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Traveling Waves: Lossless Lines

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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.

Lossless Lines

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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...

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Related Experiment Video

Updated: Jun 25, 2026

Quasi-light Storage for Optical Data Packets

Quasi-light Storage for Optical Data Packets

Published on: February 6, 2014

Referenceless phase velocity mapping using balanced SSFP.

Jon-Fredrik Nielsen¹, Krishna S Nayak

¹Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, California, USA. jfnielse@umich.edu

Magnetic Resonance in Medicine

|February 21, 2009

Summary

This summary is machine-generated.

This study introduces a referenceless phase contrast MRI (PC-MRI) method using balanced steady state free precession (SSFP) for faster, accurate blood flow velocity measurement. The technique reduces scan time by up to 50% for 1D and 3D flow imaging.

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Area of Science:

Magnetic Resonance Imaging
Biomedical Engineering
Cardiovascular Imaging

Background:

Phase contrast MRI (PC-MRI) is crucial for in vivo blood flow velocity measurement.
Balanced steady state free precession (SSFP) PC-MRI offers superior SNR efficiency compared to GRE PC-MRI.
Current PC-MRI techniques can be time-consuming, limiting clinical applications.

Purpose of the Study:

To develop a novel referenceless PC-MRI approach utilizing balanced SSFP.
To accelerate blood flow imaging acquisition times.
To enable accurate velocity estimation and advanced 4D/7D flow imaging.

Main Methods:

Exploited the intrinsic refocusing property of balanced SSFP sequences with TE = TR/2.
Developed a referenceless phase estimation method using static tissue.
Applied the technique for 1D velocity measurements and time-resolved 3D flow imaging (7D flow).

Main Results:

Achieved accurate in vivo 1D velocity estimates.
Reduced total scan time by up to 50% compared to conventional SSFP PC-MRI.
Demonstrated feasibility of referenceless 7D flow imaging in the carotid bifurcation with only three acquisitions.

Conclusions:

The proposed referenceless balanced SSFP PC-MRI method significantly accelerates blood flow imaging.
This technique provides accurate velocity measurements and enables advanced 7D flow imaging efficiently.
Offers a promising alternative for faster and more comprehensive cardiovascular flow assessment.