CHAPTER 5 

LOOPS

Before I began my study of duplexers, the coupling loops in the filters were the most mysterious part. It was not obvious from the published designs how one goes about designing them. There seemed to be so many variations. There were fat loops and thin loops, wire loops and strap loops, side loops and top loops. Why had the designers made these choices? Which was best for my designs? I couldn't see any consistency. That's why I devoted a great deal of time to loops in my early experiments. That's what we are going to talk about in this chapter.

We'll discuss loop shape. Is that critical? We'll do the same for the placement of loops in the cavity. Does this require great precision? We'll also discuss loop materials. How important is that? My intention in answering these questions will be to take you through the experiments that gave me the answers. They all add up to a practical picture of loop design and permformance.

Loop Shape

My first question was, is there a magic shape for a loop? As I mentioned, I had inspected many duplexers, and the loops came in a baffling veriety. I wanted to know what effect loop shape has on duplexer performance. So I built a moderate sized cavity and began to experiment.

Fortunately I had a spectrum analyzer available with a tracking signal generator. The generator sweeps over an adjustable range of frequencies and the spectrum analyzer follows it. The result is an instantaneous display of the performance of a cavity, plotted against frequency.

One of the biggest difficulty one has in studying duplexers is isolating a single factor of their design. With every experimental adjustment you make, you usually unwittingly change more than just one thing. After seeing this phenomenon time and time again, in every duplexer parameter I studied, it occurred to me that this is probably one of the main reasons why duplexers are accused of being black magic. Simple intuitive understanding is difficult to extract.

Loop shape is a perfect example. When I first began making experimental changes in loop shape, I was changing more than just the shape of the loop. For examples, two loops of different geometry may have a different inductance even if you use the same amount of wire. They also have a different geometric center. Since the magnetic field in the cavity is not the same everywhere, the two loops would couple differently to the field. The complete list of differences caused by just one simple change is quite large.

What I needed was a yardstick for testing, some way to isolate individual factors, if I was going to arrive at intuitive understanding. As you may appreciate, it took me some time to find the answer. It is not a perfect answer -- there isn't one, but it works. It eventually occurred to me that performance is a good yardstick. I figured that if two loops differing in only one characteristic were made to perform the same, then the effect of the single difference would be more visible. I have found that this idea works well for studying almost any duplexer chactersitic.

To determine the effect of loop shape, I adjusted each pair of different loops to yield equal bandwidth and equal loss. Both were installed, one at a time, in the same cavity, in roughly the same position. I tested circular loops, rectangular loops and loops of irregular shape. What I discovered was that the shape of the loop makes very little difference, once is is made equal in performance to another shape. 

This led me to see that only the area of the loop matters. To be precise, coupling is proportional to the square root of the area. But if two loops have the same area, they will perform almost identically in the cavity even if their shape and the amount of wire is quite different. This simple generalization has limits of course, but for practical purposes, loop shape is not a significant factor in duplexer design. Loop area alone determines how well a loop will couple to the magnetic field.

Where to Put the Connectors?

Another factor, that I wanted to know about, is where do you put the connector that feeds the loop? Also what is the best way to ground the loop?. I had seen a lot of variations in both of these in commercial and amateur-built duplexers.

Two locations seemed to be common. The connectors were either installed directly in the shorted end of the cavity or a short distance down the side wall from the shorted end. 

Loop Construction Materials

Next I wanted to know if the size and shape of the conductor in a loop matters. I knew for example that when used as a transmission line, conductors of different dimensions have different characteristic impedances. Is this important in a cavity? Since the loop is fed with a 50 transmission line, perhaps the loop itself had to be constructed to also look like a 50 ohm line section.

So again, I began experimenting. I tired wires of widely differing diameters. As before, I adjusted all factors until the performance of each loop was equal to the others under comparison. I also tried strip conductors. I had noticed that in some commercial cavities that loops made of flat strap are used.

After trying all these variations, while keeping performance equal, I came to the conclusion that conductor size and shape has almost no effect of loop performance. Ordinary wire is perfectly acceptable. In fact, it is probably the best choice.

The only factor that does matter in the type of material used in loop construction is current handling capacity. Notice figure xx. It shows RF current at corresponding output powers.
 
1 watt  .14 Amps
3 watts .25 Amps
10 watts  .44 Amps
30 watts  .77 Amps
100 watts 1.4 Amps
300 watts  2.5 Amps
1000 watts  4.4 Amps

Figure xx Current vs. Power at 50 Ohms

These values may not seem high if you think of them in DC terms, but RF needs much larger conductors due to skin effect. We will go into the problems caused by skin effect in a later chapter, but as a general principle here, above about 100 watts, loops should be built with heavy wire. Below that power level, 16 AWG wire is completely adequate. Flat strap is not as good a choice. It has worse skin effect problems. It is just a little easier to bend into loops for cavities used at higher power levels.

Loop Placement

In the last chapter I stated how a loop must be placed to couple most effectively to the magnetic field. The H field, as you will recall, lies in concentric circles around the center conductor of the cavity. To couple best to it, the loop must be perpendicular to the field. This would be parallel to the length and parallel to the diameter of the cavity.

Also, for maximum coupling a loop needs to be at a point where the magnetic field is strongest. As we learned, this is near the shorted end of the cavity near the center conductor. If the loop is moved, or rotated in any way, coupling will be less.

The question is, does that matter? Must loops always be at a maximum field spot for the cavity to work well? I spent a lot of time researching this point, and concluded that the answer is no. Again using performance as a comparison guide, I experimented with loops at all possible locations, near the shorted end, away from the shorted end, near the center conductor, away from the center conductor. I also experimented with rotated loops.

With every different location, if I merely changed the area of the loop, I could get it to perform just as well as at any other location. Insertion loss and bandwidth do not suffer.

Loop Grounding

Armed with the knowledge above of how tolerant loops are, it then came as no surprise to me to discover that it also does not matterhow or where you ground a loop. That's probably why you see many variations in commercial and amateur designs. Three common configurations are: a. Side of Cavity b. End of Cavity c. To the Connector

As we have learned, only the loop's area matters. For side grounding, a section of the loop is actually a part of the cavity's wall. The area contained by the wall and the remainder of the loop performs the coupling. My personal favorite for loop grounding is to the connector. If you ground the loop on the body of the connector that feeds the loop, the loop and the connector become a removable and rotatable assembly. The convenience of this method makes it a common loop grounding configuration, even in commercial cavities.

Chapter Summary

Loop shape is not critical. Only the area of the loop determines how much it will couple to the magnetic field.

The location of the connectors is not critical. The side or the top works equally well.

Round wire is best for loop construction. 16 AWG is suitable for all power levels up to 100 watts. Above this, larger wire is needed to handle the RF current, due to skin effect.

Loop placement is not critical. Equal performance can be obtained from a wide range of positions in a cavity.

Loop grounding is also not critical. Grounding to the connector is the most convenient method.

All this leads to a Golden Rule. Nothing about a loop matters significantly. All you must do is to change the area and orientation of the loop until it couples to the magnetic field to the desired degree. At this point it will work almost identically to any other loop configuration.