Time-domain study of transient fields for a thin circular loop antenna

2002 ◽  
Vol 80 (9) ◽  
pp. 995-1003 ◽  
Author(s):  
S T Bishay ◽  
G M Sami
Keyword(s):  
Time Domain ◽  
Analytical Form ◽  
Loop Antenna ◽  
Inverse Laplace Transform ◽  
Wave Number ◽  
Earth Model ◽  
Circular Loop ◽  
Wave Forms ◽  
Displacement Currents ◽  
The Time Domain

The transient fields in the time-domain of a thin circular loop antenna on a two-layer conducting earth model are expressed in analytical form. In these expressions, the displacement currents both in the two-layer ground and in the air region are taken into consideration. The closed-form expressions of the time-domain are obtained as the inverse Laplace transform of the derived full-wave time-harmonic solution. These time-domain solutions are obtained as a summation of wave-guide modes plus contributions from branch cuts in the complex plane of the longitudinal wave number. Numerical examples are given to indicate the important features in the wave forms of the surface fields due to step and pulsed current excitation. These features provide the means of detecting the earth's stratification, measuring the overburden height, and determining the ratio of the conductivities of the layers. PACS Nos.: 41.20Jb, 42.25Bs, 42.25Gy, 44.05+e

Natural-frequency concept utilized in remote probing of the earth

2003 ◽  
Vol 81 (4) ◽  
pp. 705-712 ◽  
Author(s):  
S T Bishay ◽  
O M Abo-Seida ◽  
G M Sami
Keyword(s):  
Natural Frequency ◽  
Analytical Form ◽  
Step Response ◽  
Earth Model ◽  
Induced Voltage ◽  
Diagnostic Features ◽  
Vertical Magnetic Dipole ◽  
Remote Probing ◽  
Displacement Currents ◽  
Layered Ground

The complete time-domain fields due to a vertical magnetic dipole on the surface of a two-layered earth model are derived in an analytical form using the natural-frequency concept. In these expressions, the displacement currents in the earth's layers are taken into consideration. The step responses of the induced voltage in a horizontal receiving loop is found to have definite diagnostic features for the ground beneath. These features are demonstrated by numerical results and shown by figures. The clear distinction between the step response of the homogeneous and the two-layered ground suggests that this response can be used for the detection of the stratification. PACS Nos.: 41.20.Jb, 42.25.Bs, 42.25.Gy, 44.05.+e

scholarly journals Determination of the response of a class of nonlinear time invariant systems

1981 ◽  
Vol 4 (3) ◽  
pp. 615-623
Author(s):  
Sudhangshu B. Karmakar
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Inverse Laplace Transform ◽  
New Approach ◽  
Functional Expansion ◽  
Expansion Time ◽  
Time Domain Response ◽  
The Time Domain ◽  
Time Invariant

This paper illustrates by means of a simple example a new approach for the determination of the time domain response of a class of nonlinear systems. The system under investigation is assumed to be described by a nonlinear differential equation with forcing term. The response of the system is first obtained in terms of the input in the form of a Volterra functional expansion. Each of the components in the expansion is first transformed into a multidimensional frequency domain and then to a single dimensional frequency domain by the technique of association of variables. By taking into consideration the conditions for the rapid convergence of the functional expansion the response of the system in the frequency domain can effectively be obtained by taking only the first few terms of the expansion. Time domain response is then found by inverse Laplace transform.

Time‐domain solution for horizontal coaxial dipoles on a half‐space

Geophysics ◽  
1986 ◽  
Vol 51 (9) ◽  
pp. 1850-1852 ◽  
Author(s):  
David C. Bartel
Keyword(s):  
Frequency Domain ◽  
Half Space ◽  
Time Domain ◽  
Inverse Laplace Transform ◽  
Direct Solution ◽  
Current Waveform ◽  
Laplace Domain ◽  
Homogeneous Half Space ◽  
The Time Domain ◽  
The Magnetic Field

The practice of transforming frequency‐domain results into the time domain is fairly common in electromagnetics. For certain classes of problems, it is possible to obtain a direct solution in the time domain. A summary of these solutions is given in Hohmann and Ward (1986). Presented here is another problem which can be solved directly in the time domain—the magnetic field of horizontal coaxial dipoles on the surface of a homogeneous half‐space. Solutions are presented for both an impulse transmitter current and a step turnon in the transmitter current. The solution in the time domain is obtained by taking the inverse Laplace transform of the product of the frequency‐domain solution and the Laplace‐domain representation of the current waveform.

scholarly journals ADI-MRTD Algorithm for Periodic Structures Analysis

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Xiaohua Dong ◽  
Yiwang Chen ◽  
Pin Zhang ◽  
Yichao Teng ◽  
Xiaobo Zhuansun
Keyword(s):  
Time Domain ◽  
Periodic Structures ◽  
Sampling Rate ◽  
Wave Number ◽  
Wavelet Theory ◽  
Alternating Direction Implicit ◽  
Alternating Direction ◽  
Structure Simulation ◽  
The Time Domain ◽  
Difference Time

In this paper, a novel algorithm based on the alternating direction implicit (ADI) multiresolution time-domain (MRTD) method for periodic structure simulation is proposed. By applying the multiresolution analysis in accordance with wavelet theory, the spatial sampling rate of the conventional finite-difference time-domain (FDTD) is significantly reduced by the MRTD method. The ADI method is then used to remove the Courant-Friedrich-Levy (CFL) limit that the MRTD method experiences. The periodic boundary condition (PBC) is directly implemented in the time domain using a constant transverse wave-number (CTW) wave. Numerical results are presented to confirm the efficiency and accuracy of the proposed method.

ELECTROMAGNETIC TRANSIENT RESPONSE OF A CONDUCTING SPHERE EMBEDDED IN A CONDUCTIVE MEDIUM

Geophysics ◽  
1973 ◽  
Vol 38 (5) ◽  
pp. 864-893 ◽  
Author(s):  
Shri Krishna Singh
Keyword(s):  
Transient Response ◽  
Time Domain ◽  
Massive Sulfide ◽  
Displacement Current ◽  
Static Approximation ◽  
Electromagnetic Transient ◽  
Conducting Sphere ◽  
Quasi Static Approximation ◽  
Displacement Currents ◽  
The Time Domain

This paper is concerned with the time‐domain electromagnetic prospecting of massive sulfide ore bodies which are surrounded by conductive host rocks. The electromagnetic transient response of a permeable and conducting sphere embedded in a finitely conducting infinite space is derived. The source is a magnetic dipole of arbitrary orientation which is located outside the sphere. The contributions from the displacement currents have been neglected. The solution thus obtained is compared with the known solution under “quasi‐static” approximation in which the displacement current in the sphere and both the conduction and the displacement currents in the outer medium are neglected. From the numerical results presented, it is clear that the validity of the quasi‐static approximation in the time domain, if the outer host rock is conductive, must be carefully investigated. If the finite outer conductivity is taken into account, magnetic modes are modified and electric modes become important. Five response functions, each a function of five parameters, are required to describe the secondary magnetic field.

scholarly journals Effect of East Gyro Drift and Initial Azimuth Error on the Compass Azimuth Alignment Convergence Time

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Dongxu He ◽  
Xinle Zang ◽  
Lei Ge
Keyword(s):  
Laplace Transform ◽  
Time Domain ◽  
Oscillation Period ◽  
Inverse Laplace Transform ◽  
Convergence Time ◽  
Initial Error ◽  
Error Band ◽  
Alignment System ◽  
The Time Domain ◽  
Gyro Drift

The effect of gyro constant drift and initial azimuth error on the convergence time of compass azimuth is analyzed in this article. Using our designed compass azimuth alignment system, we obtain the responses of gyro constant drift and initial azimuth error in the frequency domain. The corresponding response function in the time domain is derived using the inverse Laplace transform, and its convergence time is then analyzed. The analysis results demonstrate that the convergence time of compass azimuth alignment is related to the second-order damping oscillation period, the gyro constant drift, and the initial azimuth error. In this study, the error band is set to 0.01° to determine convergence. When the gyro drift is less than 0.05°/h, compass azimuth alignment can converge within 0.9 damping oscillation periods. When the initial azimuth error is less than 5°, compass azimuth alignment can converge within 1.4 damping oscillation periods. When both conditions are met, the initial error plays a major role in convergence, while gyro drift has a smaller effect on convergence time. Finally, the validity of our method is verified using simulations.

On the Electromagnetic Pulse Response of a Dipole Over a Plane Surface

1974 ◽  
Vol 52 (2) ◽  
pp. 193-196 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Transient Response ◽  
Time Domain ◽  
Electromagnetic Pulse ◽  
Plane Surface ◽  
Low Frequency ◽  
Pulse Response ◽  
Frequency Region ◽  
Earth Model ◽  
Vertical Electric Dipole ◽  
The Time Domain

Using a surface impedance description, the electromagnetic fields of a vertical electric dipole are considered for a plane earth model. Particular attention is paid to the low-frequency region where the range to the observer may not be electrically large. The consequences in the time domain are also considered. Here, it is shown that the tail of the transient response is sensitive to the traditional low-frequency approximations that are usually accepted without question.

Optical phenomena in the time domain

Optics f2f ◽  
2018 ◽  
pp. 111-126
Author(s):  
Charles S. Adams ◽  
Ifan G. Hughes
Keyword(s):  
Dispersion Relation ◽  
Time Domain ◽  
Free Space ◽  
Slow Light ◽  
Group Velocity Dispersion ◽  
Time Dependent ◽  
Wave Forms ◽  
Optical Phenomena ◽  
The Time Domain ◽  
Fast Light

This chapter discusses a sum of many waves with different frequencies, resulting in wave forms with particular time dependence. The propagation of the time-dependent wave solution through free space, or media with a particular dispersion relation, are analysed. Interesting cases such as the effect of group velocity dispersion, slow light, and fast light are highlighted.

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