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Transmission-Line Differential Equations01:26

Transmission-Line Differential Equations

429
Transmission lines are essential components of electrical power systems. They are characterized by the distributed nature of resistance (R), inductance (L), and capacitance (C) per unit length. To analyze these lines, differential equations are employed to model the variations in voltage and current along the line.
Line Section Model
A circuit representing a line section of length Δx helps in understanding the transmission line parameters. The voltage V(x) and current i(x) are measured...
429
Transmission Line Design Considerations01:23

Transmission Line Design Considerations

222
Aluminum has become the material of choice for overhead transmission lines, surpassing copper due to its abundance and cost-effectiveness. The most prevalent type is the aluminum conductor, steel-reinforced (ACSR), which combines aluminum strands around a steel core. Other variants include all-aluminum conductors (AAC), all-aluminum alloy conductors (AAAC), aluminum conductor alloy-reinforced (ACAR), and aluminum-clad steel conductors. Advanced designs, such as aluminum conductors with steel...
222
Bewley Lattice Diagram01:12

Bewley Lattice Diagram

892
The Bewley lattice diagram, developed by L. V. Bewley, effectively organizes the reflections occurring during transmission-line transients. It visually represents how voltage waves propagate and reflect within a transmission line, making it easier to understand the complex interactions that occur.
892
Traveling Waves: Lossless Lines01:27

Traveling Waves: Lossless Lines

207
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.
207
Boundary Conditions: Lossless Lines01:21

Boundary Conditions: Lossless Lines

161
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...
161
Mesh Analysis for AC Circuits01:12

Mesh Analysis for AC Circuits

430
In the domain of radio communication, the significance of impedance matching must be considered. It is crucial to ensure the efficient transmission of signals between radio transmitters and receivers. Achieving this balance involves using impedance-matching circuits, with one fundamental configuration comprising a resistor, capacitor, and inductor.
The process of harmonizing these impedances begins with a clear understanding of the input and output signals. Once these signals are known, the...
430

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Related Experiment Video

Updated: Sep 22, 2025

Simulation, Fabrication and Characterization of THz Metamaterial Absorbers
13:44

Simulation, Fabrication and Characterization of THz Metamaterial Absorbers

Published on: December 27, 2012

15.5K

Static MLC transmission simulation using two-dimensional ray tracing.

David P Adam1, Bryan P Bednarz1, Sean P Frigo2

  • 1Department of Medical Physics, University of Wisconsin-Madison School of Medicine and Public Health, Madison, Wisconsin, USA.

Journal of Applied Clinical Medical Physics
|May 21, 2022
PubMed
Summary
This summary is machine-generated.

The transmission function of multileaf collimators (MLCs) is not constant with position, impacting treatment planning systems. This study reveals deviations from assumed constant transmission, crucial for accurate dose calculations.

Keywords:
HDMLC calibrationMLC modelingray tracing

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Area of Science:

  • Medical Physics
  • Radiation Oncology
  • Radiotherapy Physics

Background:

  • Multileaf collimators (MLCs) are critical components in modern radiotherapy, shaping radiation beams.
  • Current models in treatment planning systems (TPSs) often assume a constant transmission function for MLCs, simplifying calculations.
  • This assumption may lead to inaccuracies in dose calculations and quality assurance (QA) if the transmission varies with leaf position.

Purpose of the Study:

  • To investigate the hypothesis that the transmission function of rounded end linearly traveling MLCs is constant with position.
  • To determine the implications of non-constant MLC transmission on treatment plan QA results and clinical practice.

Main Methods:

  • Developed and validated a 2D ray-tracing tool to generate MLC transmission curves as a function of leaf position.
  • Analyzed transmission curves for clinically relevant leaf tip positions to determine beam edge location and broadening.
  • Simulated generalized scenarios to understand trends related to leaf tip radius.

Main Results:

  • Identified two distinct regions in the Varian high-definition MLC: a quasi-static central region and an outer region with significant deviations.
  • Observed a phenomenon where the half-attenuation X-ray (XR) position and beam edge broadening (BEB) increase dramatically at specific distances from the central axis (CAX).
  • Found that a smaller leaf tip radius parameter results in a larger quasi-static region.

Conclusions:

  • MLC transmission curve properties vary with position, affecting MLC calibration and modeling in TPSs.
  • Two-dimensional ray tracing is effective in identifying regions where MLC behavior deviates from simple models.
  • These findings can guide improvements in MLC modeling for enhanced fluence and dose calculation accuracy in radiotherapy.