Lossless Line
Lossless Line - Related Videos
01:23
Lossless Lines
0 Views •
2024
In electrical engineering, a lossless transmission line is characterized by a purely imaginary propagation constant and a resistive characteristic impedance. The ABCD parameters, which describe the relationship between the input and output voltages and currents, indicate an equivalent π circuit with an imaginary series impedance and a shunt admittance. This results in a transmission line that, when the product of the phase constant (beta) and the length of the line is less than pi, exhibits...
01:21
Boundary Conditions: Lossless Lines
0 Views •
2024
Consider a single-phase, two-wire, lossless transmission line terminated by an impedance at the receiving end and a source with Thevenin voltage and impedance at the sending end. The line, with length, has a surge impedance and wave velocity determined by the line's inductance and capacitance. At the receiving end, the boundary condition states that the voltage equals the product of the receiving-end impedance and current. This relationship is expressed as a function of the incident and...
01:27
Traveling Waves: Lossless Lines
0 Views •
2024
The provided content explores the behavior of traveling waves on single-phase lossless transmission lines. It begins with a single-phase two-wire lossless transmission line of length Δx, characterized by a loop inductance LH/m and a line-to-line capacitance C F/m. These parameters result in a series inductance LΔx and a shunt capacitance CΔx. The voltage v(x,t) and current i(x,t) at any position x and time t on the line are expressed using Kirchhoff's Voltage Law (KVL) and Kirchhoff's Current...
10:33
Assessing Cell Viability and Death in 3D Spheroid Cultures of Cancer Cells
0 Views •
Cited by 34 •
2019
Here, we present several simple methods for evaluating viability and death in 3D cancer cell spheroids, which mimic the physico-chemical gradients of in vivo tumors much better than the 2D culture. The spheroid model, therefore, allows evaluation of the cancer drug efficacy with improved translation to in vivo conditions.
12:09
Network Analysis of the Default Mode Network Using Functional Connectivity MRI in Temporal Lobe Epilepsy
0 Views •
Cited by 35 •
2014
The Default Mode Network (DMN) in Temporal Lobe Epilepsy (TLE) is analyzed in the resting state of the brain using seed-based functional connectivity MRI (fcMRI).
FAQs
Setting conductor resistance and dielectric conductance to zero removes the model’s dissipative terms, so electromagnetic energy is analyzed without power loss along the line. The remaining distributed inductance and capacitance determine how voltage and current propagate. This separation is useful because it lets engineers study wave behavior itself before considering the additional effects introduced by losses in practical cables.
Characteristic impedance provides the voltage-to-current relationship for a propagating wave on the line, while the phase constant describes how that wave changes phase along its length. Together, these quantities determine the spatial behavior of voltage and current. Engineers use them to interpret propagation and assess whether connected circuit conditions support transmission or produce reflections.
Reflections occur when the conditions at a line termination do not match the line’s characteristic impedance. The incident and reflected waves then combine, producing spatial voltage and current patterns known as standing waves. Studying these patterns allows engineers to evaluate impedance matching and understand how a load affects signal behavior, especially in high-frequency transmission systems.
Unlike a practical cable, the ideal model does not attribute changes in signal amplitude to conductor resistance or dielectric conductance. Consequently, differences between predicted and observed behavior can be associated with real-line losses rather than the basic propagation model. This comparison makes the lossless line a reference case for evaluating transmission systems, microwave circuits, antennas, and interconnects.
A basic analysis begins by representing the conductors and dielectric with zero resistance and zero conductance, respectively. The distributed inductance and capacitance are then used to characterize propagation through the line. Engineers can next examine characteristic impedance, phase constant, reflections, standing waves, or matching, depending on the design question. This workflow isolates the relevant ideal behavior.
Because voltage and current vary along the line, their spatial distributions reveal how propagation and line conditions shape the transmitted wave. Comparing these distributions helps identify standing-wave behavior and evaluate impedance matching. In engineering analysis, this information connects ideal line parameters with behavior expected in high-frequency circuits and communication transmission systems.
The model is especially useful when analyzing transmission systems, microwave circuits, antennas, and interconnects, where wave propagation and impedance behavior are central concerns. Its ideal assumptions provide a controlled baseline for studying reflection, standing waves, and matching. Engineers can then evaluate designs while recognizing that real cables introduce losses absent from the model.