimated from step response data for the HVOR and VVOR in both normal and aroused pigeons. In comparison, the mean value of the dominant or cupular time constant (tau c) of normal pigeon SCPAs was approximately 10 s as estimated from frequency response data. These results indicate that tau vor is shorter than tau c in the pigeon. 5. At higher frequencies, the pigeon HVOR and VVOR exhibit an increasing phase lag unaccompanied by a gain change--characteristics produced by a pure time delay. The value of this time delay was about 7 ms for both the HVOR and VVOR in both normal and aroused pigeons. The HVOR and VVOR in normal and aroused pigeons lacked the higher frequency lead characteristics present in the frequency responses of most pigeon SCPAs.

scholarly journals Understanding the Input Signal Frequency Effects on the Resistive Window of Memristors

2020 ◽  
Author(s):  
Marcos Maestro Izquierdo ◽  
Mireia B. Gonzalez ◽  
Francesca campabadal ◽  
Enrique Miranda ◽  
Jordi Suñé
Keyword(s):  
Input Signal ◽  
Signal Amplitude ◽  
Electrical Stimulus ◽  
Balance Model ◽  
Signal Frequency ◽  
Electrical Behavior ◽  
Memory State ◽  
Input Signal Frequency ◽  
Input Signal Amplitude ◽  
The Difference

As theoretically predicted by Prof. Chua, the input signal frequency has a major impact on the electrical behavior of memristors. According with one of the so-called fingerprints of such devices, the resistive window, <i>i.e.</i> the difference between the low and high resistance states, shrinks as the frequency increases for a given input signal amplitude. Physically, this effect stems from the incapability of ions/vacancies to follow the external electrical stimulus. In terms of the electrical behavior, the collapse of the resistive window can be ascribed to the shift of the set/reset voltages toward higher values. Moreover, for a given frequency, the resistance window increases with the signal amplitude. In this letter, we show that both phenomena are the two sides of the same coin and that can be consistently explained after considering the snapback effect and a balance model equation for the device memory state.

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