Finite Time Constant Research Articles

A direct-coupled phase-sensitive detector

A direct-coupled phase-sensitive detector is described. This circuit avoids problems which can arise when finite coupling time constants are used at low frequencies.

Analog-to-Digital Conversion by Means of Delta Modulation

It is shown that normal delta modulation can be used for the transmission of dc signals. A circuit is described in which a delta modulator is combined with a counter for analog-to-digital conversion of a dc signal. Several factors contributing to the accuracy are developed. One of these factors which has not been dealt with previously is the size of the steps in the reconstructed signal due to the finite integrator time constant. Two examples of delta modulators are described; one of them a high precision system, the other a simple design of moderate precision.

The correction of magnetic and pure quadrupole resonance line shapes for instrumental broadening

Explicit expressions are derived for the correction of electron and nuclear magnetic resonance, and pure quadrupole resonance, line shapes for distortions due to finite amplitudes of frequency and magnetic field modulation of various forms and to the use of circuits with finite time constants.

Uniaxial Anisotropy in Polycrystalline Garnets

In samples of polycrystalline yttrium and lutetium iron garnet which exhibit domain-wall relaxation effects, it is possible to establish uniaxial anisotropy by cooling to low temperature in a magnetic field. This magnetic anneal leads to the development of rectangular hysteresis loops. In lutetium iron garnet,where a particularly strong anneal is found, a uniaxial anisotropy energy of 4500 erg/cc is obtained. After cooling, the easy axis can be shifted in direction by altering the orientation of the applied field; the shift in axis occurs with a finite time constant (order of 15 sec for LuIG).

Short-Time Autocorrelation Functions and Power Spectra

The reciprocal relations between autocorrelation functions and power spectra, known as Wiener's Theorem, axe extended in a modified form to the case of experimental results obtained by means of filters with finite time constants. If the short-time autocorrelation function φt(τ) and power spectrum Gt(ω) are properly defined, it is found that φt(τ)=eα|τ|2π ∫ −∞∞Gt(ω)cosωτ dωGt(ω)= ∫ −∞∞e−α|τ|φt(τ)cosωτ dτ where 1/α is a time constant. These equations may be used to relate the autocorrelation-function representation of a speech wave to the corresponding spectrographic representation.

Some theoretical and practical considerations of pulse modulation

This paper gives a summary of theoretical and practical studies on the properties of pulse-phase modulation, developed mainly in 1943.The properties of pulse-phase modulation are studied by means of Fourier transformations. Although some approximations are introduced, the calculations lead to the following definite conclusions:(1) Pulse-phase modulation introduces no amplitude distortion except at sub-multiples of the recurrent frequency.(2) The harmonic distortion, if any, is negligible and this method of modulation can be used for high-quality broadcasting.(3) Pulse-phase modulation is subject to a special type of distortion called “cross-distortion,” produced by side bands of the recurrent frequency appearing in the signal bandwidth. Curves of the approximate amount of this type of distortion are given, and it is shown that, in practical multi-channel systems, this distortion is negligible, provided that the recurrent pulse frequency is at least double the highest signal frequency to be transmitted, and preferably equal to, or greater than, three times this frequency.This study is followed by considerations on the signal/noise ratio in pulse-phase modulation. Pulse-phase modulation is compared with amplitude modulation and a formula, giving the improvement in the signal/noise ratio due to pulse-phase modulation, is established by very simple considerations. It is shown that this ratio improves as the frequency bandwidth used in pulse-phase modulation.It is shown how an improvement of 3 db in signal/noise ratio can be obtained by suppressing the noise on the synchronizing pulse, and a practical circuit developed and applied in 1943 by the author is described.Finally, a typical example of pulse technique is given. In practical circuits the modulator and demodulator pulses are not perfectly shaped, because of the departure from linearity due to finite time-constants. This introduces harmonic distortion. It is shown how this distortion can be practically eliminated by designing circuits so that the time constant is equal at modulation and demodulation.

The Application of Feedback to Wide-Band Output Amplifiers

A mathematical analysis is made of a typical two-stage output amplifier designed for the amplification of a wide range of frequencies incorporating feedback over the two stages. In wide-band amplifiers the use of output transformers is usually ruled out due to frequency limitations, and it is found that the time constant of the feedback circuit cannot be neglected. The effect of the feedback circuit is to give rise to peaks in the response curves at both the high- and low-frequency extremities of the band. The finite time constant of the feedback circuit greatly affects the latter. Design curves are included giving the response and phase shift for both the low- and high-frequency regions in terms of the feedback factor, the grid-coupling time constant, and the feedback-circuit time constant for the low-frequency region, and the feedback factor and the time constants for the shunting circuits in the plate circuits of both stages for the high-frequency region. Complete derivations of all formulas are given in the two appendixes.