Parti - Transmission Lines


Last month we examined some of the basic principles upon which antennas and radio-wave propagation operate, and promised to continue the discussion in this issue.

This time we ll to into an area which has been the subject of possibly more discussion—and fewer hard facts— than any other in all radio, amateur or otherwise. What well come out with won't be new-but we may offer you some new light on it along the way.

The questions from the FCC Extra Class study list which we'll be covering are:

22. Can a lossy transmission line be used to transmit signals? Explain.

32, Explain the properties of a quarter-wave section of radio-frequency transmission line.

44, What are the current and voltage characteristics along a transmission line when it is matched, and when it is mismatched?

55. A 70-ohm transmission line is connected to a 35-ohm antenna. Calculate the standing wave ratio (SWR), the reflection coefficient; and the percent reflected power. If 10 amperes are flowing in the antenna terminals, what is the current in a transmission line node?

79, Describe brietly some well-known types of antennas and antenna systems used by amateurs which do, and do not, reduce harmonic radiation.

As usual in this series, well rephrase these five questions into new ones which will hopefully include all the subject matter of Ihese five together with enough additional related material to provide complete coverage of the subject-

Four of the five questions deal with transmission iines; only one deals directly with antennas. A logical first question for us, then, is "What Is A Transmission Line?" From this foundation, we can then ask

"What Are The Major Characteristics of a Transmission Line?" We will find that one of the major, although secondary, characteristics is our old friend SWR; this ieads to our third question, "What Is a Standing Wave Ratio?"

By this time we should have waded through more information than most of us ever want to know about transmission lines and their properties, so we can return to antennas, ¡he major properties of antennas were covered last month, but with the main emphasis being placed upon their directional effects. Let's turn now to their frequency-sensitive sides and ask "How Are Operating Frequency and Antenna Design Related?" With that taken care of7 well close our examination of antennas and transmission lines by determining "What Are Trie Most Popular Types of Antennas in Ham Use?"

All set? Let's get going.

What is a Transmission Line? Strictly speaking, of course, a transmission lin^ might be considered as a "line that transmits/' However, when engineers use the term they mean any line which is conducting electrical energy, and when we as amateurs (or the FCC examiners) use it we usually mean an rf transmission iine, which is a special type of cable conducting rf energy.

Two general types of transmission line are in wide use; they are parallel line, of which the familiar TV twinlead and the open-wire feedline are common examples, and coaxial cable. While coax is probably in wider use because of a number of practical advantages it has over the parallel type, it's much easier to see the theory of what happens in the parallel variety so we will be talking primarily about parallel lines.

Before we dos though, we might as well summarize the advantages of coax; the reasons why they are advantages will come out as we proceed. In a coaxial line, the rfi&

essentially confined to the interior of the cable and thus cannot radiate so easily. Neither can noise contaminate received signals. Coax is relatively insensitive to its surroundings as well, These three points are the major advantages; counteracting them the facts that coax is (1) more expensive and (2) has higher losses, in general, than parallel lines.

Having disposed of coax cables for now, let's turn our attention to parallel imes to determine what a transmission line amounts to.

Any line conducting alternating current, at any frequency, loses at least some of that energy by radiation. The radiation is a direct consequence of the flow of alternating currents in the line, which create (or at least are accompanied by) reversing magnetic fields about the line.

A flow of current, though, requires two conductors, and if the two conductors are located very close to each other the radiated energy from one is effectively cancelled by that from the other. The net result is that almost no radiation occurs.

If the conductors are separated an appreciable fraction of a wavelength, however, this mutual cancellation cannot occur. Whenever the size of the circuit is physically such that no mutual cancellation is effective, energy will be radiated.

The terminated or "travelling-wave" antennas we examined last month were examples of "transmission lines," which had only one-way net cuirent flow (ground serves as the second conductor in this example). SucU a "transmission line" is an excellent radiator of if energy-if it's big enough.

Mere physical size is not enough, either. The dimensions must be large in comparison to a wavelength. A cross-country power distribution highline fails to do much radiation of its 60-cycle power although it's many miles long, because its conductors are spaced only a minute fraction of a 60-cycle wavelength, apart and their fields mutually cancel. A 6-meter antenna, on the other hand, radiates nicely from elements which are much shorter than the distance between highline conductors, and a microwave circuit can provide appreciable gain from a beer can!

Since a transmission line consists of two conductors, which are insulated from each other, then it must have some capacitance between them. In addition, each of the conductors also has some self-inductance, and of course at least a little resistance as well.

Let's look at a very short section of a very long line, such as that shown in Fig. 1, In even this very short distance along the line, the voltage between wires is not the same at all points, nor is the current in either wire.

For instance, the current flowing through the wires must by Ohm's Law result in at least some voltage drop across the resistance and inductive reactance of each tiny portion of each wire. I hat is, the voltage from A to D indicated by dotted line 1 is greater than that from B to C indicated by dotted line 2, because of the two voltage drops—one from A to B and the other from C to D— caused by the current flow.

Similarly, alternating current effectively "flows" through a capacitance, so that the current flowing from E to F is greater than that from F to G, because of the leakage current through the line's capacitance from F to H,

Since this is ac we're discussing, to be theoretically accurate we would have to resort to a set of differential equations-but for all ham purposes it's adequate to think in terms of Ohm's Law for ac. This tells us that the effect of the inductance and

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capacitance as illustrated in Fig. 1 upon the voltage and current in the hue must be an impedance> since only an impedance can relate voltage and current in an ac circuit.

And impedance, like a resistance, is essentially independent of voltage or current, It s determined by the physical characteristics of the device or component, not by the signal that happens to be applied or the devices to which it may be connected.

In the case of our transmission line, the impedance is determined by the inductance and capacitance of each tiny part of the line, Both the inductance and capacitance are distributed over the entire length of the line, rather than being lumped into coils or capacitors, and thus the impedance is an essential built-in part of the line.

Incidentally, this capacitance which helps form the impedance is no theoretical fiction. Should you ever be in need of small precision capacitors, you can cut them to measure from rf feedline such as TV twin-lead. All these lines are rated for capacitance in picofarads per inch; simply cut off as many inches as you need. It's a handy trick to keep in mind when electrically small capacitors are necessary.

What Are The Major Characteristics of a Transmission Line? We ve already met some of the characteristics of a transmission line. its impedance is one of the most important, for rf use. But impedance is not the only characteristic—and a length of line lying on the floor has far different characteristics than does the same line when trimmed to dimension and installed in an rf circuit. Let s look both at the intrinsic characteristics of a feedline, such as impedance, capacitance, inductance* etc., and also at the effective characteristics or properties of specific lines of special length or with special terminations.

We have seen that the impedance of a line is determined by the inductance and capacitance distributed throughout the line's length. For rf transmission lines, the impedance is approximately equal to the square root of the ratio of inductance to capacitance. If the resistance of the wires in the line were absolutely zero, and the leakage resistance of the insulator separating the wires were infinite, then the line's impedance would be exactly equal to the square root of inductance divided by capacitance—and in rf lines the wire resistance is low enough and the leakage resistance great enough that we don't get into trouble.

However, the wire and leakage resistances do exist, so we can t ignore them completely, They contribute to losses in the line, and so provide a characteristic of the Line which is called attenuation. Attenuation in any type of transmission line increases as the signal frequency goes up, because the wire resistance goes up and the leakage resistance goes down with increasing frequency. In most practical applications the attenuation of any line is given as a "decibels per 100 feet" figure; a line rated for 3 db/100 feet attenuation will lose half its power in every 100 feet of length. If you pump a kilowatt of rf into a 300-foot length of such a line, you'll get out only 1 25 watts. The first 100 feet of the line will lose half the input power or 500 watts, leaving only 500 to go on. The next 100 feet will lose half of that remaining 500, and the final 100 feet will dispose of half of the 250 watts which had survived the middle portion.

The attenuation of a line is at least as important as its impedance. The attenuation figures tell you how much power is going to make it through the line, and they also will affect the way in which the line looks to your transmitter-as we shall see shortly.

In Fig. 1, we assumed that the power going through our short section of transmission line was all going from a source to a load. That ist the line was carrying power only one way.

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