Name: transmission line reflections at both ends
Uploaded: 2024-11-21T14:54:41.000Z
Duration: 1 min 21 s
Channel: JoVE

Home electrical wiring systems can be conceptually represented as a single-phase, two-wire, lossless transmission line.
These begin at the transmitting end, where power enters from the main grid with a specific voltage and impedance. At the receiving end, appliances and devices, each with a unique impedance, utilize this power as loads.
Boundary conditions are set to dictate how the voltage and current behave at both ends of the wiring system.
The receiving-end voltage equals impedance times its current. Solving this equation introduces the receiving-end voltage reflection coefficient, where transit time is the time a wave takes to travel the length of the wire.
Utilizing the established voltage and current relationships, modified expressions are obtained.
The transmitting end&#39;s boundary condition is set by the gap between the source voltage and the impedance-current product.
This relationship yields an expression in terms of the forward-traveling voltage wave.
Upon solving this expression, a coefficient reflecting the voltage at the sending end is established.
With the integration of this into the voltage and current relationships, a comprehensive solution is derived.

boundary conditions: lossless lines

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&#39;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 reflected voltage waves in the Laplace domain. The receiving-end voltage reflection coefficient characterizes how the wave reflects at the receiving end.
At the transmitting end, the boundary condition involves the difference between the source voltage and the product of the sending-end impedance and the current. This boundary condition leads to an equation for the incident voltage wave in terms of the sending-end reflection coefficient. This coefficient indicates the proportion of the wave reflected towards the source due to impedance mismatch.
The complete solutions for voltage and current along the transmission line are derived using the established boundary conditions and the reflection coefficients. These solutions incorporate both the incident and reflected waves, demonstrating how they combine to form the overall voltage and current at any point on the line. These solutions account for the effects of reflections at both the sending and receiving ends.
The line&#39;s characteristic impedance is derived from its inductance and capacitance per unit length, and these parameters also determine the wave velocity. By integrating these boundary conditions and parameters, a comprehensive understanding of the behavior of traveling waves on single-phase lossless transmission lines is obtained.

Boundary Conditions: Lossless Lines

Home electrical wiring systems can be conceptually represented as a single-phase, two-wire, lossless transmission line.
These begin at the transmitting ...

Education

JoVE Core

Electrical Engineering

Unit 1

Transmission Lines: Transient Operation

KEY TERMS AND CONCEPTS

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 written in the Laplace domain using the incident and reflected voltage waves. The receiving-end voltage reflection coefficient describes how much of the wave reflects back at that end.

At the sending end, the boundary condition uses the source voltage and the sending-end impedance. It compares the source voltage with the product of the sending-end impedance and the current. From this condition, the incident voltage wave can be written in terms of the sending-end reflection coefficient. This coefficient shows how much of the wave is reflected toward the source when the impedances do not match.

Using both boundary conditions, the voltage and current along the line can be solved. The full solution includes both the incident and reflected waves at any point on the line. It also shows the effects of reflections at the receiving end and the transmitting end. The characteristic impedance comes from the line inductance and capacitance, and these same values determine the wave velocity.

Transmission Line Reflections at Both Ends

transmission-line-reflections-at-both-ends

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.

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...

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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...

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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,...

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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

Explore how incident and reflected waves behave on a lossless transmission line, including boundary conditions, reflection coefficients, and wave velocity.

Transmission Line Reflections at Both Ends | 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.

Transmission Line Reflections at Both Ends

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