science

Wilkinson power divider

Wilkinson power divider is a science 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 Wilkinson power divider rather than just read about it. In short: In the field of microwave engineering and circuit design, the Wilkinson Power Divider is a specific class of power divider circuit that can achieve isolation between the output ports while maintaining a matched condition on all ports. The Wilkinson design can also be used as a power combiner because it is made up of passive components and hence is reciprocal.

Key takeaways

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

Reference excerpt

In the field of microwave engineering and circuit design, the Wilkinson Power Divider is a specific class of power divider circuit that can achieve isolation between the output ports while maintaining a matched condition on all ports. The Wilkinson design can also be used as a power combiner because it is made up of passive components and hence is reciprocal. First published by Ernest J. Wilkinson in 1960, this circuit finds wide use in radio frequency communication systems utilizing multiple channels since the high degree of isolation between the output ports prevents crosstalk between the individual channels. It uses quarter wave transformers, which can be easily fabricated as quarter wave lines on printed circuit boards. It is also possible to use other forms of transmission line (e.g. coaxial cable) or lumped circuit elements (inductors and capacitors).

Theory

The scattering parameters for the common case of a 2-way equal-split Wilkinson power divider at the design frequency is given by

[ S ] = − j 2 [ 0 1 1 1 0 0 1 0 0 ] {\displaystyle [S]={\frac {-j}{\sqrt {2}}}{\begin{bmatrix}0&1&1\\1&0&0\\1&0&0\\\end{bmatrix}}}

Inspection of the S matrix reveals that the network is reciprocal ( S i j = S j i {\displaystyle S_{ij}=S_{ji}} ), that the terminals are matched ( S 11 , S 22 , S 33 = 0 {\displaystyle S_{11},S_{22},S_{33}=0} ), that the output terminals are isolated ( S 23 , S 32 {\displaystyle S_{23},S_{32}} =0), and that equal power division is achieved ( S 21 = S 31 {\displaystyle S_{21}=S_{31}} ). The non-unitary matrix results from the fact that the network is lossy. An ideal Wilkinson divider would yield S 21 = S 31 = − 3 dB = 20 log 10 ⁡ ( 1 2 ) {\displaystyle S_{21}=S_{31}=-3\,{\text{dB}}=20\log _{10}({\frac {1}{\sqrt {2}}})} . Network theorem governs that a divider cannot satisfy all three conditions (being matched, reciprocal and loss-less) at the same time. Wilkinson divider satisfies the first two (matched and reciprocal), and cannot satisfy the last one (being loss-less). Hence, there is some loss occurring in the network. No loss occurs when the signals at ports 2 and 3 are in phase and have equal magnitude. In case of noise input to ports 2 and 3, the noise level at port 1 does not increase, half of the noise power is dissipated in the resistor. By cascading, the input power might be divided to any n {\displaystyle n} -number of outputs.

Unequal/Asymmetric Division Through Wilkinson Divider If the arms for port 2 and 3 are connected with un-equal impedances, then asymmetric division of power can be achieved. When characteristic impedance is Z 0 {\displaystyle Z_{0}} , and one wants to split power as P 2 {\displaystyle P_{2}} and P 3 {\displaystyle P_{3}} , and P 2 {\displaystyle P_{2}} ≠ P 3 {\displaystyle P_{3}} , then the design can be created following the equations: A new constant K {\displaystyle K} is defined for ease of expression, where K 2 = P 3 P 2 {\displaystyle K^{2}={\frac {P_{3}}{P_{2}}}}

Then the design guideline is:

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Wilkinson power divider

Start with the simplest possible case. Write down what Wilkinson power divider 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 Wilkinson power divider 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 Wilkinson power divider 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 Wilkinson power divider

In research: Wilkinson power divider 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 Wilkinson power divider 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: Wilkinson power divider is common in secondary-school and first-year university syllabi. It links to neighbouring topics Microwave technology, Radio electronics, so understanding it makes those chapters shorter.
In everyday life: Look for Wilkinson power divider 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.

Ask Teacher Smith questions about this articleOpens your AI tutor with a question about “Wilkinson power divider” →

Affiliate

Preply — study more efficiently by working with a personal tutor. 50% off.

How to study Wilkinson power divider in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Wilkinson power divider 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 Wilkinson power divider out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Wilkinson power divider in simple terms?

Why does Wilkinson power divider 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 Wilkinson power divider?

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 Wilkinson power divider.