Showing papers on "Frequency response published in 1972"

Synthesis of feedback systems with large plant ignorance for prescribed time-domain tolerances†

Abstract: There is given a minimum-phase plant transfer function, with prescribed bounds on its parameter values The plant is imbedded in a two-degree-of freedom feedback system, which is to be designed such that the system time response to a deterministic input lies within specified boundaries Subject to the above, the design should be such as to minimize the effect of sensor noise at the input to the plant This report presents a design procedure for this purpose, based on frequency response concepts The time-domain tolerances are translated into equivalent frequency response tolerances The latter lead to bounds on the loop transmission function in the form of continuous curves on the Nichols chart The properties of the loop transmission function which satisfy these bounds with minimum effect of sensor noise, are derived

A program for the design of linear phase finite impulse response digital filters

Abstract: This paper presents an algorithm that can be used to design finite impulse response (FIR) digital filters with linear phase. The presentation is in the form of a block diagram together with the Fortran IV listing of the program.

The estimation of the frequency response function of a mechanoreceptor

Abstract: Widespread use has been made of linear systems theory to describe the input-output relations of receptors. The frequency response function of an insect mechanoreceptor, the tactile spine of the cockroach, has been estimated by using deterministic inputs (sines and step functions), deterministic inputs added to a stochastic, auxiliary signal (band-limited white noise), and a stochastic input alone. When a stochastic input is used, spectral analysis provides methods for estimating the coherence function as well as the frequency response function. The coherence function of the tactile spine is low, suggesting that the linear frequency response function is not a good characterization of the input-output relation of the receptor. Two non-linearities, rectification and phase-locking are described. Rectification can reduce the absolute value of the frequency response measured using sine waves of all frequencies without changing its form. Phase-locking changes the form of the frequency response function at high frequencies. Use of a stochastic auxiliary signal linearizes the input-output relations of the receptor in the sense that the cycle histograms obtained with sinusoidal inputs are more sinusoidal and the form of the frequency response function agrees with that predicted from the step response over a wider range of frequencies.

High‐Frequency Response of Josephson Point Contacts

Abstract: For a current‐driven Josephson junction shunted by an Ohmic resistance, the dc voltage response and impedance to external high‐frequency currents is calculated with a second‐order perturbation method based on the unperturbed solution for the time evolution of the voltage as given by Aslamazov and Larkin. The response is proportional to signal power and has three characteristic‐frequency regions depending on whether the internal self‐generated Josephson frequency, ω0, is larger than, equal to, or smaller than the signal frequency, ω. For ω0 ω the response could be expressed by easily observable parameters of the dc voltage‐current characteristics. This permits comparison of the predictions with experimental results obtained on point‐contact junctions whose dc characteristics were only approximately represented by the simple model chosen for analysis. For ω0≪ω the response is found to be proportional to (i) the slope of the dc characteristic, (ii) the inverse square of the applied frequency, (iii) the inverse battery current in terms of the critical current, and (iv) the voltage amplitude of the inherent Josephson oscillations. For ω0≫ω ``classical'' detection proportional to curvature is obtained. For ω0∼ω resonance detection occurs, which depends to a considerable degree on fluctuations of the average contact voltage. These predictions are in reasonable agreement with experiments in which point‐contact junctions were illuminated with klystron radiation at 10 and 90 GHz. Evidence is presented that the voltage fluctuations limiting the resonance response are the result of noise generated in the junction. Comparison of the noise‐equivalent power expected from the simple model with measured results suggests that parasitic elements, such as shunt capacity, are not negligible at 90 GHz.

Voltage dependence of bilayer membrane capacitance

Abstract: The change in capacitance of cholesterol-hexadecyltrimethylammonium bilayer membranes upon application of relatively high dc and ac potentials was measured as a function of frequency. Capacitance increases proportional to the square of voltage were observed (0.5–1% for 100 mV dc). The amplitude of the ac component of the capacitance variation decreased with frequency until a break frequency was reached, above which the capacitance response was constant at a value about two orders of magnitude lower than the dc response. By comparison with the elastic response of the membrane and border, it was concluded the capacitance response at higher frequency was due to bilayer thickness decrease with voltage (electrostriction) while the lower frequency response was associated with a bilayer area increase. Agreement was obtained between the measured electrostriction and that calculated from membrane elasticity. Area increases with voltage calculated assuming border shrinkage as a result of an increase in contact angle were in order of magnitude agreement with the observed dc response. The effects of lenses and bowed membranes are discussed.

The frequency response of frog muscle spindles under various conditions.

Abstract: 1. Nerve impulses were recorded from afferents from non-contracting spindles from the isolated extensor longus dig. IV muscle of the frog during small sinusoidal changes in muscle length at frequencies from 0·001 to 100 Hz. A computer of average transients was used to average the spike distribution during a number of cycles, and hence to determine the spindle response in impulses/sec at different phases of the cycle. 2. At any one frequency the response could be described by a sinusoid, whose amplitude was approximately proportional to the amplitude of the stretch and whose phase was approximately constant, together with a non-linearity dependent principally upon non-linearities in the static response. 3. The frequency response was estimated from the sinusoid responses. In conventional terms, it consisted of a straight line of positive slope below 2 Hz and a maximum between 7 and 16 Hz. 4. The slope of the frequency response was dependent on the mean length of the preparation, typically varying from zero to about 0·5 (3 db/octave) over the physiological range of the passive muscle. The shape of the peak appeared to depend on the mean firing frequency. 5. The responses to ramp stretches of one second duration and up to 2 mm in amplitude were also measured. Responses predicted from the sinusoid measurements were the same shape as the measured responses, but were larger by a factor of about 1·4. 6. The shapes of both the frequency responses and the responses to ramps were hardly affected by an operation that removed most of the polar parts of the spindles. 7. The results are discussed in terms of internal spindle mechanisms.

Stability Conditions Derived from Spectral Theory: Discrete Systems with Periodic Feedback

Abstract: By use of the spectral theory of linear operators, necessary and sufficient conditions are derived for the stability of a class of discrete time feedback systems with a periodically time-varying feedback gain. These conditions involve a Nyquist plot for an equivalent time-invariant system which may be determined from the frequency response function of the system under consideration. In the special case of a scalar-input scalar-output system, these conditions may be given in a particularly simple form.

Generator Models Established by Frequency Response Tests on a 555 MVA Machine

Abstract: An accurate model of a turbogenerator is required for excitation and transient stability studies. Frequency response tests have been made on a 555 MVA unit to determine direct and quadrature axis transfer functions under operating conditions. Digital and analog computations were performed on line in the course of system tests. The performance of the model derived from the test results compares satisfactorily with the behaviour observed in service.

Sound reproducing system utilizing motional feedback

Abstract: A sound reproducing system utilizes motional feedback to reduce loudspeaker distortion and to extend the loudspeaker''s frequency response. The system substantially comprises an amplifier which is jointly responsive to the input source signal and to a feedback signal, a moving-coil loudspeaker including a main electromagnetic structure which is responsive to the amplifier''s output signal for effecting axial speaker-cone motion, motional sensing means for providing a signal which is functionally related to axial cone velocity, and an equalizer exhibiting a predetermined nonlinear attenuation versus frequency characteristic and which is responsive to the motional signal for providing the feedback signal. The feedback signal is degeneratively applied to the amplifier which, in turn, forces the loudspeaker to respond linearly to the input source signal and thereby provide a uniform sound energy output. It is a feature of the present invention that the loudspeaker cone exhibits a substantially constant acceleration at low frequencies and a substantially constant velocity at higher frequencies.

Direct measurement of the (baseband) frequency response of multimode fibers.

Abstract: Incoherent light, transmitted via multimode fibers, represents a potential carrier for information that is directly modulated on the light envelope. The amplitude and phase characteristics of the envelope (baseband) signal are affected by the fiber waveguide because of group delay differences among the modes. We report on a technique that determines the baseband frequency response of the fiber system by comparing the beat spectra of light from a free-running laser before and after transmission through the fiber. As an example, we describe the measurement of 30 m of cladded multimode fiber. The 3-dB bandwidth was 700 MHz, somewhat larger than predicted on the basis of the computed group velocity differences.

Frequency response modifier for fixed-tuned IF amplifiers

Abstract: This disclosure depicts methods and apparatus for effectively varying the frequency response of a television IF amplifier whose selectivity is determined by non-variable tuning elements such as SWIFs (surface wave integratable filters). Specifically, a variable bandwidth means, capable of exhibiting either a narrowband or wide-band frequency response, is coupled to the output of the fixed-tuned IF amplifier. This variable bandwidth means is responsive to a control voltage for selecting one of the frequency response characteristics to be cascaded with the fixed response of the IF amplifier. The selection of the wide-band response allows the overall frequency response characteristic to remain essentially that of the fixed-tuned IF amplifier itself; the selection of the narrow-band response causes the overall frequency response characteristic to be changed to an extent dependent on the selectivity of the narrow-band response.

Structural Response to Segmented Nonstationary Random Excitation

Abstract: This paper presents a procedure for calculating the mean square response of a single-degree-of-freedom linear structural system to a particular type of nonstationary random forcing function. The forcing function, herein referred to as segmented nonstationary, is a stochastic process generated by adding a series of covariance stationary zeromean random forcing functions which are each shaped by deterministic functions of time that do not overlap in the time domain. The system's mean square response is formulated in terms of the segments' time-dependent frequency response functions and the forcing functions' stationary spectral density functions. The results are specialized to consider the response to forcing functions time-modulated by rectangular pulses. Nomenclature er(t) = deterministic modulating function of rth segment fr(t) = covariance stationary forcing function of rth segment H(a)) = system frequency response function relating displacement response and excitation Ir(t, a>) = time-dependent frequency response function m = mass q(t) = oscillator displacement Q(t] = input excitation Rfrfa(tltt2) = cross-correlation function relating fr(t-^ and fs(t2) Sfrfs((o) = cross-spectral density function between forcing function /r(r)and/s(t) co0 = system undamped natural frequency C =

Some New Configurations for Active Filters

Abstract: Some new active-filter configurations based on the pole-zero cancellation technique are introduced. First, for the range Q \leq 50 a singleamplifier circuit is suggested. For higher selectivity (50 a twoamplifier circuit is proposed. Another easily cascadable two-amplifier circuit with a reduced number of capacitors is discussed. In the latter case the filter function is determined by certain resistive ratios. All the configurations proposed-employ integrated circuit operational amplifiers (OAs). The sensitivity problem is discussed in detail. Effects of the finite OA frequency response are also investigated.

Stable electron density fluctuations in a plasma in the presence of a high‐frequency electric field

Abstract: The recent series of ionospheric heating experiments conducted by NOAA in Boulder and by Rice University at the Arecibo Observatory have shown that a powerful high-frequency transmitter can excite parametric plasma instabilities in the ionosphere. In this paper a theory is developed to describe the changes in the fluctuation spectrum that take place for excitation levels below those required for the instabilities to develop. These stable changes, which can be predicted in detail from theory, might prove valuable as a diagnostic tool if they can be studied by incoherent scatter techniques. It is shown that the raised shoulders in the normal incoherent scatter spectrum can be strongly enhanced when the HF pump frequency is slightly above the plasma frequency. For sufficiently high pump power, these shoulders are transformed into lines upshifted and downshifted from the center frequency by an amount corresponding to the ion acoustic velocity, and they approach infinity at a critical HF field strength. When the pump frequency lies at the frequency for longitudinal electron plasma oscillations, a single maximum occurs in the spectrum centered on zero frequency offset. This maximum also approaches infinity for a critical pump field slightly higher than in the former case. A similar situation exists in the vicinity of a frequency offset either upward or downward from zero frequency by the pump frequency when the latter is near the plasma frequency. The ion acoustic features have counterparts in two spikes centered on the pump frequency but with the stronger spectral feature always on the zero frequency side of the pump. The zero frequency line in the ion acoustic spectrum has a counterpart at the pump frequency. The variation of the spectral shape with various parameters is illustrated by sets of curves in which one parameter is varied at a time. The height regions over which the stable distortions in the spectrum will occur in the ionosphere will normally be so thin that observation of the phenomenon by incoherent scatter techniques may be at best difficult. For a pump frequency near the maximum plasma frequency of the F layer, however, observation of the spectral distortion might be possible.

Analysis of Closed-Loop Conveyor Systems

Abstract: A closed-loop conveyor system having a single loading station, a single unloading station, and operating with time-varying input and output flow rates, is analyzed. The balance of flow on the conveyor is represented by a difference equation. Solutions of that difference equation appear naturally in terms of a Fourier series expansion. An important description of the system is its frequency response. Singularities in the frequency response represent cases of incompatibility. Incompatibility is shown to depend on the ratio T/P of conveyor period to work-cycle period, and on the presence of harmonics in input and output flow rates. Solutions for several specific cases are presented graphically.

A Simple Fourier Analysis Technique for Measuring the Dynamic Response of Manual Control Systems

Abstract: From a practical standpoint most dynamic response analysis techniques are complicated, expensive, and time consuming to mechanize and operate. These techniques usually require digital or special-purpose analog equipment, and the computations are often performed sometime after data are collected. Adaptive paramater tracking techniques partially overcome these faults: but they either have prescribed forms, which is an undesirable restriction for basic research, or in the case of free-form methods the computational requirements become excessive. To overcome these drawbacks, an on-line Fourier analysis technique has been developed which deals only with the input and error signals in a manual feedback control system. Several sine waves are used for the input, and the on-line data measurement includes the error variance and a simple means for obtaining the sine and cosine transforms of the error signal at each of the input frequencies. From this relatively small amount of data, we show simple ways to compute the open- and closed-loop dynamic response at input frequencies and the relative amount of linearly correlated power in the error signal. This paper describes the rationale and theory for the technique and discusses two methods for mechanizing it; one involving standard analog computer components and one based on conventional electromechanical components. Finally, a typical application of this method is presented.

Describing function properties of a magnetic pulse-width modulator

Abstract: An analysis is presented for the transfer functions of a particular pulse-width modulator and power switch subsystem that has been widely used in practical switching-mode d-c regulator systems. The switch and filter are in a "buck" configuration, and the switch is driven by a constant- frequency variable duty-ratio push-pull magnetic modulator employing square-loop cores. The two transfer functions considered are that with modulator control signal as input and that with line voltage as input. For a-c signals, the corresponding describing functions (DF) are derived. It is shown that current-source drive to the modulator extends the control DF frequency response over that with voltage drive, and that complete cancellation of the effects of line variations can be obtained at d-c but not for a-c. Experimental confirmation of the analytical results for the control DF are presented.

Broad-Band Coupling to High-Q Resonant Loads

Abstract: Broad-band coupling between a resistive source and a resonant load is considered for coupling networks consisting of a uniform transmission line of impedance Z/sub I/ and length equal to a quarter wavelength at the load resonant frequency. An approximate analysis is used to show that either maximally flat or ripple insertion loss frequency response can be obtained by proper choice of Z/sub I/, and the 3-dB bandwidth obtained in either case is always greater than 1/Q. Depending on the ratio of load and source resistances, the bandwidth may be greater than 1 octave. Network design curves for maximally flat operation with a variety of load parameters are computed without approximation. The design of lumped element approximations for the transmission line network is also described.

Design and High‐Frequency Response of Resistive SQUID Frequency Converters

Abstract: Several resistive SQUID frequency converters (R‐SQUID) have been constructed and their properties studied in the frequency regimes 26.5–40 and 67–73 GHz. A brief outline of the theory of the device is presented together with constructional details for a Nb–Nb point‐contact version. The device response is complicated by the effects on the ac Josephson current of distributed circuit elements, and a broad range of complex behavior is presented which is only partially understood. A useful amplification effect for the detected signal has been discovered, which gives the device good broad range sensitivity (∼ 10−7–∼ 10−12 W/Hz1/2) and reasonably narrow linewidths (Q‐values of ∼ 104 at 70 GHz).

Interactive minimax design of linear-phase nonrecursive digital filters subject to upper and lower function constraints

Abstract: The general Remes exchange algorithm and its implementation are discussed briefly An analog of the exchange algorithm is applied to the problem in which upper and lower constraints are imposed on the frequency response of a nonrecursive digital filter with linear phase. A typical design example is presented with rather tight constraints in the passband

Dynamic Analysis of Cable Systems

Abstract: The method incorporates a discrete parameter representation of cables and utilizes the Method of Imaginary Reactions to evaluate statical behavior and to determine the force-displacement characteristics of the system. The procedures presented make it possible to first evaluate statical system behavior and then to determine either its characteristic or force-motion response to a prescribed loading. Dynamic analysis can be carried out under any condition of loading or system deformation. As the basis of the dynamic method lies in the approach taken to statically analyze and compute the force-deformation characteristics of the structure, any system amenable to static analysis can be subject to dynamic analysis as well. By means of a linear transformation from the physical to a complex coordinate system, the method can accomodate the evaluation of force motion under linearly damped situations. The necessary fundamentals of the method are presented along with an illustrative example explaining its usage.

Small-signal characteristics of lateral transistors

Abstract: This paper considers the small-signal characteristics of lateral transistors made on epitaxial layers of finite thickness, as is the case in most monolithic integrated circuits. For tractability and ease of comprehension, one-dimensional approximations are made, but these are usually adequate for predicting the essential features of the frequency response. Various circuit models are proposed, including the low-frequency charge control model whose validity can be extended to higher frequencies by the use of frequency-dependent elements. Alternatively, multilump models with frequency-independent elements can be used at the higher frequencies. Experimental data on small-signal common-emitter current gain is presented in support of the theory.

Frequency comparison indicating apparatus

Abstract: A gating system for use with a frequency discriminator which will provide a positive indication of whether or not two input signals are the same frequency or, if they are not the same frequency, which one is the higher. The apparatus is for use with a frequency detector providing logic ''''1'''' and logic ''''0'''' outputs indicative of the highest frequency and providing an alternating output when the two frequencies are identical. The output of the frequency discriminator is utilized to steer flipflops to provide the necessary positive outputs.

Digital signal record systems

Abstract: A digital magnetic recorder uses up to twice the Nyquist bandwidth of a data signal, plus a clock signal at a frequency exactly equal to the bit rate for reliably exchanging data signals with a magnetic media. The frequency response of the recording system is greater than twice the Nyquist bandwidth of the data signals to be recorded. Optionally, additional control signals at frequencies above or below the clock frequency but within the available recorder bandwidth may be recorded. Preferably, in a multi-track magnetic recording system, a signal component is added at a frequency near the clock frequency such that the difference between this signal and the clock have a wavelength of the magnetic media greater than the maximum skew of the multi-track system. Such signal component is usable as a resynchronization pattern. Additionally, write errors are detected during recording with special control indicia recorded on the media indicating such errors. Without stopping the media, a write retry is effected in a predetermined relationship with the special indicia. Various forms of the indicia are described including special data patterns, special signal components, and the like. Special circuits established for handling data signals using framing techniques are described.

Effects of FFT coefficient quantization on bin frequency response

Abstract: A method is presented for analyzing the effets of quantization of coefficients on the frequency response of any frequency bin of the fast Fourier transform (FFT) algorithm. Although more detail is easily obtained, we concentrate on predicting the locations and sizes of all spurious sidelobes in the frequency response which are above any specified level. Certain sidelobes are present due to the particular window or weighting function that is being used. Spurious sidelobes or artifacts are extra sidelobes which are introduced if the FFT coefficients are quantized.

Frequency extension of circularly polarized antenna

Abstract: The frequency response of a cavity-backed planar microwave antenna having an element including a pair of spiral antenna tracks fixed to a substrate of insulating material is substantially extended by connecting a pair of cavity-backed outwardly extending dipole elements to the outer ends of each of said spiral tracks. The lower range of useful frequency response is thereby changed from a minimum operating frequency wherein the diameter of the spiral tracks constitutes approximately one-half wave length to a value wherein one-half wave length is approximately equal to the width of the antenna elements including the dipoles. This composite structure may be curved to some degree to enable it to conform to the inside surface of a curved radome.

Predicting servomechanism dynamic errors from frequency response measurements

Abstract: A theory is presented for analytically relating frequency domain criteria to time domain performance criteria. Third-order models are shown to adequately predict dynamic errors in a wide variety of high order physical systems with bandwidths differing by more than 100 to 1. Model coefficients lie in a relatively small region of the coefficient plane, suggesting that check-out spot frequencies and tolerances previously established empirically may be of general use.Good agreement is observed between predictions based on design data and experimental frequency response results obtained under field conditions on tolerancing an electro-hydraulic servo to satisfy dynamic error constraints on time domain inputs. When used in reverse, the technique predicts system filter properties from time domain measurements. Results are applicable to both manual and automatic test procedures.The general form of low-order model permits a reasonable approximation to frequency domain tolerances by inspection, reducing costly development and field tests.