Circular WG Frequencies, more accuracy, more experiment data.
- Category: Technical Articles
- Published: Friday, 01 May 2020 18:26
- Written by Dick Knadle, K2RIW, SK
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RIP Dick, K2RIW,
To: The 10 GHz Savvy Microwave Gang.
From: Dick Knadle, K2RIW 7/3/1999
Re: Circular WG Frequencies, more accuracy, more experiment data.
1. INTRODUCTION -- I've received 8 E-Mails with some nice words of encouragement about circular WG. There seems to be a thirst for knowledge on this subject -- The "poor man's" high performance WG. Some people wanted the extra decimal places and some wanted more description of the 10 GHz 3/4" copper pipe experiments of "The Ten-X Group" on Long Island. Two years ago we burned a lot of "midnight oil" at the QTH's of N2LIV (Bruce, the president) and N2NKJ (Ron) while performing the pipe WG experiments. On the fourth night in three weeks, we again ended our experiments (with blood shot eyes) as the sun was rising; we then knew we were pretty serious or a little crazy.
It was the Shepherd's Crook Dish Feed assembly of the San Bernardino Microwave Society (WA6EXP design, I believe) that got us started in the experiments. At first there were a few East Coast microwaver's who thought the 3/4" copper pipe WG feed assembly (with four elbows) would have high loss; we found that it actually has about as low a loss as you can get.
Here is a repeat of the previous submission, with the new info added. I'll warn you, this is long-winded (about 5 pages). If your server won't let you receive it all, I can divide it up, if you desired.
2. CIRCULAR WG FREQUENCIES -- If a 3/4" water pipe had exactly 0.7500 inch inside diameter, it would support the TE11 circular mode (the Dominant mode) between the absolute min/max frequencies of 9.225 GHz and 12.045 GHz.
Here are the first 6 cut-off, "absolute" frequencies (no guard bands) for 0.7500" ID pipe:
Frequency (GHz) Mode(s), Circular
9.225 to 12.045 TE11
12.045 to 15.301 TM01
15.301 to 19.192 TE21
19.192 to 21.053 TE01 & TM11
21.053 to 28.002 TE31
Above 28.002 TM21
Some day I'll explain where all the extra digits are coming from. We've devised a way of getting Bessel functions to 12 decimal places; I was on a project that needed that.
3. FREQUENCY SCALING -- Once you know the ID of your "pipe", you can scale all these frequencies. So-called 3/4" water pipe comes in K, L, and M styles where each has a different wall thickness and slightly different ID.
There are also multiple kinds of soft copper pipe, as well as some corrugated pipes, that will make great "semi-rigid" waveguide that can be bent Around corners. You can measure the exact ID of your pipe with calipers and inversely scale all the above frequencies accordingly (bigger diameter is a lower frequency for each mode). If you intentionally deform the soft copper pipe with a good roller mechanism, you will make "poor man's Elliptoflex".
Elliptoflex has a slight loss increase (for the same circumference) but it forces a particular polarization and has a slightly wider frequency range for the dominant mode. More on elliptoflex at another time.
The mathematics called Bessel functions predict FM modulation and circular WG characteristics. Most of the books on circular WG are not Very clear. One kind of Bessel function, of multiple sets, predicts the TM circular modes and the other kind of derivative Bessel, of multiple sets, predicts the TE circular modes. There's got to be a better way that "they" (or we) can explain all this.
4A. BOOK #1 -- The best reference I've found on the subject (I had to read the circular WG section ~ 10 times) is, Theodore Moreno, "Microwave Transmission Design Data", Dover Publications, 1948 (original), 1958 reprint, available for $8.00 at ABEbooks.com, book # 01775.
4B. BOOK #2 -- Concerning WG components, here's THE BOOK: George Southworth, "Principles and Applications of Waveguide Transmission", D. Van Nostrand Co., 1950; 689 pages (an oldy but goody). It contains some of the best PICTURES of how rectangular and circular WG really works with lots of performance curves (you won't need the math to understand the pictures (pages 166 & 169), it's almost an animation) -- amazing stuff for 1950. Page 121 (A & B) has pictures are 21 of the circular WG modes (with the relative sizes of pipe shown, same frequency) made with an "RF absorbing camera".
The book shows some great transition devices, hybrids, mode killing devices & devices for launching higher modes (pages 354 to 362), round WG components (pages 269, 327 & 328), circular guide fin line (page 133), a great section explaining choke flanges (page 201), a circular pipe polarization rotating device that's "home brewable" (page 207), the shapes of circular and rectangular WG (of constant periphery) that give minimum loss (page 193)(the popular ones are not optimum), "skeleton WG" (page 175), about 15 kinds of WG irises (page 246 & 255), circular WG filters (page 307), the Qualcomm duplexing filter explained (page 309); linear, binomial, gaussian, and exponential WG impedance stepping functions for broadband impedance matching (pages 269 to 276), 14 designs for dummy loads (pages 368 to 371), about 25 attenuator designs.
(Southworth continued) rotary vane phase shifter (page 333), rotary vane attenuators defined (page 375), a way of designing a variable conductance dissipative film (page 377), 33 pages of horn data (only portions have appeared in other WG or antenna books), 8 kinds of "backfire" feeds including the Cutler (pages 448 to 454), eight types of WG slot antennas (pages 425 & 430), five kinds of corner reflectors, waveguide lens antennas, some TWT and magnetron info, etc. The picture on page 186 shows me how I could make S-band WG out of rain gut ter down spout tubing. Let a Microwaver stand in a good hardware store with that book in hand and I think he'll get some great and crafty microwave ideas.
5. SAME WG MODES -- It is interesting to note that the main pipe WG mode, TE11 circular, and the main rectangular WG mode, TE10 rectangular, are the exact same mode. They use a different definition of the subscripts for circular and rectangular that makes them look different, they're not.
Once we realize this it becomes easy to construct (HOME BREW!) devices that transition from rectangular to circular. We of the Long Island "Ten-X Group" of microwaver's did a fair number of experiments in this area two years ago.
Here are some of the results.
6. RECTANGULAR TO CIRCULAR TRANSITIONS -- Our "Elegant Transition" was a carefully constructed slow transition (over a 1 foot length) from rectangular to circular. It had an S11 of -35 dB (VSWR = 1.04). A "sloppy transition" was made by crushing one end of a 3/4" copper pipe in a vise and forcing it into a WR-90 WG flange. It had an S11 of -23 dB (VSWR = 1.15). To make these measurements we used that Super WR-90 20 dB coupler (50 dB of directivity) I described on the Reflector on 5/28/99 (A Singer/Alfred Model 950786).
7. DUMMY LOADS -- In circular WG are quite easy to construct. Simply sharpen a 3/4" broom stick handle and force it into the 3/4" copper pipe. About 3" of taper and 2" of non-taper is FB. The usual moisture in the wood makes a great "slow absorber", which makes it more forgiving of errors. The main difference between a -35 dB S11 dummy load (VSWR = 1.04, [sharp tip]) and a -20 dB S11 (VSWR = 1.22) seems to be how sharp the point was at the tip of the broom stick handle and was the taper too abrupt (too short). There may be some variations caused by knots in the wood, but we didn't seem to have that problem.
The completed circular WG dummy load consists of a ~ 7" piece of 3/4" pipe with the tapered broom stick handle (absorber) in it plus a copper pipe coupler at the open end. Some of the broom stick absorber can stick out the pipe far end, if you prefer. It is easy to place this load on any other piece of circular WG, while running component tests. These really are "sexless" connectors. For experienced rectangular WG users, it will feel strange to make connections in 2 seconds and not worry about screwing down the flanges to get a good VSWR.
8. LAUNCHERS -- A circular WG to SMA launcher consisted of a 3/4" copper pipe end cap, soldered onto ~ 1.5" length of 3/4" copper pipe and an SMA Female to Female (bullet) is fed through a hole in the side of the end cap plus pipe, ~ 1/4 wave away from the closed end (it is either threaded into the end cap and use a nut or solder it). A ~ 1/4 wave long wire probe inside does the launching. A pipe coupler is slipped over the 1.5" length of pipe that protrudes. The completed launcher can be placed on any piece of circular WG in 2 seconds by the "sexless" connector (pipe coupling) method. Proper adjustment of the position and length of the probe wire is a bit tedious.
Place a circular WG load on the launcher output and measure the VSWR at the SMA connector to find the proper probe length; it's an unambiguous operation. Once you get the hang of it you will make quite a number of launchers at once. The one component of the launcher that costs anything is the SMA bullet.
9. PADS -- We never did this, but it would be easy to design circular WG fixed attenuators by decreasing the length of broom stick absorber and tapering both ends to have a good impedance match from either direction. In this case I would recommend painting the absorber to keep the moisture content (absorption) constant.
10. COUPLER (SEXLESS CONNECTOR) -- There is a kind of copper pipe coupler that has no internal ridges or dimples. These will allow the 3/4" pipes to directly touch (butt against each other inside the coupler) without any gap. A gap will have a larger inside diameter, within the coupler. Even with a gap, the VSWR impact was very small. If these couplers are unavailable, a purist can remove the ridges or dimples with a round file or an adjustable reaming tool. However, you will find that the molded copper fittings are hardened and the reaming/filing operation is a quite difficult.
11. OTHER COMPONENTS -- We discovered that many of the hardware store 3/4" plumbing fittings were almost "designed" for us microwavers. A 45 degree elbow and a 90 degree elbow gave us VSWR's of ~ 1.3 and 1.4, as I remember. The copper pipe "coupler" makes a great trombone and polarization twister. The end caps are a great way of constructing 3/4" circular to SMA launchers. When the circular WG components are properly plugged together with "sexless" connectors, we haven't found any fittings that change significantly in VSWR as you do or do not solder them. Test everything by plugging them together, solder them later. Soldering seems to only be required for mechanical reasons.
You will find that many circular WG components are VSWR sensitive to rotation (at the sexless connectors). Many circular WG objects can create elliptical polarization. Southworth's book covers this subject on page 206.
A liberal sprinkling of septums within launchers, horns, etc. will force a linear polarization at the output point (usually without loss) and they insure that the elbows and other non-symmetric components don't create elliptical polarization. A septum consists of a thin sheet of metal soldered across the diameter of the circular WG at right angles to the desired polarization. A screw protruding into the guide makes a great way of correcting VSWR; however, depending on its polarization, it could also create some elliptical polarization -- so use a septum in the vicinity of the circular WG output.
Find the best location for the screw by using a steel BB inside the WG and positioning it with a magnet on the outside. Copper transitions from 3/4" to 1" and 3/4" to 1.5" make nice feed horns.
A 3/4" soldered-pipe to threaded-pipe adapter makes a convenient flange for the center of a dish antenna. That's where you feed the Shepherd's Crook 3/4" circular WG through the dish. Two large washers and a large nut can hold this assembly in the dish center. It is also possible to mount a copper 4 hole flange to the back of the dish center and feed the round WG through it. In each of these cases it will be necessary to ream out the shoulder within the fitting to allow the 3/4" pipe to pass through the fitting. We purchased a mechanically adjustable ream to accomplish this. The operation was quite difficult because of the hardening of the molded fittings. With a lathe this operation was a lot easier, when there was enough metal to mount in the lathe chuck.
12. WG POLARIZATION -- I must give you a warning. If you are using a long length of pipe as WG up your tower (K2TXB and W2DRZ did this), the ellipticity of the pipe (the "run out") could cause a horizontal polarization, launched at the bottom, to become a vertical polarization at the top of the tower (the polarization can rotate). By simply rotating the launchers at the top and bottom of the WG, you will find the lowest loss combination for that "pipe WG". There is this added danger; when you are in your Home Depot Hardware Dept., with your calipers, while buying 10' lengths of pipe that have no run out, you will find the following: (1) one pipe in 3 has almost no run out, that's the ones you want to buy; (2) The Department Foreman will watch you during this process and he will say, "Oh no, another one of those crazy engineers who's doing a precision plumbing job in his house!" You will have to suffer some ridicule in the pursuit of your art. You probably will not succeed in explaining what you are really doing, just remember -- you're tough and can take this ridicule, you are pursuing a far off goal, that great 3 cm DX!
13. CIRCULAR WG DISH FEEDS -- For a 0.6 F/D dish, the W2IMU Dick Turrin Horn intentionally launches the TE11 and TM11 circular modes at just the right amplitude ratio and relative phase. That's what gives it such a beautiful pattern; no edge currents, no sidelobes and great control of the electronic phase center versus azimuth, elevation, or diagonal scans. Any shift in the electronic phase center of a horn versus observation angle creates the same antenna pattern degradation as if you had the same amount of error (like a dent) in that area of the parabolic reflector it is illuminating. With this understanding, it becomes more obvious why this horn achieves higher dish efficiency. For deeper dishes (~ 0.3 F/D) the Scalar feed (the one with the multiple rings) does almost the same job.
But, be careful; the W2IMU multi-mode circular horn can get a microwaver involved in an altercation or a law suit. I constructed my 2287.5 MHz W2IMU horn from food cans for Apollo 15 and 16 reception "Houston This is Apollo" (QST June 1972) and "A 12 Foot Stressed Parabolic Dish Antenna" (QST August 1972). I measured the diameter of all the food cans in the local super market. The store manager became alarmed. and asked me to leave. He thought I was a Ralph Nader advocate and was about to start a litigation (I had to endure ridicule way back then too). I settled on Scotts Oatmeal cans, purchased from a Foods of All Nations Store; they had the correct diameter for the launcher and RHC polarization section.
14, CONCLUSION -- I hope y'all enjoy the above info. There are a few more 10.368 GHz 3/4" copper pipe experiments to be described later. Please feel free to correct the errors or add to the info.
73 es Good SHF DX,
Dick, K2RIW, FN30HT84DC27