### Engineering Aspects of Open Wire Transmission Design

### By Tom Hagen

The following article was submitted by our newest Editorial Contributor, professional engineer Tom Hagen.

**D.C. Transmission Line Modeling-Initial Studies on Telegraph Lines**

Introduction

This set of articles is intended to be an introduction to transmission lines and transmission line parameters. I’m hoping that anybody interested in this topic will get a good intuitive feel on why open parallel wire communication systems are built the way they are. This subject can be very technical if you go into the mathematical details. It took a number of first rank physicists several decades in the 19th Century to get to the point where the behavior of parallel open wire systems could be definitively modeled, characterized, engineered, and reliably operated in the real world.

I’ll add to this section of Doug’s website as time permits, so check back every few months and I hope to add one or two more articles after the first one.

Sections:

DC Transmission Line Modelling:

● Theory of capacitance and resistance

● Underground vs. overhead telegraph lines, early work

● Undersea telegraph cables

● William Thomson (Lord Kelvin) efforts

● Thomson’s square law

Travelling Wave Transmission Line Modelling:

The work of the Maxwellians

● Comparison of DC and AC transmission line characteristics

● Distributed parameters of the transmission line

● Characteristic Impedance of the transmission line

● Travelling waves on transmission line

● Group delay problems on transmission line

Practical examples:

● Distributed inductance to improve telegraph cable speed

● Loading coils on telephone lines

Open Wire Telephone Lines:

Application of transmission line characteristics to open wire lines

Could technology have been extended, if needed?

Some Basics

The first inklings that long wires behave differently than short ones came about during the early development of the first telegraph systems in the early to middle 19th Century. It was observed that a wire acts one way when it is mounted overhead on poles and insulators and another way when it was laid underground. Experiments performed in the 1820’s showed that a wire laid underground or in water passes electrical signals more slowly that a wire held overhead in air. Michael Faraday (1791-1867) explained this effect as an effect of the electrical capacitance between the wire and the medium surrounding it. Electrical capacitors were known to scientists by this time because the first electrical charge storage device, the Leyden Jar, was invented in the middle 18th Century.

*Michael Faraday, 1791 – 1867, [English] , contributed to electromagnetism and electrochemistry studies. Electromagnetic induction, diamagnetism and electrolysis investigations were among his discoveries.*

Referring to the below figures, an electrical capacitor [Figure 1] is formed between the wire and the medium. An electrical capacitor stores energy in the form of an electric field between two conductors that are in near proximity.

A long wire buried in the ground can take on an electrical charge if you connect a voltage source such as a battery to it and a ground rod driven into the ground. This is similar to giving a balloon a charge of static electricity when you rub it against a cloth.

Under the right conditions, i.e., if the wire is long enough and if the charge leakage to the earth is low enough, you can measure the retained charge that results in a measurable voltage between the wire and the earth [see Figure 2].

Figure 1

Figure 2

Figure 3

*In this case, the wire and the earth form what’s called an electrical capacitor. [Figure 3]*

* *

The concept of electrical capacitance is explained with the use of the diagrams to the right. A parallel plate capacitor is formed by placing two conducting plates close together and not touching. To demonstrate capacitance, the capacitor is connected in series with a battery and a switch. When the switch is closed, current in the form of free electrons in the circuit connecting the plates flows into the plates of the capacitor and charges up the plates.

Electrons are added to one plate from the negative terminal of the battery and are removed from the other plate of the capacitor to the positive terminal of the battery. This separation requires work, or energy, and the stored energy in the battery supplies the energy to do this. [Figure 4]

If the capacitor is disconnected from the battery, the plates remain charged, and an electric field is formed between the plates. This field represents stored energy in the form of electric potential or voltage across the plates. [Figure 4]

*Figure 4*

*Figure 4*

Since energy flows from the battery into the capacitor at a finite rate, it takes a finite period of time to transfer energy to the capacitor in the form of a charge. If energy flowed instantaneously, then the battery would have to be an power source of infinite power!

Another way to look at the charging process is to compare it to a water bucket filling up from a large reservoir. The large reservoir doesn’t change level in a measurable way when a small amount of water is removed from it: Imagine taking a bucket of water from the Atlantic Ocean.

The battery supplying current to the wire is represented by the large reservoir and the capacitor is represented by an empty bucket. When the valve between the reservoir and bucket is opened, water flows into the bucket and when the water levels are equal, water flow ceases.

The resistance to water flow is set by the diameter of the pipe connecting the reservoir and the bucket. The electrical analogy for this is the internal resistance of the battery and the resistance of the wires connecting the battery to the capacitor.

Electrical capacitance is one of the factors limiting the speed at which signals can be sent over a long wire. If you imagine that the bucket in the above analogy represents the electrical capacitance of buried or submerged wires, then the overhead wire could be represented as seen in the diagram below.

You can see that the water level takes less time to reach equilibrium with less volume (or capacitance) to fill up with a flow of water or electrical charge. In addition, if you can reduce the resistance to the flow of the water or charge, in both cases, the final water level is reached faster.

Electrical signalling over a wire is done by charging the line voltage up to source voltage to represent a “high” signal and then letting it drop to zero voltage to represent the “low signal. Analogously, you can send a signal with the water setup by filling the bucket to the top and then

draining it to the bottom to represent the dit’s and dah’s of the Morse Code (or for you modern folks, the binary 1’s and 0’s of a digital signalling system).

So in our water “signalling” system, we can send data faster with the smaller bucket than we can with the larger bucket. In other words, it takes less time to fill and drain the smaller bucket than the larger bucket, thus we can signal at a faster rate. This is analogous to the speed-limiting effect of electrical capacitance.

A simple model for a telegraph line is seen in the diagram below. A basic telegraph setup may use one wire on poles with glass insulators attached to the pole. All electrical circuits must have an outgoing path and an incoming path to the power source (a battery in this case). The circuit is considered complete because the current can flow from the – terminal of the battery to the + terminal. The current loop is completed to the battery through the earth. (Yes, the earth is a good conductor because the cross-section of such a conductor is enormous.)

When the key on the left is closed, current flows through the line and into the receive relay coil. The magnetism of the coil pulls the relay contacts closed and lights up the light bulb. The capacitance of the line to ground is represented by the capacitor symbols and the leakage currents to ground are represented by the resistor symbols at the insulators on the poles.

This simple model illustrates the behavior of a telegraph line in terms of charge moving into and out of the line in a direct current (DC) model. Three DC characteristics are modeled: Series resistance of the wire, line capacitance, and line leakage. This model is adequate for solving the problems of very long undersea telegraph cables.

About twenty years before the invention of the telephone the first telegraph cable was laid across the Atlantic Ocean between Ireland and Newfoundland and was completed in 1858 after a couple of failures, starting in 1857. The combination of crude detection techniques and signal delay on this cable limited its data rate to about 1 word every 10 minutes! Unfortunately this cable was worked for only a few months before its insulation failed due to an ill advised attempt to increase the signalling voltage to thousands of volts. When the first successful transatlantic cable was laid in 1866, the data rate was up to a whopping 8 words per minute. This did at least allow the cable to be a viable business proposition.

Undersea Telegraph Cables

A number of undersea cables of shorter length had been operated before this time, starting between the British Isles and continental Europe. Signal delay on these shorter cables had already been observed, and the word per minute rate on a given cable was set according to the time delay of that cable.

Undersea telegraph cables are made of a single insulated conductor surrounded by an outer jacket of steel wire armoring wrappings. For signalling, the center conductor and outer jacket are connected to a battery. Current flows and charges the entire length of the cable to battery voltage. One polarity represents a “high” or “dah” Morse Code signal. The battery connection to the cable is reversed, the cable discharges to 0 V and then charges to the opposite polarity. The opposite polarity represents a “low” or “dit” Morse Code signal.

The return path for the current is provided by the surrounding armor jacket and the adjacent seawater. The seawater and armored jacket create one side of the capacitance of the cable and the center conductor is the other side. This capacitance, the current leakage between center and shield conductors, and the resistance of the center conductor were the effects studied by the engineers involved with designing and laying cables.

*William Thompson, later Lord Kelvin (1824-1907).*

William Thomson, later Lord Kelvin (of the temperature scale fame) solved most of the problems to get the first transatlantic cable working successfully. In addition to inventing very sensitive receive instruments, Thomson applied principles of heat transfer and Fourier mathematics to the problem of signal delay by developing a square law stating that signal retardation (delay) on a cable is proportional to the square of its length. This model is analogous to heat transfer in a heat-conducting rod. For example, a cable 2 miles long will have 4 times the signal delay as a cable 1 mile long. This delay is dependenton the resistance of the center conductor, leakage between center and jacket conductors, and the capacitance of the center conductor to the steel jacket. Since not much can be done to reduce the capacitance of the cable, Thomson focussed on minimizing leakage and center conductor resistance. The center conductor was made of copper as large in diameter as possible and of the highest purity (conductivity) possible. The purity of the gutta percha insulation around the center conductor was controlled carefully and the center conductor was also kept at the exact center of the insulation to minimize current leakage.

After Thomson had solved the major cable problems, he was able to signal across the Atlantic with a battery the size of his finger! This is mostly a testament to the sensitivity of his mirror galvanometer and later, the siphon recorder. But this feat would not have been possible without first understanding and then later correcting the DC issues involved with long undersea cables.

Conclusion

The first problems with long telegraph lines became very apparent with the development of the first undersea telegraph cables. After many trials and false starts, the science of long distance telegraphy was worked out, primarily by William Thomson.

The initial work was based on a DC, or direct current, model for the long cable. It involved understanding how electric charges behave in a system with resistance, capacitance, and current leakage between the conductors. It is analogous to the rate of heat transfer lengthwise in a conductive rod.

The next steps in modelling transmission line behavior require electromagnetic field theory to explain how travelling waves move on the conducting guides formed by pairs of parallel wires. This effort began in 1861 when James Clerk Maxwell published his electromagnetic theory and continued through the 1890’s by the group of physicists known as the “Maxwellians”.

### Traveling Waves on Transmission Lines: The Maxwellians

Introduction

This article is a continuation of the first article on DC characteristics of transmission lines and transmission line parameters.

What I want to cover in this article:

Travelling Wave Transmission Line Modelling:

The work of the Maxwellians

Who were the Maxwellians?

Comparison of DC and AC transmission line characteristics

Distributed parameters of the transmission line

Characteristic Impedance of the transmission line

Travelling waves on transmission line

Group delay problems on transmission line

Practical examples:

Distributed inductance to improve telegraph cable speed

Loading coils on telephone lines

Background: The Maxwellians

Starting with the publication of various papers in the early 1860’s, James Clerk Maxwell of Scotland began to work out the laws of electrodynamics and electromagnetic field theory.

*James Clerk Maxwell (1831-1879)*

Electromagnetic field theory explains just about everything relating to electricity and magnetism. Conduction of current in wires, radio waves, and light to name a few examples are all phenomena that are explained by this extensive theory.

By the time he died in 1879, Maxwell had worked out the basics of electromagnetic field theory. His major contribution to knowledge in this area was joining the effects of electricity and magnetism in the form of fields. Field theory was a new approach to electrodynamics and was an alternative to the “action at a distance” theories of physicists mostly located in continental Europe.

One of Maxwell’s breakthroughs in developing classical electrodynamics is the prediction that light is actually a wave made up of travelling electric and magnetic fields. Additionally, the theory predicted what was then called “dark light”, or electromagnetic waves whose wavelength is longer that of light and thus is invisible to the eye.

Additional results of the theory elucidate how electrical power is transmitted through wires and how electrical machinery such as motors and generators work.

Maxwell’s original theory utilized quantities known as vector and scalar potentials to predict behavior of electrical and magnetic phenomena. In addition, he used mathematical functions called quaternions. This resulted in a somewhat large number of equations to describe the behavior of electric and magnetic fields. When students learn the theory today, they learn that only 4 vector differential equations are needed to completely describe the laws of electromagnetism. This development was due to the work of the self-named “Maxwellians”, or a group of physicists who collaborated from the 1880’s to the early 1900’s to develop further the work of Maxwell after his untimely death in 1879 from cancer.

The Maxwellians were George F. Fitzgerald (1851-1901), Oliver Heaviside (1850-1925), Oliver Lodge (1851-1940), Heinrich Herz (1857-1894), and Joseph Larmor (1857-1942). Fitzgerald was Irish, Herz was a German, and the rest were English citizens.

Of this group, Heaviside is the most interesting character. He did not have academic standing with a position at a university as did the other Maxwellians. Incredibly from childhood he taught himself physics and mathematics from library books. His efforts enabled him to take the leading role among the Maxwellians in developing the modern mathematical theory of electrodynamics from Maxwell’s initial work. Because of his relative isolation, he had to struggle by himself to work out details of the most advanced physical theory of the 19th Century. Heaviside stands as a model of brilliance and persistence!

*Oliver Heaviside (1850-1925)*

Not surprisingly, Heaviside led a very eccentric life. He was first employed by a company that built and operated an undersea telegraph cable between England and Denmark. It was there that he started thinking about signals on wires and began his studies of electromagnetism. After a period of time he left that job, moved in with his parents, and was never employed again. Heaviside was no slacker though! He published very significant work in journals that would accept articles from non-academics. Later in his life the Maxwellians were able to get Heaviside a pension from the British government that enabled him to live in relative comfort in his old age.

Regarding telegraph and telephone lines, the Maxwellians formulated transmission line theory into the form pretty much as we have it today. They added the effects of inductance of the wires to Thomson’s prior theory which included the effects of resistance, capacitance, and leakage. With the inclusion of inductance in transmission line theory, the theory was completed and all the electromagnetic effects can be accounted for. Lines could be properly designed and could be operated at optimum conditions.

In our water bucket analogy, inductance can be modeled as the mass of the water itself. If we include inertia from the finite mass of the water in the model, when the valve is opened, the water doesn’t just rise from the bottom of the bucket and stop when it reaches the level of the supply reservoir, it also overshoots the final level and oscillates up and down in decreasing amplitude until it settles down to the final level. Turbulence in the water and friction with the walls of the bucket cause the motion to eventually cease.

Water first overshoots final level.

Water next undershoots final level.

Water then settles to final level.

This behavior is similar to the effect of inductance in an electric circuit. The self-inductance of the wires causes a current to remain in motion after the driving voltage has been removed. This is important because a straight length of wire has a small amount of inductance.

The behavior of the water model with inertia and the analogous electrical model including resistance, conductance (leakage), and inductance is governed by differential equations. When the Maxwellians analyzed transmission lines using differential equations and the 4 parameters of distributed capacitance, resistance, leakage, and inductance, they realized that transmission lines are best modelled as systems of electromagnetic waves travelling in the space between the wires. The wires provide guideways for the travelling waves!

Another fallout from this analysis is the concept of characteristic impedance of the transmission line. The absolute fastest that anything can go in this universe is the speed of light. So what happens when you have a 10 mile long open wire phone line that’s left open or unterminated with a load? If you hook a 12 VDC battery to the line, does current flow into the line? The answer is a most emphatic YES. Note that when you hook up the battery, current flows into the line even though there’s an open circuit at the other end. Since it takes around 50 millionths of a second or 50 microseconds for an impulse to travel to the end of the 10 mile line, the battery doesn’t “know” that there’s an open on the other end of the line.

So what determines how much current flows into the open wire phone line with no load on the end? It’s a parameter known as characteristic impedance. If you remember Ohm’s Law, it’s E=IR where E is voltage, I is current, and R is resistance. An ideal transmission line has characteristic impedance which is purely resistive in character. So to find the current flowing into our open wire phone line, we divide the voltage applied by the characteristic impedance of the line. As it happens, the characteristic impedance of an open wire phone line is about 600 Ohms resistive. (Resistive meaning that there’s no inductive reactance or capacitive reactance associated with the impedance.) So this is how the 600 Ohm standard for audio circuits came about, by the way.