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Differential and Common Modes on Transmission Lines – Part I

July 25, 2022 Martin Blustine

Introduction

In Part I of this three-part series, we discuss what is meant by differential and common modes on RF transmission lines. Part II will discuss the construction of the Joe Reisert, W1JR, 1:1 balun [1] that may also be used as a common mode choke. Part III will present some test results for the common mode rejection of two common mode chokes, one constructed with #31 ferrite material and another constructed with #43 ferrite material.

Differential Mode

Two familiar balanced transmission line types that will support differential mode operation are open wire line and waveguide. This section will focus on open-wire lines. An ideal model of an open-wire line is shown in Figure 1. Current from the transmitter or other matched source enters the transmission line from the left. The transmission line may be thought of as an infinite number of distributed inductors and capacitors. Each infinitesimal length of the transmission line is made up of two tiny inductors, and each infinitesimal pair of lines forms a capacitor between them. All transmission line types, not only open wire lines, are characterized by values for inductance per unit length and capacitance per unit length.

Figure 1 Idealized Model of Open Wire Transmission Line. An open wire transmission may be modeled as an infinite number of distributed inductors and capacitors.

In reality, the conductors will have a resistance per unit length. If there is a dielectric present, as there might be in a window line, twin-lead or open wire line (the dielectric would be the spreaders and air), there will also be a leakage conductance through the dielectric between the conductors.

Consequently, all transmission lines are characterized by an impedance, Z_0, that is defined by,

where,

Z₀is the characteristic impedance in ohms

R is the resistance of the wire per unit length

G is the leakage conductance through the dielectric per unit length

L is the inductance of the transmission line per unit length

C is the capacitance of the transmission line per unit length.

Years ago, it was quite common for roof-mounted television antennas to be fed with 300-ohm twin-lead. Twinlead is a parallel wire transmission line in which the conductors are spaced apart with plastic dielectric. The dielectric fills very little of the volume around the conductors. There is just enough plastic to cover the conductors and space them a small distance apart. Consequently, twin-lead will be treated as though it were an open-wire line. If we assume that the resistance of the wire and the leakage conductance are negligible, we can make the approximations that,

As a result, the impedance of the transmission line may be simplified to,

By making further approximations that the wire diameter, d, is much smaller than the center-to-center spacing of the conductors, D, and that the value of the dielectric constant filling the volume around the conductors is close to unity,

it is possible to approximate the values of L and C from,

where,

and,

where,

from which we get,

Furthermore,

Thus,

Substituting the numerical values, we have,

So, by making reasonable approximations, our estimate is very close to 300 ohms.

When driven by and terminated in its real, characteristic impedance, the currents and voltages anywhere along the open wire transmission line will be mostly uniform. Assuming that the wire transmission line is well made, dissipative losses in the conductors and leakage conductance will account for any nonuniformity. Since the currents in the transmission line conductors are equal and travel in opposite directions, the transmission line is said to be operating in differential mode. Simply stated, the transmission line operates in a single mode, and what you put in one end is mostly what you get out of the other end. The transmission line will not radiate signals, nor will it receive signals and noise.

Figure 2 is greatly oversimplified, but it is adequate to explain what is meant by differential mode. We note that if we take a snapshot of the currents on each half of the dipole, i_1, and i₂, they are in the same direction as are the currents, i₁ and i₂, in the open wire transmission line. From this, we may conclude that the transmission line is operating in differential mode while the antenna is operating in common mode, and that is what is causing the antenna to radiate RF in the first place. At least for this case, we have demonstrated that we may associate common mode currents with antenna radiation (and reception, too).

Figure 2. Balanced Open Wire Transmission Line Feeds a Dipole Antenna. The unbalanced transmitter or transceiver is transformed to a balanced transmission line with a balun. The transmission line operates in a single, differential mode because the currents are opposite while the antenna operates in a common mode because the currents are in the same direction.

Common Mode

For completeness, let’s begin by calculating the characteristic impedance of an unbalanced coaxial transmission line. Coaxial cable was first employed to prevent interference between transmission lines in transatlantic cables used for telegraphy prior to 1860. It was Oliver Heaviside who first described its theory of operation.

Let’s determine the characteristic impedance of RG-400/U since our common mode chokes were constructed using this type of coax. RG-400/U was chosen because of its high power handling capability and small outer diameter. If the inner diameter of the coax shield is much greater than the diameter of the center conductor,

where,

d is the diameter of the coaxial transmission line center conductor
D is the inner diameter of the coaxial transmission line shield,

the inductance per unit length and capacitance per unit length for coaxial cable are approximated by the formulas,

where,

from which we obtain,

As before,

Substituting the numerical values, we have,

Again, reasonable assumptions lead us to the expected result.

When we speak of common mode for transmission lines, we are discussing signals that may enter or leave the conductors in the same direction. The most common cause of common mode current is an unbalanced transmission line. Imagine, if you would, a dipole antenna being fed by the coaxial transmission line of Figure 3. The currents inside the coax will be opposite. Now, suppose that the currents in the coax reach the antenna. If we take a snapshot of the currents on each half of the dipole, i_4, and i₂, they correspond to the directions of the currents, i_3, and i₁, on the inside of the transmission line (but not their amplitudes). From this, we may conclude from the currents on the antenna that the antenna operates in common mode, as before.

However, we also notice that there are currents, i₅, on the outside of the coax shield and the current, i₁, on the center conductor that are in the same direction. These currents operate in common mode. The outside of the coaxial cable shield operates as a single conductor transmission line, a distinct mode. This mode operates separately from the mode represented by currents i₃ and i₁, which operate in, essentially, differential mode. Thus, we have a transmission line system that operates in two distinct modes. The outer cable shield will radiate upon transmit and will be susceptible to receiving signals and noise upon receive.

Figure 3. Common Mode Currents on Unbalanced Coaxial Transmission Line. Because of its construction, there is no way to keep the current i₃ from dividing into currents i₄ and i₅. Since currents i₁ and i₅ are in the same direction, they operate in common mode. Since the currents i₁ and i₃ are in opposite directions, they operate in differential mode. Thus, we have a transmission line system that operates in two distinct modes. The common mode conductor will radiate and also be susceptible to receiving signals and noise.

To reiterate, since one side of our dipole antenna is connected to the shield, any current that is traveling inside the shield may split between the antenna and the outside of the shield. In this configuration, there is nothing to stop this from happening. Now, we have a center conductor and the outside of the shield acting like a pair of conductors with currents traveling in the same direction. This is very much like a single wire transmission line, and the outer shield will radiate and receive power quite nicely in common mode. Another observation is that the currents on the antenna halves are asymmetric, and this asymmetry will corrupt the antenna pattern. Notice that the current on the outer shield may be returned to the chassis of the transmitter. This can become very unpleasant for the operator.

A remedy for this is to convert the unbalanced coaxial line to a balanced line where it feeds the antenna and provides a means to suppress current i₅. This is done with a device called a choke balun (balanced-to-unbalanced). The choke balun effectively disconnects the inner shield from the outer shield so that most of the current will no longer flow on the outer shield. Can there still be common mode currents on the coax? The answer is yes. The shield can still couple some of the antenna’s radiated emission back to the shack, or signals and noise on the shield may originate from elsewhere. Either or both may occur because it’s not unusual to place a choke balun at the feedpoint of the antenna. RF can still couple to the coax beyond where the choke is located. For this reason, it is not unusual to place another choke at another current maximum on the coax outer shield where it may be effective and at a location that is close to the entrance to the shack. This point on the transmission line may be found with a clip-on antenna current probe like the MFJ-854 [2], or by modeling the antenna in something like EZNEC [3]. It is incorrect to assume that the placement of a common mode choke is arbitrary. If we want the common mode choke to work, it should be located near a voltage null on the outside coax shield. Another effective way to reduce the common mode signals and noise on the outer shield from reaching the shack is to bury at least some of the coax.

Baluns may be constructed from sections of coax or from wire or coax wrapped on ferrite cores. Baluns constructed from coax alone, rely upon the electrical length of the coax to work, so they tend to be narrow band. Baluns constructed from coax are more practical for UHF and VHF because of the short length of transmission line required. Coax baluns do not possess the same choking properties that ferrite baluns have.

Part II of this three-part series will discuss the construction of a Joe Reisert, W1JR, 1:1 balun that may also be used as a common mode choke.

References

Reisert, Joe, Simple and Efficient Broadband Balun, Ham Radio, September 1978, pp. 12-15. https://worldradiohistory.com/Archive-DX/Ham Radio/70s/Ham-Radio-197809.pdf
https://mfjenterprises.com/products/mfj-854
https://www.eznec.com/

Antennas, Featured, General, Newsletter

DIY 6m Moxon Antenna

July 17, 2022 Aron Insinga 1 Comment

The ARRL book Magic Band Antennas for Ham Radio by Bruce Walker N3JO has the plans for a 6m Moxon Antenna that I found interesting because, instead of wire or tubing, it uses 3/4″x1/8″ aluminum stock available in hardware stores in 4′ or 8′ lengths. No bending, just drilling! I’ve worked on it bit by bit over the last few months or so, and the CQ VHF contest this weekend gave me the extra push I needed to get it up into the air!

I got 8′ sections of the aluminum stock, but I cut the center of the parasitic element (the longest piece) into 2 pieces of less than 4′ each, in case I want to pack the antenna into a car.

The boom is PVC pipe, and for the spacers between the active element and the parasitic element, I used a 1-1/2″x3/4″ vinyl substitute for wood used for trim, which is also available in hardware stores. I cut it down to 3/4″ wide strips for the insulators between the ends of the elements. Unlike the book, I used the full width to attach the elements to the boom so that the U-bolts could be attached beside, instead of under and through, the elements. (It was not at all clear to me from the book’s drawing — no photographs — how the parasitic element was attached to the boom given the bolt positions as drawn. Also, I may have misunderstood if the author meant 1″ ID or 1″ OD pipe; since it is Pipe, I assumed it was ID.)

I made a coil balun as described in the book, and the UHF connector is mounted on a right-angle piece of plastic cut from an inexpensive outlet box which is a trick suggested in the book.

I put Noalox on the stainless steel nuts and bolts to prevent them from “welding” themselves together and also to protect the aluminum from the stainless steel.

I changed my ideas on how to get it up into the air a couple of times, and today I finally just went and got an MFJ-1911 lightweight fiberglass mast and a set of MFJ-2830X guy rings at our local “candy store.” (I wish there were a ring in the set with an even larger center hole.) I did not extend it to the full 20′ (yet, anyway) because I was concerned that the antenna was too heavy, so it is only about 14′ up in the air now.

I used hose clamps (threaded through a water drain tube, so the clamps don’t cut into the mast) above each exposed joint in the mast to give added protection against the “twist lock” mast unlocking and collapsing into itself. I put another one around the base with loops of paracord through it that I can hold down with tent stakes, in addition to putting the base of the mast against one of the raised garden beds to keep it from slipping. (I’m sorry, I don’t recall which video blogging ham I learned those hose clamp tricks from.)

The 6m Moxon Antenna ended up being tilted slightly (actually, rotated around to be almost upside-down!), but I’ve got some U-bolt saddles on order to fix that. (They’ll be the two pieces of metal besides the aluminum elements that aren’t stainless steel. Unfortunately, I used a smaller size U-bolt than what seems to be the “standard” for antenna masts of about 2″ inside diameter for the U-bolts.) I made an extension that screws in above the vertical piece of PVC pipe through the boom so that I could add support ropes for the insulators far out from the center of the antenna, but I haven’t put it on yet to save weight. (I may replace the mast with a heavier-weight product from MFJ to allow this and to raise it higher.)

As you can see below, the minimum SWR is 1.0 at about 52,140 MHz, not the point in the 6m band where I would like it for FT8, but at least it is in the lower half of the band. (I haven’t thought about how to tune it or if I need to. But I do know that I want to replace the thin coax feeding the antenna now with LMR-400.)

SWR curve hitting 1.0 at about 52,140 MHz

With much-appreciated help from my XYL Merle W1MSI, I was able to get the DIY 6m Moxon Antenna up late this afternoon and try it out before the band closed for the day. The “magic band” did what it does, and I was able to make 27 QSOs on VHF with FT8, from my shack in FN42 (southern New Hampshire) to as far as EL98 (Florida) and EN52 (Wisconsin). So I think the antenna is working pretty well. It is the first beam antenna at my shack.

For a while there, I was happily collecting DXCCs and US states on HF with SSB, but then I discovered FT8, and after that FT4, and now I’ve got grid squares to collect on VHF — so I have even more paper to chase!

Aron, W1AKI

Antennas, General, Homebrewing, Newsletter

Tilt-Over Bases for Antenna Masts That You Can Build

June 30, 2022 Martin Blustine

Introduction

Most of us have installed temporary antenna masts and have looked for a way to raise, lower and guy the masts while working alone. This was the case when I wanted to raise three masts for temporary antenna testing. When I couldn’t find any tilt-over bases that were sturdy, I decided to design and build some of my own from readily available materials.

I wanted mast bases that were rugged and heavy, not thin and flimsy. I discovered that mild steel [1] with its high carbon content is easy to weld, so I settled on that material. I also found a source for mild steel hinges [2]. They were perfect matches for mild steel plate. (In case you prefer aluminum, heliarc welding has become routine. It all depends upon what the welder quotes for a price and how heavy you want the bases to be.)

A sketch of what was built appears in Figure 1. All of the dimensions are based upon available materials. The only cutting required was to fabricate a steel shim [3]. When the tilt-over base is in its upright position, this shim, which is the same thickness as the hinges, maintains the spacing between the steel plates.

Figure 1. Design Sketch. The small holes in the left base plate accommodate 3/8” spikes (see text). The steel tube is welded to the rear side of the right top plate (see text).

A local welder assembled three tilt-over base mounts from supplied 8″ x 8″ x 1/4″ mild steel plate, 3″ OD 11 gauge steel tube, 6″ x 6″ steel hinges, and 3/4″ x 3/4″ x 6″ steel bar stock. The steel plate, hinges and bar stock were ordered from Amazon, while the tubing [4] was ordered from Coremark. The ID of the base tube is 2.75″ (70mm), 11ga. This is a loose fit for the cap at the bottom of most fiberglass masts. I used felt blankets [5] as shims for a tighter fit and to protect the masts. The base mounts are anchored to the ground with 3/8″ x 12″ galvanized spikes [6]. Four ½” holes drilled in the bottom plate for this purpose are visible. The spikes prevent the bases from sliding while the masts are being raised and lowered.

Once welded, the welding flux should be removed. Since high carbon steel will rust, the welded assemblies were cleaned and prepped with phosphoric acid [7] and steel wool before priming with spray metal primer [8]. The primed bases were spray-painted [9]. The finished product is shown in Figure 2.

Figure 2. Tilt-Over Bases. These tilt-over mast bases are sturdy and stable when anchored to the ground with 3/8″ x 12” galvanized spikes. The tilt-over feature makes it easy to raise and lower portable telescoping and non-telescoping masts while working alone.

A typical installation is shown in Figure 3. The 33’ (10m) masts shown were guyed at two levels with guy rings. Four Dacron paracord guy ropes were used on each guy ring. Fluorescent orange paracords were used for enhanced visibility. Temporary ground anchoring is accomplished with polycarbonate Orange Screws [10] as shown in Figure 4. Taut-line hitches are used to tighten the guying ropes – a useful knot to remember.

The mast is raised with two lower guy ropes in place. The ropes are adjusted to hold the mast a few degrees past vertical until the final two lower guy ropes are placed. Finally, the upper four guy ropes are placed.

Figure 3. Typical Installation. Guying is performed at two levels. The mast is raised while working alone with two lower guy ropes in place. The ropes are adjusted to hold the mast a few degrees past vertical until the final two lower guy ropes are placed. Finally, the upper four guy ropes are set. A post level, visible on the mast, is used to true it up. Photo courtesy of N4UM.

Figure 4. Guy view. The masts are guyed at two levels. Eight Dacron paracord ropes are used. The paracords are fastened to the guy rings with snap hooks. Tensioning is adjusted with taut-line hitches. Photo courtesy of N4UM.

Figure 5. Orange Screw Ground Anchors. The guy ropes are adjusted with taut-line hitches. During antenna range testing, the Orange Screws were set in sandy soil. Three masts remained standing during two weeks of rain and stiff winds.

Figure 6. Antenna Range with 3 Tilt-Over Bases in Use. An antenna range was constructed with three fiberglass masts and tilt-over bases. The dimensions of the range are as pictured. This 140’ range was left unattended during 2 weeks of Florida spring wind and rain. Note that paracord back-guys were employed at the very tops of the north and south masts to relieve the lateral loading due to the weight of the wire. Without back-guying, the top sections of the telescoping masts are apt to snap off.

References*

[1]https://www.amazon.com/s?k=8+x+8+x+1%2F4+steel+plate&crid=188CJTXB7VM3W&sprefix=8+x+8+x+1%2F4+steel+plate%2Caps%2C585&ref=nb_sb_noss_2
[2]https://www.amazon.com/Hinge-Weld-Heavy-Metal-Doors/dp/B0821HQQSJ/ref=sr_1_5?crid=3UEBPDTTXJFF8&keywords=6%22%2Bsteel%2Bhinges&qid=1656544819&sprefix=6%2Bsteel%2Bi%2Caps%2C107&sr=8-5&th=1
[3]https://www.amazon.com/1018-Drawn-Steel-Square-Stock/dp/B09GY7MQ2V/ref=sr_1_3?crid=3DB0BOW75U320&keywords=3%2F4+steel+bar+stock&qid=1656544926&sprefix=3%2F4+steel+bar%2Caps%2C192&sr=8-3
[4]https://www.coremarkmetals.com/electric-welded-erw-round-steel-tube
[5]https://www.homedepot.com/p/Everbilt-2-in-x-4-in-Heavy-Duty-Self-Adhesive-Beige-Felt-Blanket-3-Pack-804614/306229475?
[6]https://www.lowes.com/pd/Grip-Rite-12-in-x-3-8-in-Spike/3610436
[7]https://www.homedepot.com/p/Klean-Strip-1-Gal-Concrete-Etch-Metal-Prep-and-Rust-Inhibitor-GKPA30220/100406369
[8]https://www.homedepot.com/p/Rust-Oleum-Stops-Rust-12-oz-Flat-White-Clean-Metal-Primer-Spray-7780830/100143442
[9]https://www.homedepot.com/p/Rust-Oleum-Stops-Rust-12-oz-Protective-Enamel-Semi-Gloss-White-Spray-Paint-7797830/205585926
[10]https://www.sportsmans.com/camping-gear-supplies/tents-shelters/tent-accessories/orange-screw-small-ground-anchor-4-pack/p/1531885?channel=shopping&gclid=Cj0KCQjw8O-VBhCpARIsACMvVLMO-RmVGrVvtXURmIiQcQRsAo_r91rbskWRWtAzqqAUniop6Wnm5QYaAutREALw_wcB
[11]https://www.amazon.com/Orange-Screw-Ultimate-Ground-Anchor/dp/B01D3UIA5A/ref=asc_df_B01D3UIA5A/?tag=hyprod-20&linkCode=df0&hvadid=167119746601&hvpos=&hvnetw=g&hvrand=17637355299886752168&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9002271&hvtargid=pla-307839372670&psc=1

*The references cite readily available sources of supply. You may be able to find lower prices for materials or substitutions elsewhere.

Nashua Area Radio Society

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