Name: tracing transient waves with a bewley diagram
Uploaded: 2024-11-21T14:54:41.000Z
Duration: 1 min 12 s
Channel: JoVE

Sending an email from a computer is analogous to an electrical signal moving along a single-phase lossless line.
The Bewley Lattice Diagram aids in understanding what happens when this signal encounters obstacles or changes in the line.
It graphically represents time in transient time units and line position, with diagonals illustrating traveling waves.
When waves encounter an obstacle, reflected waves are calculated by multiplying the incoming wave by the reflection coefficient.
The voltage at any point on the line can be determined by summing all the terms directly above that point in the diagram.
For instance, when a signal comes across a junction of two lossless lines, it experiences reflection along the original line and refraction onto the new line.
Equations for the voltage and current at the junction can be written to calculate the reflected and refracted signals in terms of the incoming signal.
This process can be extended to junctions of more than two lines, enabling the understanding of complex networks of transmission lines.

bewley lattice diagram

Bewley Lattice Diagram

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.
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In the diagram, the vertical scale represents the line's transient time, while the horizontal scale represents the line position x. The diagonal lines in the diagram represent traveling waves. Each reflection is calculated by multiplying the incident wave arriving at an end by the reflection coefficient at that end.
The reflection coefficient's value is known for both the receiving and sending ends. These coefficients determine the magnitude and direction of the reflected waves when an incident wave reaches the respective ends of the transmission line.
When an incident voltage wave travels along the line and reflects at the receiving end, the reflected wave then travels back and reflects again at the sending end, and this process continues. Each interaction, reflection, and the resulting wave is represented in the diagram, showcasing how the waves propagate over time.
To determine the voltage at any point on the diagram, sum all the terms directly above that point. This approach allows one to understand how the combined incident and reflected waves contribute to the overall voltage at any given location and time.
The Bewley lattice diagram is a powerful tool for visualizing and analyzing wave propagation in transmission lines. It is particularly useful for understanding the behavior of transients and ensuring the efficient design of electrical systems. By organizing the reflections and transmissions, engineers can predict the voltages and currents at various points in the system, aiding in the design and troubleshooting of transmission lines.

Sending an email from a computer is analogous to an electrical signal moving along a single-phase lossless line.
The Bewley Lattice Diagram aids in ...

Education

JoVE Core

Electrical Engineering

Unit 1

Transmission Lines: Transient Operation

KEY TERMS AND CONCEPTS

tracing transient waves with a bewley diagram

The Bewley lattice diagram organizes voltage-wave reflections in transmission-line transients. It helps students follow how a signal moves along a line and bounces back from each end. The diagram was developed by L. V. Bewley.

The vertical axis shows transient time, and the horizontal axis shows the line position x. Diagonal lines show traveling waves. These lines make the wave motion easier to read because each segment marks a wave moving through the line.

Each reflection is found by multiplying the incident wave that reaches an end by the reflection coefficient at that end. The reflection coefficient is known for both the receiving end and the sending end. These values control the size and direction of the reflected wave when the incident wave arrives.

An incident voltage wave can travel to the receiving end, reflect there, and then travel back to the sending end. It can reflect again, and the process continues over time. The diagram shows each interaction and the wave that results from it.

To find the voltage at any point on the diagram, add all of the terms directly above that point. This sum shows how the incident and reflected waves combine at a given place and time. The Bewley lattice diagram is a useful tool for visualizing wave propagation, studying transients, and supporting the design and troubleshooting of transmission lines.

Tracing Transient Waves with a Bewley Diagram

tracing-transient-waves-with-a-bewley-diagram

traveling waves: lossless lines

Wave Speed on Lossless Transmission Lines

Traveling waves on a lossless transmission line are shaped by the line’s inductance and capacitance. The model starts with a single-phase, two-wire line of length Δx. It has loop inductance L H/m and line-to-line capacitance C F/m. A short section of the line can then be treated as a series inductance LΔx and a shunt capacitance CΔx. Voltage v(x,t) and current i(x,t) are written for any position x and time t along the line. Kirchhoff’s Voltage Law, or KVL, is used for the voltage relation.

boundary conditions: lossless lines

Transmission Line Reflections at Both Ends

Single-phase, two-wire, lossless transmission lines show how voltage and current waves reflect at both ends of a circuit. In this model, the line has a length, a surge impedance, and a wave velocity. These are set by the line’s inductance and capacitance per unit length. A home electrical wiring system can be treated this way in a simple circuit model. At the receiving end, the boundary condition says that the voltage equals the receiving-end impedance times the current. This relationship is...

The Bewley lattice diagram organizes voltage-wave reflections in transmission-line transients. It helps students follow how a signal moves along a line and bounces back from each end. The diagram was developed by L. V. Bewley. The vertical axis shows transient time, and the horizontal axis shows the line position x. Diagonal lines show traveling waves. These lines make the wave motion easier to read because each segment marks a wave moving through the line. Each reflection is found by...

lossy lines and overvoltages

Signal Attenuation and Power Losses

Transmission lines with series resistance and shunt conductance can weaken signals, change wave shape, and waste power. These effects are called attenuation, distortion, and power losses. They matter in long power lines and other practical transmission systems. When constant resistance and conductance are present, the voltage and current equations change. The propagation constant shows that the wave includes both forward-traveling and backward-traveling parts. As the wave moves along the line,...

insulation coordination

BIL and Surge Protection for Power Equipment

Insulation coordination matches electric equipment insulation strength with protective device settings to guard against expected overvoltages. Engineers choose these levels using judgment and cost. The goal is to keep equipment safe while avoiding unnecessary expense. Equipment can usually survive short, high transient overvoltages. Repeated tests with the same waveform can still give inconsistent results. For that reason, standard impulse voltage waveforms are used in testing. These waveforms...

key terms and concepts

Follow voltage waves as they reflect along a transmission line. Learn how the Bewley lattice diagram uses time, position, and reflection coefficients.

Tracing Transient Waves with a Bewley Diagram | JoVE K12

JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

Tracing Transient Waves with a Bewley Diagram

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