Neper

Key takeaways

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

Reference excerpt

The neper (symbol: Np) is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. The unit's name derives from the name of John Napier, the inventor of logarithms. As is the case for the decibel and bel, the neper is a unit defined in the international standard ISO 80000. It is not part of the International System of Units (SI).

Definition Like the decibel, the neper is a unit in a logarithmic scale. While the bel uses the decadic (base-10) logarithm to compute ratios, the neper uses the natural logarithm, based on Euler's number (e ≈ 2.71828). The level of a ratio of two signal amplitudes or root-power quantities, with the unit neper, is given by

L = ln ⁡ x 1 x 2 N p , {\displaystyle L=\ln {\frac {x_{1}}{x_{2}}}\mathrm {~Np} ,}

where x 1 {\displaystyle x_{1}} and x 2 {\displaystyle x_{2}} are the signal amplitudes, and ln is the natural logarithm. The level of a ratio of two power quantities, with the unit neper, is given by

L = 1 2 ln ⁡ p 1 p 2 N p , {\displaystyle L={\frac {1}{2}}\ln {\frac {p_{1}}{p_{2}}}\mathrm {~Np} ,}

where p 1 {\displaystyle p_{1}} and p 2 {\displaystyle p_{2}} are the signal powers. In the International System of Quantities, the neper is defined as 1 Np = 1.

Units

The neper is defined in terms of ratios of field quantities—also called root-power quantities—(for example, voltage or current amplitudes in electrical circuits, or pressure in acoustics), whereas the decibel was originally defined in terms of power ratios. A power ratio 10 log r dB is equivalent to a field-quantity ratio 20 log r dB, since power in a linear system is proportional to the square (Joule's laws) of the amplitude. Hence the decibel and the neper have a fixed ratio to each other:

1 Np = 20 log 10 ⁡ e dB ≈ 8.685889638 dB {\displaystyle 1\ {\text{Np}}=20\log _{10}e\ {\text{dB}}\approx {\text{8.685889638 dB}}}

and

1 d B = 1 20 ln ⁡ ( 10 ) N p ≈ 0.115129255 Np . {\displaystyle 1\ \mathrm {dB} ={\frac {1}{20}}\ln(10)\ \mathrm {Np} \approx {\text{0.115129255 Np}}.}

The (voltage) level ratio is

… excerpt ends here. Continue reading the full article.

Illustrations

Neper: John Napier after whom the unit is named — John Napier after whom the unit is named

Worked examples

Example 1 — a first encounter with Neper

Start with the simplest possible case. Write down what Neper claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, 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 Neper 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 Neper 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 Neper

In research: Neper appears in science 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 Neper 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: Neper is common in secondary-school and first-year university syllabi. It links to neighbouring topics Units of level, so understanding it makes those chapters shorter.
In everyday life: Look for Neper 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.

How to study Neper in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Neper means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Neper out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Neper in simple terms?

The neper (symbol: Np) is a logarithmic unit for ratios of measurements of physical field and power quantities, such as gain and loss of electronic signals. The unit's name derives from the name of John Napier, the inventor of logarithms.

Why does Neper matter?

Because it connects several science 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 Neper?

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 Neper.