CHAPTER FOUR

CAVITIES

Now that we understand what a duplex must do, let's talk about the device itself. In this chapter we'll begin to look inside by examining the filters that make up a duplexer, cavities.

We'll discuss the physical design of the filters and the electrical properties. We'll find out how energy gets in and out of them. We'll also talk about the three main configurations, bandpass (Bp), band reject (Br) and Bandpass-Band reject (Bp-Br).

Some of what follows in this, and in the next several chapters, will be theory. As I mentioned earlier, it's necessary. I won't go into anything that does not have a direct application to the day-to-day world of duplexers.

Basic Duplexer Filter Properties

With very few exceptions, the filters in duplexers have four basic characteristics. (1) They are passive. They have no amplifying devices in them. (2) They are high-level. They handle power. (3) They are high Q. A duplexer must do lot of filtering. (4) They are low loss. We don't want to lose any signal in the duplexer that we don't have to.

We need these characteristics for one simple reason -- we don't have a choice. Think about it, a duplex must live in an antenna system. It goes between your repeater and your antenna. Only one type of filter is suitable, an LC filter -- a combination of coils and capacitors. LC filters are passive. They can handle power. With proper design, can be low loss and high Q. Active filters do not possess all these properties.

Wait a minute, you are probably thinking. Duplexers don't use LC filters. Oh, but they do, just a special kind. Conventional LC filters, made of discrete coils and capacitors, have serious shortcomings at VHF and UHF frequencies. Above roughly HF frequencies, discrete LC filters have too little Q to act as duplexer filters.

Instead, we use a type of filter called a cavity resonator. These are a class of LC filters that behaves just like a conventional LC filter, but doesn't exhibit the the high losses. That's why essentially all duplexers use cavity resonators as filters. The equivalent circuit of a cavity resonator, nor surprisingly, is a parallel resonant LC circuit.

The Cavity Resonator

The cavity resonator is little more a hollow volume, enclosed by conductive walls. It functions much like a soft drink bottle when you blow over its mouth. The only difference is, the energy inside of it is an oscillating electro-magnetic field, not a virbrating column of air.

Cavity resonators take many shapes in the radio world. The simplest is a rectangular box. A hollow conductive sphere would be the best shape, but isn't not very practical, except as a theoretical model. The class of shape that interests us, and which finds several other applications in the radio world, is a stretched version of the half-reentrant cavity.

Figure xx Basic Shape of a Duplexer Filter

If you'll think about it, we now have a short length of large diameter coaxial transmission line, with one end shorted and the other end open. Virtually all duplexer filters take this form.

In an actual duplexer filter, we cover the open end. The cover has little effect on the action of the filter. It would work perfectly well as a filter with the end open, but would be subject to external fields. In a duplexer we must keep it closed.

It's a bit more precise to say then, that duplexer filters are transmission line filters. They are, of course, also cavities. We use the transmission line shape, as we shall see in a moment, because it is better than a plain cavity as a duplexer filter.

Field Strength and Orientation

Inside the cavity resonator, the signal takes the form of an electro-magnetic or E-H field. In the transmission-line shape the electric lines of force (E) lie parallel to the length of the cavity. The magnetic lines of force, lie at right angles, concentric to the center conductor

The magnetic field (and the current) is strongest at the shorted end of the line and weak at the open end. The electric field (and the voltage) is just the opposite. It is strongest at the open end and weak at the shorted end. Both fields are stronger near the center conductor and weaker near the outer wall. These are important factors in knowing how to couple energy in and out of the filters.

Resonant Frequency of Cavities

Returning for a moment to our soda bottle analogy, if one blows gently across the open end of the bottle, we will produce the bottle's fundamental frequency. If one blows harder, we can eventually cause it to break into an overtone mode. The frequency will be much higher.

This is similar to a brass musical instrument, like a trumpet. It's the reason it can make so many notes with only a few keys. The column of air can be excited into numerous modes of vibration simply by blowing harder. On the trumpet, without using the valves, one can can actually produce a complete musical scale.

The same idea works for resonant cavities. Cavity resonators have many possible modes of ooscillation. Therefore, they have many natural resonant frequencies. In a duplexer filter, however, we must avoid the harmonic modes. They exhibit high loss. To prevent harmonic modes in a coaxial cavity, we make the length of the filter a quarter wavelength at the operating frequency. For example, at 450 MHz this is roughly 6 inches. On other bands it is proportioal to the wavelength.

Also, in a quarter wavelength coaxial cavity, the resonant frequency depends only on the length of the center conductor. The other conductor, or any other dimension of the filter, has almost no effect on the resonant frequency. This isn't true for other cavity resonator shapes. In cavities of other shapes, tuning is a complex function. This is another reason why virtually all duplexer filters are quarter wavelength coaxial filters.

A related point that I'll return to in a later chapter, is the maximum diameter of the filter. Theory dictates that it must not be larger than a third wavelength. Above this diameter, the cavity automatically breaks into a harmonic mode of oscillation. At 450 MHz the diameter limit is roughly 8 in. It is proportional to wavelength on other bands.

Coupling Energy to the Cavity

Now that we have an efficient resonant device for VHF and UHF, we need a way to couple signals in and out for filtering. There are four basic ways, loops, probes, ports and taps. In my experiments, I investigated each thoroughly. The results surprised me. I'll explain after we look at each.

Loop Coupling

The most common method to couple energy in and out of a resonant cavity is to insert a single-turn loop through the cavity wall. The loop is grounded at the end. Notice figure xx. The loop is analogous to link coupling to a parallel LC circuit.

Figure xx Equivalent Circuit to a Loop in a Cavity Filter.

The loop will couple best to the cavity when it lies perpendicular to the magnetic field. Since the H field, as we learned, is concentric to the center conductor, the loop will work best if we place it parallel to the length of the cavity and on the radius of the cylinder.

Also, the loop will couple best where the H field is strongest. This, as we have learned, is near the shorted end of the filter and near the center conductor. Figure xxa shows the maximum coupling position for a loop.

Figure xx, Maximum Coupling Position of a Loop

Probe Coupling

The second, less frequently used, coupling method is a probe. The probe is essentially a single-plate capacitor. As opposed to a loop, which is grounded, a probe is open ended. As you might expect, a probe couples to the electric field instead of the magnetic field. Similar to a loop, a probe couples best when it is perpendicular to the E field at a point where the field is strongest. This, as we've learned, is at the open end of the filter near the center conductor. Notice figure xx b. It shows the maximum coupling position for a probe.

Figure xx, Maximum Coupling Position of a Probe

In my experiments, I discovered that probes work just as well as loops, but they are mechanically difficult. Since one end must be open, we must provide all support from the other end. Mechanical rigidity is difficult to obtain and the cavity becomes subject to frequency drift.

Also, since probes utilize the E field, we must place them at the high voltage end of the cavity. A loop, on the other hand, which utilizes the H field is located at the low voltage end. At the high voltage end, arcing can be a problem, even at moderate power levels.

Remember that a 100 watt transmitter places a 71 volt signal on a 50 ohm transmission line. The Q of a cavity is high Q, often exceeding 1000. The voltage multiplies by the Q value. Therefore, very high voltages exist in a cavity at the location of a probe.

Port Coupling

The third way to couple energy is to cut a hole in the outer wall of the cavity and let the field leak through to the next cavity. This is called port coupling. A few duplexer designs use this method.

The main difficulty with this, again is mechanical. Loops and probes are relatively easy to adjust, ports are not. One must alter the size of the hole to change the coupling. This precludes easy experimentation. Also, since duplexer filters are usually made of cylindrical tubing, a port between cavities is very difficult to fabricate, especially for the home builder. Therefore, I only mention port coupling in passing.

Tap Coupling

The final method is illustrated in Figure xx. Section (a) shows an actual cavity (b) is the equivalent LC circuit.

a. Actual cavity b. LC Circuit Equivalent

Figure xx Coupling by a Tap

We may couple energy into a parallel LC circuit, by tapping the coil directly. It's like treating the coil as an autotransformer. The same can be done in a coaxial filter. By correctly positioning the tap, we can find a good impedance match and provide efficient coupling. In small duplexers, where large loops would be inconvenient, a tap is an easy way to obtain tight coupling.

The disadvantage of tap coupling is isolation. If the type of cavity you wish to use requires two ports, an input and an output port, good, isolation between the ports is difficult to achieve. Tap coupling finds its best application in single port cavities. We will discuss cavity types in a moment.

Which Type is Best?

Getting practical now, which type is best? Is one a lot better than another? Quite simply, no. As I said, I was surprised to find that all four coupling methods work more or less the same. Once you get each adjusted, the results are essentially the same.

Mechanically, however, they are not equal. Experience has led me to the practical conclusion that the loop is the single best choice, especially for the home builder. If a loop will physically fit, you can get it to perform just as well as any other method. For this reason, I'll stick to loop coupling in the rest of this book.

Cavity Types

Depending on how we configure the loops we can create three types of cavity filters from the same 1/4 wave section of transmission line. The types are, bandpass (Bp), band reject (Br) and bandpass-band reject (Bp-Br). Each has unique qualities which makes it better at solving the specific responsibilities. Let's return briefly to theory.

As we've learned, a quarter wavelength section of transmission line, shorted at one end, acts like an LC parallel tuned circuit. Notice Figure xx. It is a classic diagram found in most electronic theory textbooks. We won't labor over it. Let's notice only a couple of important points.

Figure xx Terman, Impedance/Reactance of a Parallel LC

Bandpass Cavities

For a bandpass cavity we take advantage of the total impedance curve of figure xx. When a parallel LC circuit is off resonance, its total impedance is low. At resonance, the total impedance rises rapidly to a maximum. How rapidly it rises depends on the Q of the circuit elements. We obtain this response when we place the cavity in series with the transmission line. Notice Figure xx.

Figure xx Bandpass Configuration

In this configuration, all of the energy must pass through the cavity. It is coupled into the cavity by an input loop and exits by another. At the center frequency, the highly resonant cavity easily absorbes the energy supplied to it by the input loop.

Exactly the opposite happens at the output loop. The E-H field in the cavity easily couples back into the transmission line at the output loop. Very little energy is lost in the entire process, at the resonant frequency.

Off resonance, however, the efficiency of energy transfer falls off rapidly. Non-resonant energy is attenuated in direct proportion to the overall impedance curve of Figure xx a. Figure xx is an acutal bandpass cavity displayed on a spectrum analyzer.

Figure xx Photo of Bandpass Response

Band Reject Cavities

If however, instead of placing the cavity in series with the transmission line, we place it in parallel, we create a band reject filter. Figure xx shows four common ways this is done.

a. Tee b. Parallel L c. Parallel C d. Tap

Figure xx Common Notch Cavity Configurations

In section (a) the cavity is shunted across the line by using a "tee" connector. It has only a single loop. In (b) and (c) there are two loops, as in a bandpass cavity, but with an inductor or a capacitor between the loops. The coil or capacitor is actually the transmission line. In (d) the transmission line passes through the cavity in the form of a single loop. In all cases, however, the cavity is a shunt across the transmission line.

The action of the notch configuration is to reject a small band of frequencies. That's why we generally call this class of cavities a band reject cavities. It is also sometimes called a notch or "suck out" cavity. The shunt cavity "sucks out" a small band of energy as it is passing on the transmission line.

This characteristic behavior of band reject cavities is caused by the reactance curve of Figure xx. As you can see, a long way off frequency the cavity is moderately reactive. Low in frequency it is inductive. High in frequency it is capacitive. As we approach resonance, the reactance increases rapidly to a maximum, and falls quickly to zero at resonance. On the opposite side of resonance, it does the same, but now as the opposite type of reactance. The net result is a response curve similar to the one shown in figure xx. It is typical for all band reject cavities.

Figure xx Response curve of a Typical Band Reject Cavity

Bp-Br Cavities

It is often said that there is a third class of cavities. It has both bandpass and band reject characteristics. How is it different? Actually it isn't. All band reject cavities have both a notch and a bump. When the frequency is significantly off resonance the filtering action is small, only a few dB. Near resonance one of the reactance excursions produces a small bandpass "bump". The opposite reactance excursion makes the deep characteristic notch. In some the bump is very small and the cavity is considered a simple notch cavity. In truth, however, all band reject cavities are actually bandpass-band reject cavities.

When a cavity is designed to be a bandpass-band reject cavity, the configuration shown in figure xx, c is used. A small variable capacitor is installed between the intput and the output. By selecting apporpriate loops and capacitor a small but useable bandpass bump is created.

Of great importance to duplexer design is whether the bump is higher or lower in frequency than the notch. For transmit filters it has to be one way, for receive filters, the other. This, however, is easy to arrange. Notice again Figure xx b and c. On this type of notch cavity it is easier to visualize the effect.

If the short section of transmission line bypassing the cavity is inductive, as in b, the notch will be on the high side of resonance. If the line is capacitive, the notch will be on the low side. Figure xx gives some actual examples.

a. Bump high, notch low b. Bump low, notch high

Figure xx Bump and Notch Orientations

The orientation of the notch and the bump compared to resonance is very important. In a duplexer, the transmit filters must always be one way and the receive filters the other way. Which way is determined by the repeater's frequency split, that is, whether the transmitter is higher or lower in frequency than the receiver. We'll get to the specifics later.

Bandpass vs. Notch

The final piece of basic theory that we need, is to compare the performance of the two(three) types of cavities. This will let us know which is best in a given situation.

At the bandpass bump, both notch and bandpass cavities perform in the same way. The low-loss peak or bump is tuned to the frequency that we want to pass, receive or transmit. At that frequency the filter is essentially transparent to the energy on the transmission line. That is, the line does not know that the filter is there.

Other frequencies, however, are blocked. The key issue in deciding which type of filter to use is how much. A bandpass cavity blocks everything except the small band near where it's tuned. A notch cavity blocks only a small band where it is tuned. It let's everything else pass.

You might be thinking, why use notch cavities at all? The bandpass cavity does exactly what we want, doesn't it? After all it passes what we want and gets rid of what we don't want. Isn't that the perfect answer? Well, yes and no. The key word is perfect.

A bandpass cavity does exactly what its name implies, it passes a band of frequencies, not just a single frequency. If it were good enough, that is, if its bandwidth were small enough, it would be the universal answer to duplexer filters. But in most real situations it is not narrow enough, and its losses are too high, to be the only type of filter used. This is why the notch filter is a common choice.

The notch in a notch cavity is much deeper and sharper than the bump in a bandpass cavity. Notice Figure xx which shows the same cavity configured as a bandpass and a notch filter.

a. Bandpass b. Notch

Figure xx Notch vs Bandpass in a 2" 450 MHz cavity

The notch cavity is no good at all at rejecting anything but a single off channel signal. But that's all that we need to keep a transmitter out of a receiver. For the neighbor's transmitter, however, a notch filter is of little value.

Therefore, on hill tops, a combination of both notch and bandpass cavities is best. The notch cavities fulfill the basic job of providing isolation between a repeater's receiver and transmitter. The bandpass filters provide isolation from neighboring transmitters.

Duplexer that are used on radios where there are no neighbors, such as a mobile installation, are generally notch only duplexers. Many radio amateurs make the mistake of using this type of duplexer on hill tops. They are attracted to the small size and low cost of many notch only duplexers.

When they do, they forget that their repeater is wide open to interferance from nearby transmitters and from all the mixes and intermodulation products that you normally find at such a site. It isn't a smart practice.

If economy is imperative however, you can use this kind of duplexer successfully on a hill top, but you will need to add some outboard bandpass cavities to take care of the neighbors. I have built several high performance hill top duplexers from low cost mobile duplexers and a couple of large bandpass "bottles." I'll show you later how to correctly couple the two.

The third type of duplexer, the bandpass-band reject duplexer is an attempt at a compromise. By maximizing the small bandpass bump in notch style filters, a modest amount of bandpass is obtained. If the cavities are large enough this approach is often satisfactory on a hill top. Many commercial duplexers are of this design.

Chapter Summary

In the chapter we first learned that duplexer filters are high-level, high-Q, low-loss, passive filters. This is due to the fact that a duplexer is antenna line filter.

Next we saw that duplexer filters are a special type of LC filter, the cavity resonator and that they are equivalent to a parallel tuned circuit.

Then we saw that the filters in a duplexer are a specially-shaped cavity resonator, a quarter-wavelength of transmission line, shorted at one end. The reason is to make the resonant frequency dependant on only one dimension of the cavity, the length of the center conductor.

Then we learned that to couple energy into the cavity, that we can use either a loop, a probe, a port or a tap. All work very much the same, but the loop is the easiest to construct and tune.

The loop couples to the magnetic field. It does this best when it is parallel to the length and the diameter of the cavity and when it is nearest the shorted end and the center conductor.

Then we saw that there are two basic filter configurations, bandpass and notch and a third which is a special case of the notch configuration. A bandpass filter is installed in series with the transmission line. The notch filter is a shunt filter.

The notch filter passes everything expect a small band of frequencies. This makes it useful only for receiver/transmitter isolation. The bandpass filter passes only a small frequency band. This makes it much better at eliminating outside interferance, but it is less effective than the notch filter for RX/TX isolation.

The best economy will be achieved by matching the right amount of notch and bandpass filtering to each situation.