Understanding Circular Waveguide—Experimentally

1 Jan/Feb 2001 37 Old-fashioned microwave Paul Wade, W1 GHZ161 Center RdShirley, MA CircularWaveguide Experimentally1 Notes appear on page is an excellent mi-crowave transmission line,with low loss and predictableperformance, usable at any frequencyby choosing the proper dimensions. Themost common type of commercial wave-guide is precision rectangular tubing,which is only affordable on the surplusmarket. Elliptical waveguide is alsoused commercially for microwavetransmission line. Many microwavestructures, particularly antennas, havea round cross section and are bettersuited to Circular (cylindrical) wave-guide. Unfortunately, commercial cir-cular waveguide is rare and unlikely tobe found surplus. As luck would have it,ordinary copper water pipe works justfine and is universally available at lowcost. In particular, 3/4-inch copper pipeis perfect for 10 microwave design today is donewith the aid of computers. However,only a few programs handle electro-magnetics with the capabilities re-quired for Circular waveguide , and theirprices are somewhere between a fancycar and a new house.

2 Solving the prob-lems without good software involvessome difficult math, and the solution isprobably only approximate. The re-maining alternative is old-fashionedempirical microwave ham s favorite design technique,reverse engineering (copying some-thing that works!) is made difficult bythe lack of commercial Circular - waveguide examples. Reference bookshave extensive information on rectan-gular waveguide but very little infor-mation on Circular waveguide . The pio-neering work on waveguides was doneby George Southworth before WorldWar II, but I only recently located acopy of his I was afraid that Ihad duplicated some of his work, butthat s a good way to learn. On firstreading, it appears that he did a lot ofwork on waveguide fundamentals, butvery little on waveguide -to-coax tran-sitions, probably because good coaxialcable and connectors were not avail-able prior to the wartime WaveguideWe all know that electromagneticReprinted with permission; copyright Jan/Feb 2001waves travel through space that swhat radio is all about.

3 They can alsotravel inside a hollow pipe of any shape;if the dimensions are right, the pipemakes a very low-loss transmissionline, much better than any coaxialcable. In order for the waves to travelwith low loss, the pipe dimensions mustbe large enough for the lowest-orderwaveguide mode, the TE11 mode, topropagate. In Circular waveguide , thecutoff wavelength for this mode D (diameter) so the minimumwaveguide diameter is 1 , . The diameter of the copper wa-ter pipe I used is nominally 3/4-inch,type M, which has a larger inner diam-eter than other types. The typical innerdiameter is inches, but that mayvary slightly because this is not preci-sion tubing. Thus, the cutoff wave-length is inches, so the minimumfrequency is GHz. Clearly, 10 GHzis comfortably above the in the other direction, alarge waveguide diameter would per-mit additional higher-order wave-guide modes to propagate. While theadditional modes also propagate withlow loss, they often arrive at the farend with different phase, so that theyinterfere with the TE11 wave and weare unable to extract them withoutlosses.

4 The next mode, TM01, needs aminimum diameter of to propa-gate, setting the maximum operatingfrequency without any additionalmodes. For the 3/4-inch pipe, this up-per frequency limit is GHz, butit isn t a hard limit like the lower cut-off frequency. At higher frequencies,the waveguide still propagates en-ergy, it s just difficult to predictablycouple that energy , a hollow round pipe is an ex-cellent waveguide for wavelengths be-tween and times the insidediameter. Standard USA 3/4-inch cop-per water pipe, type M, has an innerdiameter of at GHz, so itis ideal for 10-GHz operation. It isreadily available in almost any hard-ware store at a cost much lower thanthat of coaxial cable suitable for VHFuse. Copper water pipe does come inother versions, but type M is preferablesince it has the largest inner design style is old-fashionedempirical microwave engineering. Empirical is a fancy word for cut andtry, but it is only engineering if wemake measurements, record data andtry to understand the most important measurement weneed is impedance in the , impedance measurements aremade using a network analyzer, prefer-ably one that is automated, with com-puter control and error aren t any waveguide networkanalyzers; they are all based on coaxialtransmission lines.

5 For the most popu-lar standard sizes of rectangular wave-guide, good coaxial transitions and cali-bration kits are available to allow net-work-analyzer measurements, with thecomputer correcting errors caused bythe transitions. Of course, none of thisis available for Circular waveguide ifwe had a quality coax transition to copy,we d be one giant step closer to usingcircular network analyzers, micro-wave impedance measurements weremade using a slotted line. A narrowlongitudinal slot in the outer conduc-tor of a coaxial line does not interruptany current flow in the line, so it has noeffect. A small probe may be insertedin the slot to measure the voltage in theline, and moved to measure the voltageat other points along the line. If the lineis mismatched, the voltage varies in apattern referred to as a standing , we measure the ratio be-tween the minimum and maximumvoltages of the standing wave and callit the standing wave ratio, or a slotted line is becoming a lostart, but the technique is covered prettywell in a recent book by waveguide , a slot will have no ef-fect if it does not interrupt any rectangular waveguide , this locationis easy to find.

6 It s in the center ofthe broad wall. In Circular waveguide ,there is no obvious orientation; we mustorient the guide so that the E-field issymmetrical around the slot and theprobe is parallel to the built a slotted line for Circular wave-guide by cutting a longitudinal slot in apiece of 3/4-inch copper pipe. To fit thepipe to a surplus slotted-line carriage,I made a pair of plywood blocks. Thecarriage is designed for interchange-able line sections of coax or differentsizes of rectangular waveguide , so thecircular section had to fit the samemounting points for the probe to travelin the slot correctly. Fig 1 is a photo-graph of the slotted line. Later, I founda sketch3 of Southworth s slotted line section was similar, but with-out the advantage of a surplus carriage,he had to build a sliding mechanismas feed RF energy to the slotted line,I started with a surplus coax-to-WR-90rectangular waveguide section. I thenmade a rectangular-to- Circular transi-tion by hammering one end of a 3/4-inchcopper pipe until it fit into a WR-90waveguide flange.

7 This makes a goodtransition if the shape is a long, smoothtaper. I added a WR-90 isolator be-tween the coax transition and the ta-pered section to absorb any reflectedpower so that the signal generatorwould not change frequency or poweroutput due to loading. Finally, at theinput to the slotted section of pipe, Iadded a septum (a flat plate across thediameter of the pipe) perpendicular tothe probe; only energy polarized paral-lel to the probe will propagate past theseptum. This polarization is important,so that the E-field is parallel to theprobe otherwise the probe and slotmight upset the fields and convert en-Fig 1 Homebrewslotted line forcircularwaveguidemounted in asurplus 2001 39ergy to unwanted waveguide modes,with unpredictable results and voltage in the slotted line issampled by the probe inserted throughthe slot; if the probe is inserted too far,it will affect the fields in the waveguideand produce erroneous readings.

8 Onthe other hand, a deeper probe producesmore output voltage, so less RF poweris necessary for the measurement. Theproper probe depth is found experimen-tally, by increasing the depth until themeasured SWR starts to change, thenbacking probe assembly shown in Fig 1contains a diode detector with a tuningmechanism; when it is adjusted forresonance, much more detected voltageis available. The output from the detec-tor goes to a standing-wave meter suchas an HP415; other manufacturersmade similar instruments. The meteris an ac voltmeter tuned to 1 kHz, sothe RF source must be AM modulatedat 1 kHz; most signal generators havethis the slotted line was working, Iquickly discovered two things:1. The wavelength at 10 GHz isnearly twice as long in 3/4-inch wave-guide as it is in free This means that the probe musttravel near the end of the slot to mea-sure a full the probe approached the ends ofthe slot, I could see that there was aneffect. A well-matched horn antennahad a low indicated SWR with the probenear the center of the slot, but a higherindication when it was near the commercial rectangular-wave-guide slotted sections taper the end ofthe slot to a point, I used a tapered fileto trim the ends of the slot to smooththe in the waveguide ismeasured by shorting the end of thewaveguide with a flat plate; this pro-duces a standing-wave pattern with anull every /2 from the short.

9 I knewthat guide wavelength, g, would belonger than the wavelength in freespace, 0, (phase velocity is greaterthan the speed of light), but hadn trealized how much longer. Fig 2 shows g versus frequency; as the cutoff fre-quency is approached, g increasesdramatically, while 0 increases lin-early with decreasing is measured and calcu-lated graphically by plotting SWR andphase on a Smith chart. Phase is mea-sured by the location of the standing-wave minimum voltage on the slottedline. The distance between two stand-ing-wave minimums is g/2. With ashort circuit on the end of the slottedline, we can locate two voltage nulls onthe line to provide the reference pointsfor our measured location. A classicSmith chart has a wavelength scalearound the perimeter that is used toplot phase; the circumference of thechart equals a Smith chart, the impedance isnormalized to the characteristic imped-ance of the transmission line. Commoncoaxial lines have characteristic imped-ances near 50.

10 For waveguide , we usewave impedance rather than character-istic impedance. The wave impedancefor TE modes in Circular waveguide iscalculated as:Z0=Zfs g 0 (Eq 1)where Zfs is the impedance of freespace, 377 . From Fig 2, the guidewavelength, g is longer than the free-space wavelength 0, so our circularwaveguide impedance is greater than377 . Unlike coaxial transmissionlines, the impedance varies with fre-quency. At GHz, Z0 is about650 ; however, it is about 1130 at9 GHz and 580 at GHz. For ourpurposes, the exact impedance doesnot matter, as long as we can match itempirically and achieve a low SWR. Infact, I did not calculate Z0 until afterI had completed all the experimentalwork described phase measurements, the slottedline includes a vernier scale to measuredistance traveled; the scale is quiteaccurate if used carefully. However,once I realized that many slotted-lineFig 2 Wavelength does not vary linearly in 3/4-inch Circular 3 Construction of a 3/4-inch pipe waveguide Jan/Feb 2001measurements would be required, Iadded a dial indicator (shown in Fig 1)to the slotted line.