Fundamentals of Electromagnetism



Web page 2614


Measuring a TEM Wave

(Transverse Electromagnetic Wave)


The measuring instrument may be a voltmeter or an oscilloscope. In the text we will call it a “scope”.


This article refers to my A4 book Electromagnetism 1, pub. Westfields Press 1994, and republished in A5 size at Electromagnetics 1, 1995. (Available from the author for 7 pounds sterling post free.)


Figures 12 and 13 of that book show a series split. Figures 14, 15 illustrate the way in which a TEM wave behaves when confronted by a series split in the transmission line along which it is travelling from the west. Part of the incident wave advances to the north, up the spur.


Figure 21 represents the opposite kind of split in the transmission line, here defined as a parallel split. The behaviour of a TEM wave reaching a parallel split is generally the opposite of the behaviour of a TEM wave reaching a series split.


In figure 21, there are four spurs at the central point, going west, north, east and south. We will omit the southern spur, giving us a three way parallel split.


The Western Signal.


A signal travels from west to east down a 50 ohm cable, approaching the three way parallel split. The northern branch is a 5,000 ohm voltage probe made up of a 4950 ohm resistor in series with a 50 ohm transmission line. The signal travelling north towards the measuring instrument is a TEM wave, but with a voltage 100 times smaller than the signal measured. The measuring instrument (scope) makes the appropriate amplitude adjustment to register 100 times the signal it receives, so as the give the proper value for the signal measured.


The polarity of the signal delivered to the measuring instrument is as shown in figure 15. [Treat this statement with care, because figure 15 is a series split, whereas we are discussing the opposite, a parallel split, figure 21.]


The important point to notice is that the instrument does not measure the voltage between the two conductors at the point measured. Rather, it captures a portion of the TEM wave as it travels from west to east, and redirects that portion towards the measuring instrument, to the north.


The Eastern Signal


If, instead of delivering a TEM wave from the west, we deliver one from the east, a portion of it will be captured by the probe and redirected to the north, in the direction of the scope. A study of figure 21 will show us that the polarity of the signal delivered to the scope is the same for this TEM wave from the east as for the TEM wave from the west. Study of figure 22 will make this clear.


Either a west TEM wave or an east TEM wave will end up with the same measurement on the scope to the north.


The Oscilloscope.


The oscilloscope probe creates a parallel split.


The series instrument (sin) [measuring current].


It would be possible to insert a 0.5 ohm resistor in series with (figure 12) the inner conductor (or the upper conductor as in figure 13), and measure the resulting voltage developing across this resistor. As before, it would be one hundredth of the signal to be measured. However, this time, although a TEM wave from the west would still register a positive value, a TEM wave from the east would register a negative value. This is because of a subtle difference in the way the signal was captured and delivered to the north in the case of a series split, compared with a parallel split.


The sin [= current] measurement is just as valid as the scope measurement. In both cases, every signal under investigation is captured, turned through 90 degrees, and sent off towards the measuring instrument. Neither instrument actually measures the voltage in the original transmission line going from west to east.


[Ivor Catt. 18mar04. Every kind of instrument will not measure the actual voltage of the TEM wave passing by. Rather, it will capture a small fraction of it using its probe, and deliver that portion to the measuring instrument. During that process, information as to the direction in which the original TEM wave was travelling will be lost. This is “proved” by noting that whether the instrument is measuring voltage or current, the two TEM waves passing by will either be said by the instrument to have caused a doubling of the signal measured, or a cancellation. My later discussion of the two bicycle lamps is an attempt to argue that the light from one lamp shining through the light from the other lamp does not cause cancellation (or addition). They merely passed through each other, each going on his own way. In another publication, I have argued that if the number of cars per hour driving south on the M1 is 500 and the number travelling north is 300, the subtraction (or addition) of the numbers to give 200 or 800 serves no purpose and has no physical significance for highway engineering.  Ivor Catt. 18mar04]




If a TEM wave is sent from west to east and a second TEM wave is sent from east to west, a portion of each TEM wave is captured by the scope probe, turned through 90 degrees, and delivered towards the scope to the north. The scope receives double the signal, and concludes that a signal of double amplitude existed in the original transmission line.


However, had a sin [= current] measurement been made, the scope would have concluded that there existed no voltage in the transmission line.


Both these conclusions are false. In both cases, the instrument tried to give one figure for the amplitude of two signals, and failed to do so. The two signals each had amplitude 10 volts, and neither a 20 volt nor a 0 volt signal existed. The signals were not voltage signals. They were TEM Waves, which had amplitude and also direction.


If two bicycle lamps are shone at each other, the light intensity in between them is not doubled. If a large cube is introduced, then the two lamps merely illuminate two faces whereas one lamp illuminates only one face. No meaning can be attached to summing the two fluxes; the flux of light travelling to the east through the flux of light travelling to the west.


Ivor Catt       3june02




Ivor Catt 8aug01

Fundamentals of Electromagnetism

There is no instantaneous action at a distance. Space is that which prevents instantaneous action. Thus, what happens at a point in space is only the result of what is present at that point at that instant in time.

While researching the interconnection of high speed (1nsec) logic in Motorola, Phoenix, in 1965, I came across the Transverse Electromagnetic Wave (TEM Wave). This comprises an electric field, a magnetic field, and a velocity. These three factors are at right angles to each other. The electric and magnetic field are in a fixed ratio 377, and the velocity is a fixed 300,000.

To understand the TEM wave, think in terms of the very difficult concepts, which are the basis of the differential calculus. Consider a line (curve) in a two-dimensional graph. In the same way as a curve has a definite slope at a point, although at that point the curve has no length, and therefore no slope, so a TEM wave exists at a point but also exists in a region of space. (At a point it has only energy density, but in a region it has energy.) As another conceptual aid, consider the concepts mass and density. A body has density (but no mass) at a point, but it also has mass in a region of space. In the same way, a TEM wave is distributed through space. A portion of the wave at one point has no knowledge of the rest of the TEM wave.

In around 1887 Oliver Heaviside (OH), and 80 years later, independently, I myself conceived of the TEM wave of fixed magnitude travelling without change at the speed of light (300,000). OH called it a slab of energy current, which was a Morse pulse travelling unchanged down the undersea coaxial cable from Newcastle to Denmark. I saw it as a logic pulse travelling unchanged along a printed circuit board from one logic gate to the next, guided between the signal line and the 0v return line.

In this exposition, the term "wave" does not in any way imply a sine wave. There are no sine waves in my theory, which is based on the square pulse. The sine wave is not a Primitive, because it does not exist at only one point at one instant in time. Thus, it is anti-relativistic. It is regrettable that Einstein dismissed the logic pulse as "absurd", but he did not have access to Oliver Heaviside. Einstein excluded the only Primitive which was compatible with his own concept, Relativity, of no instantaneous action at a distance.

Convinced of the existence of the TEM wave, and sympathetic to Occam's Razor, it behoved me as a scientist to construct, or explain, as much as possible of what I saw in terms of these TEM waves. I concluded that a complete science could, and should, be built out of this single Primitive

It is quite difficult to correctly state the energy density at a point in a TEM wave, and it is incorrectly stated in a footnote to my sep84 article in Electronics & Wireless World. However, energy flow rate across unit area is correctly stated as E x H.

Since a TEM wave has only one velocity, and cannot remain stationary, events at a point in space at one instant in time result from the TEM wave which is passing through that point. However, it could be passing through in any direction, and more than one such wave can exist at (= be passing through) that point at one instant in time.

If only one TEM wave is passing, then it continues in the same direction unchanged, provided the aspect ratio of the space ahead remains the same. To grasp this, think of a river with uniform banks. The water continues forward at constant velocity. However, if the width of the banks changes, or the depth of the river bed, then the flow of the water changes. Similarly, if the space ahead of a TEM wave changes, then the TEM wave changes.

We know nothing of how information on a change in the aspect ratio of the space ahead of a TEM wave is communicated laterally across the face of a slab of energy current (= TEM wave).

We know nothing of how two colliding TEM waves at a point interact, except in a very limited case, that of two which collide frontally. In this case, they pass through each other unchanged. Superposition applies, except that, strangely, a lateral physical force arises while the two TEM waves are superposed. We know little about this mechanism, except that if the space is defined by two parallel conductors, with the TEM waves guided in between, then the two conductors experience a lateral force. If the electric fields of the two waves are in the same direction, this is a force of attraction between the conductors. (If there is only one wave, the conductors experience no physical force.)

Ivor Catt 8aug01


From Electromagnetic Theory vol 2 oct 1980

P237 The nature of space and the ether.

This whole subject is confused, but I think my long experience of fast digital transmission will clarify it.

An important cornerstone of my position is as I stated to A W Holt and C Seitz some four or five years ago:

Space is the ability to accommodate energy

Consider a signal (energy) transmitted from A to B. It is best to consider a narrow digital pulse.


Assume that A and B are separated by distance. The following sequence occurs:

1.     The signal is launched from A.

2.     The signal resides in the space between A and B.

3.     The signal arrives at B.

If (3) occurs at the same time as (1), the signal has "travelled at infinite velocity." That is, it has not resided in the intervening space. That is, there is no space between A and B, and A is at the same point in space as B.

(We can get over relativity quibbles by sending the signal on a round trip A - B - A. The argument still applies.)

For space to exist between A and B, it is necessary that a signal travelling from A to B be "lost" for a period of time between A and B.

We know that velocity c is 1/ sq.rt. ue . For space to exist between A and B, c must be finite. If c = 0 , then signals will not travel from A to B, and there is no space between them; no link. Instead, there is a "brick wall". If c = infinity on the other hand, the signal arrives at B at the same time as it leaves A. Is follows that:

Space which supports infinite propagation velocity is non-space. That is, it does not exist.

There would be no means of detecting such "infinite velocity supporting" space, so that it does not exist as a scientific concept, being non-measurable and performing no function. I.e. if space cannot accommodate energy, it has no function and so does not exist.

Conclusion. We are left with the only real space, that which supports a finite velocity, and where 1 / sq.rt. ue is non-zero and non-infinite.

In this context, ether is a synonym for space. Space has the characteristics uo and eo; ether has the characteristics uo and eo.

The Charged Capacitor

I discuss the Catt, or Contrapuntal, model for the "steady" charged capacitor in Wireless World, sep84, under "Energy Current". Also I show it in Fig. 7 in my 1995 book Electromagnetics 1, pub. Westfields Press.

[Additional note planned for p29 of the next (i.e. after 2001) edition of Ivor Catt, Electromagnetics 1, 1995;]

4jan02. Ivor Catt. There is a rudimentary approach to this subject, which does not refer to my earlier dec80 Wireless World article, in the Ramo 1994 edition (but not in the 1984 edition or in the earlier 1944, 1953 versions) of the classic book by Simon Ramo et al., Fields and Waves in Communication Eelctronics, pub Wiley 1965/94, p227;

5.6 PULSE FORMING LINE .... charging a transmission line of length l to a dc voltage Vo and then connecting to a resistor [R] as shown in Fig 6a .... If .... [load] R is matched to the characteristic impedance, a pulse of height Vo/2 is formed across R for a time 2t, where t is one-way propagation time down the line and the line completely discharged. .... It may at first seem puzzling that voltage across the [load] is not just Vo when the switch is closed, but this is because a travelling wave [back into the source] is excited by the connection .... the wave [into the load] discharges half the voltage initially on the line, and the wave [back into the source] the other half ....

[The contrapuntal model for a charged capacitor is evaded by Ramo et al. 14 years after it was published in 1980 in Wireless World, which then had a worldwide circulation of 60,000.]


On page 28 my 1995 book Electromagnetics 1, pub. Westfields Press, repeats my discussion of the Reed Relay Pulse Generator touched on by Ramo (above).

Ivor Catt 5jan02