# N-way Wilkinson splitters

Click here to go to our general discussion of Wilkinson power dividers

Click here to go to our main page on couplers and splitters

Click here to go to our page on the Lim-Eom three-way splitter

Click here to go to a page on the Kouzoujian N-way splitter

Here's an analysis of planar three-way Wilkinsons.

New for January 2017: here's a method for creating any N-way power divider based on a cascade of two and three-way dividers.

Here's a page contributed by Paul Hubbard and Greg Ordy, on N-way, unequal split Wilkinsons.

Here's an example contributed by Kjer of a broadband eight-way splitter.

Here's an example contributed by Limey Mark of a unique four-way splitter.

Ernest Wilkinson's original paper was on an N-way combiner, and it is only fitting that we should deal with the subject of higher-order Wilkinson splitters here.

For N-way combiners, the number of arms is equal to N, while the number of ports is equal to N+1, at least that is the convention we will maintain here.

Radial combiners are called that because they have radial symmetry. Above N=2, the splitter cannot be laid out in two dimensions.

For N=3 split, there are two ways to realize the isolation resistors, the "star" and "delta" configurations.

A three-way Wilkinson is shown below, with "star-resistor" configuration. The arms have impedance SQRT(3)xZ0, and the resistors have impedance Z0. By the way, the figures below, and many more, are available in our download area in a Word file, ElectronicSymbols.doc, for you to use in presentations and papers.

The next figure shows a three-way Wilkinson with the "delta" resistor configuration. The arms again have impedance SQRT(3)xZ0, but now the resistors have impedance 3xZ0.

Now that we've looked at the three-way Wilkinson, it is easy to guess what higher-order Wilkinson combiner resistor networks look like. We'll give you a hint... Every port has to be connected to every other port symmetrically. The "delta" resistor pattern gets really ugly, so stick with the star pattern for N=4 or higher.

Let's state the rules for arm impedance and isolation resistors of N-way Wilkinson combiners as a Microwaves101 rule of thumb:

For a basic N-way Wilkinson combiner, the arm impedance is SQRT(N)xZ0. If you use star resistors, they are equal to Z0. If you use delta resistors, they are equal to NxZ0.

### Planar N-way Wilkinson combiners

In many instances, it is more convenient to use a two-dimensional approximation of the radial Wilkinson shown above. In this case, one of the resistors is deleted from the layout, and a "fork" arrangement is the result.

Go here for an analysis of three types of three-way splitters, in 50 ohms (very basic).

In the figure below, contributed by Lou from Honeywell, a two-stage, three-way planar Wilkinson is shown, along with its predicted responses (thanks, Lou!) Note to readers: this is a very specialized splitter, it provides 12.5 ohm impedance for the split ports and 50 ohms at the combined port.

What does this do to performance? The primary thing that you give up is isolation between the arms. Instead of greater than 20 dB, you might get 15 dB isolation. Also, there will be measurable differences between the inside and outside arms.

### An example from Limey Mark

Limey Mark is a good frend of the Microwaves101 message board and cotributed this novel design technique during October 2006. Thank you sir! Now in his own words...

It is possible to make a N-way splitter on microstrip with no cross over. This technique has been done at 100MHz. I would be interested to see if any one can do this at a higher frequency.

Below you will see the image of a four-way splitter. This representation was â€˜knockedâ€™ up in my garage with some old copper foil and a clapped out Weller soldering iron so my apologies for the unprofessional approach.

First of all this is not a multi layer board. This is a single layer board the copper ground plane is visible in the photo. There is a dielectric and another copper plane, which is where the track has been etched and is the top of the board.

Look at the photo and for the time being ignore the air brush red and yellow lines. What you see is the ground plane and four 2512 surface mount chip resistors soldered in a star point configuration, the black air brush around the solder joints are the etching which isolates it from the ground plane.

Now use your imagination and see an isolated via/post from the four outer solder joints to the top of the board.

The yellow lines represent (though not to scale) the four 90 deg 100ohm lines, the red lines are the four 50 ohm lines which between them intersect the four viaâ€™s.

Hey presto no cross over!

The board is placed on to a suitable recessed hole for the resistors.
Now obviously there will be issues at higher frequencies but I would appreciate any feed back. Good luck.

## N-way power dividers using cascaded two and three-way Wilkinsons

New for January 2017! how about five-way, six-way, seven-way power dividers?  At some point it becomes a fool's errand making a direct connection from one port to N ports. You are much better off using lower-order power dividers in cascade.  And what about odd numbers like seven-way? Some designers might create an eight-way cascade of two-way dividers (very simple!) and terminate one port, which is throwing away 1/8 of your available signal. A more efficient way is to use a combination of two and three way dividers.

This idea is credited to Ernest from Werbel Microwave (thanks!)

A useful technique for creating a "true 5-way splitter":

Common port connects to an unequal 60/40-split Wilkinson.

Let output A be the 60% (-2.21dB) path. Let output B be the 40% (-3.98dB) path.

Output A cascades to a true 3-way splitter (20% per port * 3 ports = 60%).

Output B cascades to a true 2-way splitter (20% per port * 2 ports = 40%).

Done.

Can be applied to 7-way and 10-way (2 x 5-ways as described above with a 2-way at the input) also.

The advantage is to achieve a 5-way split while minimizing the insertion loss, versus a 6-way where one output is terminated.

Note that antenna feed networks often need elaborate N-way power division, with unequal power splits to each element to form a tapered aperture.  Antenna engineers often cheat and leave out the isolation resistor (so-called reactive power dividers but it is the same idea).  Can someone send us a discussion on that?

Author : Unknown Editor