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New for October 2024. The Bagley divider a purely reactive element. Therefore, it offers no isolation between the outputs, unlike a Wilkinson power divider. However, it may have its uses in antenna feeds. It provides odd number of divisions, 3, 5, 7....
Bagley background
Thanks to Chris, we have located a reference that gives credit for this design to "G. Bagley". The reference is the "Antenna Design Handbook, Volume 2" by Runge et al. You can buy a used copy on Abe Books for short money. Here is a quote from that book:
"18.10.2 The Bagley Polygon
This device can be used as a signal combiner or power splitter. It can be thought of as a generalized form of rat race… It was devised by G. Bagley or the RAE Antenna Group, Farnborough."
G. Bagley turns out to be Geoffrey Charles Bagley. He holds three US patents, none of them mention a power divider.
Let's look at a timeline of a particular Bagley patent, number 7,835,421: Bagley filed "Electric Detector Circuit" for US patent in 1982, while working for Royal Signals and Radar Establishment (RSRE). The US bound it up with a secrecy order for decades, meanwhile, here is what happened to RSRE according to Wikipedia:
In April 1991 RSRE amalgamated with other defence research establishments to form the Defence Research Agency, which in April 1995 amalgamated with more organisations to form the Defence Evaluation and Research Agency. In June 2001 this became independent of the MoD, with approximately two-thirds of it being incorporated into QinetiQ, a commercial company owned by the MoD, and the remainder into the fully government-owned laboratory DSTL. In 2003 the Carlyle Group bought a private equity stake (~30%) in QinetiQ.
In 2010 the US secrecy order on Bagley's application was withdrawn and patent 7,835,421 was issued and assigned to QinetiQ. It does not expire until 2027. More recently (around 2020) some funny business occurred and a company called Castlemorton Wireless LLC acquired the patent. Castlemorton is a part of QinetiQ, and it seems like it was specifically created so that a publically-traded company with 6,000 employees kept their name out of the news while trying to win a high-stakes lawsuit lottery.
Castlemorton is what is politely known as a non-practicing entity (NPE), or the slang term "patent troll". They don't have a website, because they want to fly under the radar. Learn more about patent trolls here. Castlemorton seems to have been formed just to exploit just the one Bagley patent. For a excellent description of the Castlemorton's patent activities read "The Patent That Keeps. On. Going". They claimed anyone using IEEE Wi-Fi 802.11b and Wi-Fi 802.11g wireless standards is infringing on the "421" patent. Castlemorton Wireless LLC is the plaintiff in 31 lawsuits. Here are just a few of the lawsuits they propagated into the court system:
Castlemorton versus Pioneer/Onkyo
Castlemorton versus Ale
Castlemorton versus Bose
Castlemorton versus Newell
Etc., etc. They are all essetially the same, wth only the defendant's information changed from one to the next. BTW, it looks like many if not all of of the lawsuits have been dismissed. Some lawyers made a lot of money, and QinetiQ had to write it all off. No mention of the effort is in any of QinetiQ's Investor reports.
Thanks to these frivolous infringement lawsuits you can learn a lot about Bagley's life, as well as some cool history of Royal Signals and Radar Establishment (“RSRE”), a scientific research organization that was part of the Ministry of Defence of the United Kingdom. Castlemorton needed to include a history lesson in each lawsuit. We can all thank Castlemorton lawyers for doing us a solid, even if they are bottom feeders. They even included a undated photo of Mr. Bagley, he is in the standing row, second from the left.
RSRE can lay reasonable claims to inventing (or at least envisioning) the integrated circuit, satellite tracking (starting with Sputnik 1!) the touch screen monitor, and the internet.
Bagley was a well-respected and widely-known researcher, though much of his work was probably classified at the time. His career started in the 1950s and he was a member of the Radio Society of Great Britain for over 70 years. He is listed "in memoriam" on the Ancient Society of College Youths website as having passed on in either 2020 or 2021. He was probably was rolling in his grave during the recent legal activities.
The Bagley power divider
The Bagley power divider is also called the Bagley polygon divider, for reasons that will become obvious as you read this page. The divider is made up of an odd number of half-wavelength segments, with the input being in the middle of one segment and all of the outputs being at the polygon's vertices. Here is the simplest version, a three-way triangle. In life, the triangle may be associated with love; the three vertices being you, your significant other, and your side piece. Good luck to all involved!
Here is a five-way Bagley pentagon. In the United States, the Pentagon is the center of our military, near the nation's capital, Washington DC. It was constructed on an accelerated schedule during WWII. The pentagon is related to the pentagram, (a five-pointed star) which holds special meaning to Pythagoreans (it exhibits the Golden ratio), as well as modern-day Wiccans.
Here is a seven-way Bagley, a heptagon. The heptagon seems to have no cultural significance, but you will be cursing it when you lay it out, as the internal angles are 128 and 4/7 degrees!
Now let's look a schematics of the Bagley divider, starting with the three-way. All of the lines in the polygon have the same characteristic impedance, which is Z0*2/SQRT(N), with N being the number of divided ports (3, 5, 7...). For fifty ohm system it works out to ~58 ohms for the three-way. That is one of the beauties of this design, the ring impedances are easy to achieve. In all of the schematics below, the common port is on the left and the split ports are on the right.
And here is the response, a perfect 4.77 dB loss (1/3 the input power, converted to decibels). We are not going to insult your intelligence by plotting isolations or split port return loss, they all suck.
Now you are probably thinking, where have a seen a ring structure that is 3/2 wavelength in "diameter?" If this did not occur to you, consider a career change to selling time-share vacation homes. One such network is the Gysel. It looks a lot like the Bagley but the middle split-port has been eliminated and isolation resistors added to two nodes.
For comparison, here is the two-way Gysel response, a 3-dB power split. How about that, it has almost the same input match as the Bagley triangle!
Moving along, here is the Bagley five-way (pentagram) schematic. Note that the ring impedance here is ~45 ohms, again, it is readily achievable.
Here is the five-way response, a seven-dB power split. You should be able to do that dB conversion in your head. Note that the bandwidth of the network is reduced the more arms you add.
Finally, here is the seven-way schematic. Ring impedance is now 38 ohms, relatively fat lines in microstrip but not a problem at all.
Here is the seven-way response.
Before we end this page, let's take a look at the transmission phase relationship between the outputs on a Bagley divider. As you can tell by the schematics, the distance that some outputs travel can be multiple half-wavelengths compared to others. Below is the the seven-way divider phases for port 2, 3, 4 and 5 arms. They differ by 180 degrees. Consider this when you are creating a feed network.
Go to our download area and get the Microwave Office file that generated the plots on this page!
References
There are many good references on Bagley power dividers, making compact versions, unequal-amplitude versions, etc. Pier Journal has a nice paper and it is free to download.
https://www.jpier.org/issues/volume.html?paper=17051101 arbitrary power ratios, different termination impedances
https://www.jpier.org/issues/volume.html?paper=11011604 related design with even number of ports