engineering

Reflections of signals on conducting lines

Reflections of signals on conducting lines is a engineering topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Reflections of signals on conducting lines rather than just read about it. In short: A signal travelling along an electrical transmission line will be partly, or wholly, reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impedance of the line, or if the far end of the line is not terminated in its characteristic impedance. This can happen, for instance, if two lengths of dissimilar transmission lines are joined.

Key takeaways

Reflections of signals on conducting lines belongs to engineering; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Reflections of signals on conducting lines to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Reflections of signals on conducting lines from memory before moving on to harder problems.

Reference excerpt

A signal travelling along an electrical transmission line will be partly, or wholly, reflected back in the opposite direction when the travelling signal encounters a discontinuity in the characteristic impedance of the line, or if the far end of the line is not terminated in its characteristic impedance. This can happen, for instance, if two lengths of dissimilar transmission lines are joined. This article is about signal reflections on electrically conducting lines. Such lines are loosely referred to as copper lines, and indeed, in telecommunications are generally made from copper, but other metals are used, notably aluminium in power lines. Although this article is limited to describing reflections on conducting lines, this is essentially the same phenomenon as optical reflections in fibre-optic lines and microwave reflections in waveguides. Reflections cause several undesirable effects, including modifying frequency responses, causing overload power in transmitters and overvoltages on power lines. However, the reflection phenomenon can be useful in such devices as stubs and impedance transformers. The special cases of open circuit and short circuit lines are of particular relevance to stubs. Reflections cause standing waves to be set up on the line. Conversely, standing waves are an indication that reflections are present. There is a relationship between the measures of reflection coefficient and standing wave ratio.

Specific cases There are several approaches to understanding reflections, but the relationship of reflections to the conservation laws is particularly enlightening. A simple example is a step voltage, V u ( t ) {\displaystyle V\,u(t)} (where V {\displaystyle V} is the height of the step and u ( t ) {\displaystyle u(t)} is the unit step function with time t {\displaystyle t} ), applied to one end of a lossless line, and consider what happens when the line is terminated in various ways. The step will be propagated down the line according to the telegrapher's equation at some velocity κ {\displaystyle \kappa } and the incident voltage, v i {\displaystyle v_{\mathrm {i} }} , at some point x {\displaystyle x} on the line is given by

v i = V u ( κ t − x ) {\displaystyle v_{\mathrm {i} }=V\,u(\kappa \,t-x)\,\!}

The incident current, i i {\displaystyle i_{\mathrm {i} }} , can be found by dividing by the characteristic impedance, Z 0 {\displaystyle Z_{0}}

i i = v i Z 0 = I u ( κ t − x ) {\displaystyle i_{\mathrm {i} }={\frac {v_{\mathrm {i} }}{Z_{0}}}=I\,u(\kappa \,t-x)}

Open circuit line

The incident wave travelling down the line is not affected in any way by the open circuit at the end of the line. It cannot have any effect until the step actually reaches that point. The signal cannot have any foreknowledge of what is at the end of the line and is only affected by the local characteristics of the line. However, if the line is of length ℓ {\displaystyle \ell } the step will arrive at the open circuit at time t = ℓ / κ {\displaystyle t=\ell /\kappa } , at which point the current in the line is zero (by the definition of an open circuit). Since charge continues to arrive at the end of the line through the incident current, but no current is leaving the line, then conservation of electric charge requires that there must be an equal and opposite current into the end of the line. Essentially, this is Kirchhoff's current law in operation. This equal and opposite current is the reflected current, i r {\displaystyle i_{\mathrm {r} }} , and since

i r = v r Z 0 {\displaystyle i_{\mathrm {r} }={\frac {v_{\mathrm {r} }}{Z_{0}}}}

there must also be a reflected voltage, v r {\displaystyle v_{\mathrm {r} }} , to drive the reflected current down the line. This reflected voltage must exist by reason of conservation of energy. The source is supplying energy to the line at a rate of v i i i {\displaystyle v_{\mathrm {i} }i_{\mathrm {i} }} . None of this energy is dissipated in the line or its termination and it must go somewhere. The only available direction is back up the line. Since the reflected current is equal in magnitude to the incident current, it must also be so that

… excerpt ends here. Continue reading the full article.

Illustrations

Reflections of signals on conducting lines: A time-domain reflectometer; an instrument used to locate the position of faults on lines from the time taken for a reflected wave to return from the discontinuity. — A time-domain reflectometer; an instrument used to locate the position of faults on lines from the time taken for a reflected wave to return from the discontinuity.

Worked examples

Example 1 — a first encounter with Reflections of signals on conducting lines

Start with the simplest possible case. Write down what Reflections of signals on conducting lines claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Reflections of signals on conducting lines before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Reflections of signals on conducting lines ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Reflections of signals on conducting lines

In research: Reflections of signals on conducting lines appears in engineering research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Reflections of signals on conducting lines in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Reflections of signals on conducting lines is common in secondary-school and first-year university syllabi. It links to neighbouring topics Distributed element circuits, Electronic design, Signal cables, so understanding it makes those chapters shorter.
In everyday life: Look for Reflections of signals on conducting lines outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Reflections of signals on conducting lines in 20 minutes

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Frequently asked questions

What is Reflections of signals on conducting lines in simple terms?

Why does Reflections of signals on conducting lines matter?

Because it connects several engineering ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Reflections of signals on conducting lines?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Reflections of signals on conducting lines.