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The article was written by-
J A Adcock VK3ACA,
12 Albert Street,
Oak Park.
Victoria 3046
Australia.

Email  jadcock@melbpc.org.au

If the article is copied it must be copied in whole and the owners of the copyright and the author must be acknowledged.
 
 

PART ONE - INTRODUCTION

The basic difference between a 160-metre antenna and an antenna for any other band is that the 160-metre antenna is usually much shorter than a resonant length and much lower than that desirable for maximum efficiency. For these reasons, special precautions have to be taken in the design of the antenna

SUMMARY

The methods, results and conclusions given in this article are based on several years of experience on 160 metres. The main aim is to examine the basic medium frequency antennas shorter than resonant length ("T", "inverted L", sloping antenna and centre-fed horizontal). Graphs are given which have been derived from standard formulae and a number of conclusions from assumptions have been made. These conclusions have been made so that interested persons may examine them and assess their value in practice.

The article is aimed particularly at showing where horizontal and vertical polarisation is advantageous in either transmitting or receiving. Many of the curves shown could be usefully applied to 80 metre antennas. (It should be pointed out that the author is not engaged in this type of work professionally. It is an Amateur article with an electrical engineering slant.)

DEFINITIONS

The following are definitions of the terms used in this article:

A Short Antenna: In general, an antenna with each leg shorter than one-eighth wavelength, but in some cases shorter than one-quarter wavelength.

A Low Antenna: Height less than one-eighth wavelength.

Radiation Resistance (R_R): In this article, radiation resistance is taken as the part of the effective series resistance of the load of the antenna at the feed point, which produces radiated power.

Radiated power = R_R x I ²

Loss Resistance (R_L): Is the effective series resistance part of the load, which produces loss.

Power lost = R_L x I ²

Form Factor of the Current Distribution (Ref. l): Is the ratio of effective length to actual length of the radiating section being considered.

Surface Wave: Ground wave. The term surface wave was adopted in preference to ground wave as recommended in the A.R.R.L. "Antenna Book". In general, it refers to any part of the wave, which follows the earth's surface. Dividing the wave up into direct, indirect and beyond line-of-sight are not of great importance.

Fig. 1.- Illustrating the vertical radiation patterns of a short low horizontal and a short grounded vertical. The patterns shown are for antennas of equal radiated power. Although the pattern for the short horizontal may look attractive, in practice its efficiency is very much reduced.
 

HORIZONTAL AND VERTICAL POLARISATION – GENERAL

One characteristic of 160 metres is that of improved surface wave propagation. A vertical antenna will produce surface waves whereas a horizontal will produce practically no surface wave.

Vertically polarised radiation will produce good surface wave coverage during the day, whereas at night there exists a primary and secondary service area with a zone of poor reception in between, as described in standard texts on broadcast band propagation.

The horizontal antenna is rarely used commercially on medium frequencies, but it can produce useful results for the Amateur and provide coverage in the poor reception zone.

Radiation patterns in the vertical plane of a short vertical and a low short horizontal antenna are shown in Fig. 1. As can be seen from the diagram, the radiation from the vertical is zero straight up and rises to maximum horizontally, whereas the radiation from the horizontal is zero horizontally and maximum straight up.

For a vertical antenna, as far as distant radiation is concerned, the very low angle radiation is largely absorbed by the ground, as shown by the dotted line. The shape of the radiation patterns are brought about by the interaction between the direct wave and the reflected wave from the ground. This can be considered as an antenna and a virtual image of the antenna an equal distance below the ground.

Fig. 2 shows three standard antenna arrangements and the well known phenomena of how the current in the image of the vertical is in phase with the current in the antenna, but the current in the horizontal is in anti-phase with that of the image. This fact is most significant.

 The power radiated by a particular antenna depends on the effective current and the length of the antenna. If the antenna is short, a large current must flow in the wire in order to be effective and, by R = W/I²  the resistance must necessarily be low Similarly, if a short antenna is close to an antenna with, current in the opposite phase, still more current must flow to radiate the same power and its radiation resistance will be lower still. The lower the radiation resistance, the greater the proportion of loss.

 The resistance of a vertical antenna depends upon the radiation resistance obtained from calculation plus the series loss resistance. The resistance of a horizontal antenna depends upon the series loss resistance, the induced loss from the ground, and the radiation resistance, the latter two being greatly influenced by the height above the ground. For these reasons a low horizontal antenna is much more influenced by the ground proximity than a vertical.

 In practice little surface wave radiation can be produced by a horizontal antenna on 160 metres [60 dB. down as compared with a vertical has been suggested (Ref. 2)]. A horizontal antenna can be caused to inadvertently produce vertical polarisation as pointed out in the section on "Vertical versus Horizontal for Receiving", which accounts for why some apparently horizontal antenna signals are received locally at good strength. Also in addition, horizontal antennas can produce considerable sky wave propagation at night which can be received locally with some fading.

(Note.- A horizontal antenna can produce satisfactory surface propagation only if both the receiving antenna and transmitting antenna are several wavelengths above the ground, quite impossible on 160 metres, or if the receiving antenna is only several wavelengths from the transmitter. In practical cases horizontal polarisation is unsuitable for surface wave propagation beyond several miles.)
 
 

PART 2 - VERTICALLY POLARISED ANTENNAS

GENERAL

 The quarter wave antenna when fed in series with the ground will be resistive only. For a short antenna the load can be looked on as a capacitance in series with a resistance. As the antenna is shortened the resistance will become smaller and the capacitive reactance will become larger (smaller capacitance). Because the effective series reactance becomes higher, the load requires a higher driving voltage, this voltage being largely out of phase with the current. In other words the load has a poor power factor.

 This effective series reactance can be tuned with a variable series inductance, and when this is done the resistance of the load is presented to the transmitter, the value of which is equal to the radiation resistance plus the loss resistance. For a short antenna the radiation resistance reduces with the square of the length of the antenna.

In some circumstances it may be desirable to consider the load as an equivalent parallel circuit as shown in Fig. 3. For a short antenna the equivalent parallel circuit will be one with a very high resistance and a high capacitive reactance. The equivalent series circuit is the one most commonly used. The conversion formula for parallel to series circuits is not given to avoid unnecessary complication. It is necessary to know the reactance to make the calculation. Series parallel conversion and reactance have been introduced later with references as an incidental.

As the antenna is made longer and approaches a quarter wave, the series reactance approaches zero or the parallel reactance approaches infinity, and the resistance in both cases approaches 40 ohms. As the antenna is lengthened beyond a quarter wave the series resistance increases and the series reactance becomes inductive. The series inductive reactance again approaches zero as the antenna length approaches a half wave and the resistance becomes a high value.

 The distribution of current on a vertical antenna is shown in Fig. 4. The effective lengths of the antenna for the purpose of approximate calculation are also shown. Fig. 4a shows the current distribution for a quarter wave antenna, the distribution being approximately sinusoidal (Ref. 3). Fig. 4b shows the position for a short vertical. It will be noted that this distribution is approximately "triangular".

 As pointed out already, a short antenna will necessarily have a low feed point resistance and therefore a large current. The driving voltage will also be high due to the high series reactance. An equivalent series circuit of a complete tuned short antenna is shown in Fig. 5. The constants are considered lumped. From the circuit it is obvious that if the losses are to be minimal the radiation resistance should be high and steps should be taken to reduce losses. In the antenna in Fig. 4b the current will be maximum at the bottom and zero at the top. As a result, current at the feed point is twice the average current and therefore the radiation resistance is low, also a large base loading inductance is required to tune the antenna.

A much better distribution of current is achieved by "top loading", shown in Figs. 4c, d, and e. The top load can be made large enough so that the current in the vertical section is practically constant over the length considered. In fact the top can be made large enough so that the antenna will resonate.

Large capacitive top loading has the following advantages:
 

1. The current distribution in the radiating section is optimum, resulting in maximum radiation resistance.

2. Minimum tuning inductance is required.

3. The large capacitive top ensures minimum voltage stress to produce the necessary electrostatic field, hence minimum tendency to corona.

Initially in this discussion the top is considered to be symmetrical and therefore would radiate very little since currents flow in opposite directions and produce a largely cancelled field.

A symmetrical antenna with a straight wire top is very ancient and goes under the name of "T". The top load, however, can take several other forms, e.g. an umbrella, several horizontal radials, a flat disk, an inductively loaded whip, a cylinder or a sphere. An antenna with a single top wire at right angles is known as an inverted L'. A "sloping antenna" is also a vertical and these will be dealt with in a separate section.

The top loading will have an effect on the antenna like an extra length of wire vertically (non-radiating). This equivalent effective vertical is shown as length "a" in Figs. 4c, d and e, and the vertical radiating section is shown as length "b" The current distribution over the real and virtual part of the antenna in all cases except Fig. 4f is close to sinusoidal (Ref. 3). The shortening effect of a tapering antenna is only illustrated here and is not analysed.
 
 
 
 

CALCULATIONS FOR VERTICAL ANTENNAS

Radiation resistance of a vertical antenna when fed in series with the ground is given by-
 

R_R = 1580 L_E ²                                .............................. (1)
           l²

where  L_E = the effective length of the antenna.
           l = wavelength.

Table 1

Frequency	l Metre	l Feet	l /4 Feet
1.800 1.825 1.850	166.7 164.4 162.2	546.8 529.3 532.0	136.7 134.8 133.0

 Since we are considering the vertical component only any horizontal radiation resistance can be considered part of the loss. This value is usually small.

 In the graphs given here the electrical length of the antenna is taken as L/4 = 1. This was considered to be simpler for calculation than L/4 = 90°. If calculations are made from tables, angular lengths would have to be used. In the examples given here no reference is made to velocity factor or end effect as these values should make a small difference only.

The effective length of the antenna and the form factor of the current distribution are as defined earlier.
 

F = L_E¸ L

L_E = F x L                                                             ...........(2)

where F = form factor.

L = actual length over which the current distribution is being considered.

 The vertical component of the antenna, the length over which the vertical current distribution is considered, is usually the gap between the top load and the ground.

Also –

Average Current = Area under Current Distribution Graph     ..... .....(4)
                                                      L

 The form factor for a quarter wave is 2 ¸p as shown in Fig. 4a. The true form factor for a radiating section of wire is given below.

 From equations 3 and 4:
 

F = Integral(x = L to x = 0) i dx
                  LI

Fig 6 Illustrates the method used for equation 5.
 

 Consider Fig. 6. The length "a" is the equivalent electrical length of the top (not necessarily the actual length) and length "b" is the electrical length of the radiating section. The current distribution in the wire is sinusoidal. From the equation the electrical length L must be taken in radians and equals length "b".
 

F = Integral (x = a to x = a+b) sin x dx
            radian b x sin (a+b)

     = cos a – cos (a+b)                                            .......(5)
        (radian b x sin (a+b)

 a and b can be taken as the angular length L/4 = 90ø. and the figures taken from tables. Note that if (a + b) is greater than 90ø.

cos (a + b) = - cos [180 - (a + b)].

 Calculations from equation 5 are shown plotted in Fig. 7 and using equation 6 below, Fig. 8 was plotted.

 Taking:

electrical length = L ¸l / 4

R_R = 98.75 (elect. length x F)²                    ............ (6)

R_R = 98.75 x (1 x 0.636)²

= 39.9

Fig 7 Curves of "form factor" agaInst electrical length of the radiating section for various lengths of top load.

 It must be pointed out that this method of calculating radiation resistance is a simplified method and is only correct if the radiating section of the antenna is short. If it is near a quarter wavelength or longer the radiation resistance will be less by a small amount, however the results given by the formulae and graphs shown here should be sufficiently accurate within the range shown.

 According to the formula, as the antenna approaches a half wavelength the radiation resistance approaches infinity. This is obviously erroneous. If the total electrical length of the antenna is more than 1.4 of a leg length of a quarter wave. the formulae should not be used. The radiation resistance at the base of a half wave vertical cannot he accurately calculated but would be in the order of several thousand ohms.

 A choice of methods for determining the form factor of the current distribution on an antenna has been given and these are summarised as follows:
 

1. If the current distribution conforms nearly to the standard forms shown in Fig. 4, these may. be applied. F for a short vertical = 0.5 and F for a heavily loaded vertical = 1, the latter may not be sufficiently accurate on 160 metres.

2. If the current distribution curve is known, equations 3 and 4 can be applied and the areas under the current curve determined graphically or by mensuration.

3. By application of the graphs or equation 5.

Effective Electrical Length of Top Load

 This matter created some discussion as some authorities state that in the case of a "T" the effective length is equal to half the length of the top, that is, the "inverted L" section only and other authorities seem to leave the matter open.

 The following would appear to be correct (Ref. 4) :
 

1. With an "inverted L" the effective electrical length of the top is equal to the actual electrical length.

2. The electrical distance of the point being considered on the antenna from the current or voltage point (virtual or otherwise) is dependent upon the reactance component at that point.

3. The antenna can be considered as a wire with approximately 600 ohms characteristic impedance.

Fig 8. Radiation resistance of a vertical against height for various equivalent lengths of top load.
 
 

4. The no-load reactance curve for an unloaded 600 ohm line is near enough to correct except close to the voltage loop.

5. At the junction of the "T" the reactance load of each half will add in parallel to produce a reactance of half that of the individual line.

 Fig. 9 has been drawn based on wire and two wires in parallel. (The mutual capacitance and inductance between the wires was not taken into account.) From these graphs, Fig. 10 was plotted to determine the equivalent electrical length of two lengths of wire (a "T" top).

Efficiency of Antenna

The radiation resistance of the antenna is dependent mainly upon the configuration and not on the loss resistance. The actual resistance of the load of the antenna will equal the radiation resistance R_R plus the loss resistance R_L.
 

Power radiated = I².R_R
I = the current at the feed point.
Power input to the antenna = I₂.R
R = the total resistance of the load
R = R_R + R_L

Since R is an unknown quantity
 

R = W/I² ....................... (7)

W = power input to antenna.

The power input to the antenna can be estimated from the final input. For a class C amplifier, 70% efficiency is reasonable. For a sideband rig, the manual should give sufficient information to estimate the power output.

    = power radiated
      power input to antenna

  = I²R_R
     I²R

  = R_R (x 100%)                                 .................(8)
     R

 RR is found from graphs or calculation and R is found from equation 7. It is possible to use a Q meter or a bridge to obtain the load resistance but these were found to have certain difficulties as referred to in the discussion "The r. f. ammeter should be of the thermocouple type and should be checked against an ammeter at 50 Hz."

 It may be useful to obtain the loss resistance.
 

R_L = R - R_R                                                                         .................(9)

 In a grounded vertical antenna, R_L will be mainly ground resistance.

Worked Example

A "T" antenna is 45 feet high and has a 66 ft. flat top. With 100 watts input to the final the antenna current is 1.8 amps.

Electrical length of half top

(l /4 = 1)                                               ............. = 0.245

Electrical length of vertical section                             .....= 0.332

Form factor (Fig. 7)                                    .....................= 0.86

          From equation 6

R_R = 9875 x (0.86 x 0.332)²
      = 8.0 ohms.

        From equation 7
 

R = 100 x 0.7
         1.8²
    = 21.2

Efficiency of antenna = 8 ÷ 21.2
                                  = 0.38 or 38%
           R_L = 21.2 - 8.0

      = 13.2 ohms
probably mainly ground resistance.

THE CENTRE LOADED VERTICAL

 The effect of an inductance in a vertical is to increase the capacitance loading of the top from the point of view of the bottom, Fig 4e. In other words, the top is made to look larger. The top carries maximum voltage to provide the electrostatic field whereas the bottom section carries maximum current to provide the magnetic field. As well as a top whip, the loading coil can be placed below any other form of top of small dimension.

 The method has its main application where space is limited and the top is small. It is not as satisfactory as a large capacitive top load While it does make the current and voltage distribution on the antenna more satisfactory (resulting in a higher radiation resistance), it does add extra losses into the circuit The tendency to corona is increased.

 The inductance of the coil will be much greater to tune the antenna to resonance at the centre than at the base and therefore the coil will be more lossy. Care should be taken not to tune the antenna over resonance or the coil may become very lossy. The best compromise is some centre loading and some base loading. Modern practice appears to be to keep the centre-loading coil long and thin to reduce normal mode radiation loss. For idealised cases of current distribution, the radiation resistance can be calculated from equations 3, 4 and 6.

 The centre loaded whip as well as the helical whip have their main application to portable and mobile, but these applications are not discussed here.

Worked Example

 Example 1. A centre-loaded whip has a total height of 35 ft. The distance from the base to the coil is 25 ft. and from the coil to the tip of the whip is 10 ft. current was measured at the base of the antenna as 1.5 amps. and at the junction between the lower part and the coil as 1.0 amp. What is the radiation resistance?

From equations 3 and 4
 

F = (1 + 1.5) x 25 + (1 x 10)
       ___2____________2___
                 35 x 1.5

     = 0.69

Total electrical height = 0.259.

 From equation 6

R_R = 89.75 (0.259 x 0.69)²
      = 3.17 ohms.

Example 2. 1n the antenna in Example 1, it was found impossible to insert the ammeter two thirds of the way up, but it was observed that 38 micro-henries were required at the base to bring the antenna to resonance. What is the radiation resistance? (I will leave it to you to work out!)
 
 

METHODS OF FEEDING

When the antenna is series fed, methods of tuning the antenna depend upon the type of load expected. For efficiency it is desirable to use the minimum tuning circuit possible and this is usually a single variable inductance in series with the antenna capacitance. When the antenna is tuned by a series circuit the effective series resistance of the antenna will be presented as a load to the transmitter.

Circuit Fig. 11a is used where the antenna is shorter than a quarter wavelength. Since a short antenna has a low resistance, the tuning circuit of the transmitter must be adequate to handle this. The coupling capacitor of the pi network of the final tuning should be large to prevent over coupling between the two tuned circuits. Over coupling could result in harmonic radiation and makes tuning difficult. Circuit Fig. 11c is used where the antenna is over resonant, effectively more than a quarter wavelength. Where the antenna is close to resonant, it may be either slightly inductive or capacitive. If the antenna is slightly capacitive, this is simply tuned by only a few turns of inductance, but if the load is slightly inductive a small capacitive reactance is required and hence a very large capacitor. The circuit of Fig. 11b is probably the best to use here. In addition, circuit Fig. 11b may be used where no variable inductance is available.

Figs. 11d and 11e are parallel tuned circuits in which the antenna load is effectively in parallel with the tuned circuit To understand this it is best to consider the effective parallel circuit of the load, Fig 3. Here the effective parallel resistance is high and the coil behaves as a matching transformer. (It should be realised that there are several ways of locking at these circuits and whether you consider it as a circuit with low series resistance or with a high parallel resistance is a matter of convenience)

These circuits are particularly applicable where the antenna tuning unit is remote from the transmitter and/or where it is necessary to match into a line. Other arrangements such as pi coupling may also be applicable.

Shunt feeding the lower end of the antenna has some application where the antenna is permanently connected to the ground, Fig 11f. The antenna is fed with something like a gamma or a half delta match. It is suggested that this method, while satisfactory with a near resonant antenna, could be difficult with a shortened antenna. Large circulating currents would be present in the closed loop of a non-resonant antenna, which would reduce efficiency and make tuning difficult

EARTHING AND COUNTERPOISING

The most lossy part of a short vertical antenna is the ground. Ground resistance can be reduced by the use of buried earth radials. Unless these are extensive, they are nowhere near as effective as a counterpoise. If we consider the antenna top load as one plate of a capacitor and the ground as another, by using a counterpoise we replace the ground plate with a copper wire.

The counterpoise can be a large web of wire insulated from the ground, but a simple "T" wire directly beneath the top load will produce considerable improvement. If the counterpoise is connected direct to the ground the antenna current will probably drop, indicating a loss rather than an improvement. The counterpoise must be tuned (Figs 12a and 12b).

A counterpoise can be tuned by a variable inductance or variometer in series with the counterpoise and ground and in this mode it will be parasitic. The loading coils for the aerial and counterpoise must be adjusted alternately to obtain maximum aerial current when correctly adjusted. The earth current should be small and the aerial current and counterpoise current similar. In Practice an ammeter in the ground and counterpoise are unnecessary. Some other methods of tuning are shown in Figs. 12c and 12d which, when tuned correctly, should give zero ground current. These circuits are more difficult to tune than the parasitic counterpoise.

PART THREE - THE BALANCED HORIZONTAL

INTRODUCTION

A short low horizontal on medium frequencies has a very poor efficiency. Horizontal antennas should be made as large as possible, but in most cases only small dimensions are practicable. Even an antenna 120 feet long and 60 feet high is small and rather inefficient compared with a resonant antenna a quarter wave length high.

If the antenna is to be used for multi-band, the most satisfactory arrangement would be a centre fed with 600 ohm open wire feed line and tuned at the transmitter. Such an antenna will provide the dual function of a "horizontal doublet" or a "T" with the feeders in parallel.

This section will deal with this type of antenna and will endeavour to show what can be obtained from a balanced horizontal for transmission and reception.

The radiation resistance of a horizontal antenna is most affected by the presence of the ground. Because this is a secondary effect and the ground is not directly in series with the electrical circuit, the radiation resistance and the efficiency is much more difficult to predict. These estimations are difficult because the depth of the virtual ground below the actual ground cannot be known and the dielectric constant and resistivity of the ground cannot be easily measured. Even if they could, the calculations are far too involved.

In a lossless system the radiation resistance not only becomes lower the shorter the antenna, but becomes lower the closer it is to the ground, and on the ground would equal zero. In a lossy system the losses will be very large for an antenna of very low radiation resistance. If the ground is lossy the feed point resistance will be higher, but the absorption of the signal will be considerable.

Because the radiation resistance is lower for the horizontal than the vertical, the vertical mode will dominate. Therefore, if we desire to take advantage of the horizontal antenna for either transmitting or receiving, it must be perfectly horizontal and the feeders must be perfectly balanced. To obtain good balance the antenna should be geometrically balanced.

As with the vertical, the calculation of radiation resistance at the centre of a short dipole in free space is fairly simple. To determine the resistance at a distance along the feeder and to introduce the effect of the ground is much more involved. In the following sections, methods of how this can be done and some simplified methods are suggested. As discussed earlier, the load can be considered as an effective parallel or series circuit but the series circuit is most commonly used. This, together with a parallel tuning circuit, is shown in Fig. 13.

The possibility of using a horizontal counterpoise was investigated by the author, but unfortunately, this was found to be unworkable. A number of other experiments and on-air checks were tried to test the theories presented in the next sections.

CALCULATIONS FOR HORIZONTAL ANTENNAS
 

Fig 14 The curves shown represent the effective series resistance component of the load at various positions along a 600 ohm line over a range of S.W.R's. The dotted curve is the radiation resistance at the centre of a doublet in free space, the length of one leg of which is shown by the figures on the bottom line.

The radiation resistance at the centre of a balanced horizontal antenna in free space is given by:-

R_R = 790 x L_E²                                                          ..........(10)
                l²

The calculation of effective length of one leg of the antenna is the same as for a vertical. Length may be taken as L ÷ 2 for a short antenna, 2L ÷  p  for a resonant antenna, or the form factor may be calculated from equation 3 or 5 or obtained from Fig. 7. The electrical length given in the graphs has been taken as the length of one leg of the antenna compared with a quarter wavelength as with previous calculations, i.e. l/4 = 1 = 90º.

Similarly, as with equation (6) for a horizontal antenna
 

R_R = 197.5 (elect. length x F)²                               ............ (11)

The comments relating to accuracy of calculation to long verticals also apply here.

From the equations it will be noticed that the radiation resistance of a centre fed antenna is twice that of a vertical of the same leg length. In the case of a vertical, the other half of the antenna is virtual or reflected in the ground. The curves and methods for vertical antennas can be applied so long as the calculated resistance is doubled. The curves of Fig. 8 may have some application to end loaded horizontals, although capacitance to ground, etc., may increase the effectiveness of the end load. The free space radiation resistance at the centre of the antenna calculated by equation 11 is shown by the dotted curve of Fig. 14.

In order for this value to be of any use it is necessary to know what resistance should be presented to the transmitter at the end of a 600 ohm line. A series of curves have been plotted showing the effective series resistance at a point along the line for various S.W.R.'s. To prevent complication, only the effective series resistance component is shown. These curves are similar to a set in the A.R.R.L. Antenna Book which give effective series or parallel resistance or reactance. However, the curves of Fig. 14 give a wider range. The curves were based on the equation:-
 

Series R =Zo ( Zo Z_R + Zo Z_R tan² X)                       ..... (12)
                            Zo² + Z_R² tan² X

where Zo = characteristic impedance of the line (in this case taken as 600 ohms).
           Z_R = resistance at the current point.
           X = electrical distance from the current point.
 

The equation for reactance is not given here, but it was plotted and found to follow very closely the curve of Fig. 9 except close to the voltage point.

In applying the curves of Fig. 14, the distance of the current loop is taken as a quarter wavelength from the end of the antenna. If it is possible to know the reactance at the feed point, the electrical distance from the current point or the end of the antenna can be checked by using the open circuit reactance curves of Fig. 9 (ref. 4). It has been used for this purpose in the next series of this article, Part Four (Calculations and Discussions). The reactance component is also necessary if it is desired to calculate the effective parallel components of the load or it can be introduced into coil design calculations. In most practical cases of interest, it is unnecessary to consider the value of the reactive component of the load.

The measurement of the reactive component is difficult without a bridge but if r.f. voltage, current and power are known a reasonable result of both resistance and reactance can be calculated from standard formulae. The variation in radiation resistance of an antenna above a perfectly conducting ground is shown in Fig. 15. Possible applications of the change of resistance curve of Fig. 15 to determine the radiation efficiency of the antenna are discussed in the next series.

PART FOUR - PRACTICAL APPLICATION

VERTICAL vs. HORIZONTAL FOR TRANSMITTING

 As can be seen from Fig. 1., the majority of signal from a vertical is along the ground and zero in the vertical direction, whereas with a horizontal the signal is zero along the ground and maximum vertically. Since surface wave propagation is by the vertically polarised mode only, only the vertical component is useful in surface wave propagation. During the day, this mode of propagation may be useful over a distance of 100 miles over flat country, example, Melbourne to Colac; propagation is poor over mountainous country being not much use more than 10 miles. At night propagation via the ionosphere is possible.

 With the vertical antenna, signals returned via the ionosphere will be weak close to the transmitter and strong some distance away. This gives rise to a dead zone between the limits of the ground wave and the sky wave. If the lobe signal strength from a horizontal and a vertical were equal, the strength of the rays at 45° to the ground would be equal; this corresponds to a distance of approximately 350 miles. In fact, if the vertical and horizontal were of equal efficiency, the peak lobe signal strength at right angles to the wire is greater for the horizontal than the vertical.

 Antennas of equal efficiency would produce signals of equal signal strength at distances of up to 600 miles broadside to the horizontal or 400 miles end on. Inside these distances from the transmitter, the signal from the horizontal would be stronger. Outside these distances, the signal from the vertical would usually be stronger. This effect is illustrated in Fig. 17. (These figures are based on the assumption that the signals are mainly reflected by the F layer at night. This is true at least at high angle radiation. The matter is more complicated when considering lower layer reflection.)

 Where the horizontal antenna is less efficient (this includes most practical cases for short antennas close to the ground), the area in which the horizontal is advantageous becomes less. A horizontal with an efficiency of only half that of the vertical will still give an advantage over a distance from 300 to 400 miles. The use of a horizontal of very poor efficiency can provide a useful signal in the dead zone (between 20 and 100 miles at night).

 The distance over which the horizontal should be preferable to the vertical is shown in the graph Fig. 16. The graph is based on the assumption of an ionosphere height of 180 miles and a flat earth. (Efficiency referred to is power efficiency as calculated by the methods given in other sections.) These assumptions are reasonable for late at night and over the distances considered. If it is desired to apply the graphs to other ionospheric heights, the distances can be worked out by simple proportion.

VERTICAL vs. HORIZONTAL FOR RECEIVING

 For receiving surface waves the same applies to receiving as transmitting, the receiving antenna must be largely vertical for best results. For receiving signals via the ionosphere, the situation is quite different. Since a signal loses polarisation via the ionosphere it does not follow that the transmitting and receiving antennas must be of the same polarisation. The receiving patterns for the two antennas will be the same as their transmitting patterns.

 Since the main concern of a receiver is signal to noise ratio, relative efficiencies of receiving antennas are of no significance (it being assumed that the antenna noise is well above the threshold noise of the receiver). The main consideration is the angle from which the noise is coming. The majority of local noises are vertically polarised. The majority of distant static is received at a low angle and therefore received best on a vertical antenna. Local storms and storms within a radius of 500 miles will probably produce a stronger noise on a horizontal antenna.

 Because most noise is received best on a vertical antenna, very considerable advantages can accrue from using a horizontal receiving antenna. Another advantage of a well balanced horizontal is that it gives good rejection against strong local signals. The best mode of the receiving antenna under different noise conditions for different propagation distances are shown in Table 2.
 
 

Table 2.

	Low Noise Conditions	High Noise Conditions
1. Surface Wave	Vertical	Vertical
2. Intermediate distances up to 800 miles	Horizontal or sometimes Vertical	Horizontal
3. Long distances	Vertical	Either, depending on results.

It can often happen that an interstate or country signal can be almost inaudible on a vertical antenna and 5 and 9 on a horizontal.

 To take full advantage of horizontal reception it is desirable that the antenna should have practically no vertical component. This is difficult to achieve because of the tendency of the vertical component to dominate. For best results, the virtual ground should be parallel with the antenna. The antenna, feeders and tuning unit should be balanced and as symmetrical as possible. The position is complicated by surrounding buildings. Objects like drain pipes and iron roofs may be sufficiently coupled to the antenna to produce a considerable vertical component and thus destroy some of the properties of the horizontal.

CALCULATIONS AND DISCUSSION

 The purpose of this discussion is to examine results obtained in practice and to endeavour to make some useful conclusions. Most of the practical results agree with those obtained by calculations. Some of the conclusions drawn are largely supposition, but should be useful to any person who is experimentally inclined and would like to try them in practice.

 The antenna used by the author is a horizontal centre fed length of wire 84 feet long and 30 feet high. The feeders are sloping but these have been considered vertical. The feeders can be fed either in parallel against ground or as a doublet. The normal earth consists of a water pipe driven into the ground close to the transmitter plus four radials at right angles averaging 20 feet long and connected at the ends to various objects such as water pipes. A counterpoise is available for erection when required. The counterpoise is parasitically tuned against ground as in Fig. 12 (b). The power input to the class C final of the transmitter is 60 watts and allowing for 70% efficiency, is approximately 40 watts input to the antenna.

 The values of resistance in each case were initially determined by W / I² as described in Part Two. Later, measurements of both resistance and reactance were made using a Wayne Kerr type B201 bridge. An attempt was also made to make measurements on a Q meter but it was found that there was too much interference from the antenna. In general, the R values were higher than those measured by the bridge, suggesting that the estimation of power input may have been too high.

The value of resistance was found to be difficult to measure in the case of the balanced horizontal. This was because the resistance is the minor component and is more difficult to measure, and also the bridge was not balanced to ground. The values shown here were measured on the bridge except the resistance of the doublet which was calculated from W / I². If the bridge were correct, it would make the value of R about 10 ohms.

The following were the values determined for the purpose of calculation.
 

The antenna with feeders in parallel:
 R = 23 ohms.
 X = 135 ohms (650 pF.).

As above, but with a counterpoise:
 R = 7.7 ohms.
 X = 173.5 ohms (501 pF.).

Fed as a doublet:
 R = 6.2 ohms.
 X = 658 ohms (132 pF.).

Calculations for the Vertical Antenna

Series - Parallel Conversion.- In earlier sections, series-parallel conversion was referred to. It is interesting to consider this conversion although details here are not given and only the first case is considered.

Series resistance 23 ohms
Series reactance 135 ohms.

By applying the standard formula (Ref. 5):

Parallel resistance 814 ohms
Parallel reactance 139 ohms.

 This means that if the antenna were tuned by a series reactance Fig. 11a, the load presented to the line would be 23 ohms. If a parallel tuned circuit were used, such as Fig. 11d or e, the resistance of the load in parallel with the coil would be 814 ohms. To match a 50-ohm line, the turns tapping would be in the ratio Ö (814 ¸ 50) = 4 to 1.

Efficiency Case 1. - The antenna with feeders in parallel:

Electrical length of half top (l /4 = 1) = 0.312.
Equivalent electrical length of top (Fig. 10) = 0.52.
Electrical length of vertical section = 0.222.
Form factor (from Fig. 7) = 0.91.

From equation (6):
Rr = 98.75 (0.91 x 0.222)²
     = 4.03 ohms.

Electrical distance of feed point from the end of the antenna:
  0.52 + 0.22
   = 0.74.

 From Fig. 9 at 0.74, X = 250. This is not a good agreement but when calculated for a point where X = 135, R. would be 4.2 ohms. Not a large difference in this case.

From equation (8):
 Efficiency = 4.03 ¸ 23
                  = 0.175 (17.5%).

Loss resistance = 23 - 4.03
                         = 19 ohms.

 Equation (6): R. = 3.28 ohms.
 Efficiency, equation (8) = 0.43 (43%).

The Effect of the Horizontal Section.-

 Many find it difficult to believe that the horizontal section of the antenna adds nothing to the vertically polarised radiation and little to the horizontally polarised radiation even when the top is larger than the vertical section. Some mistakenly refer to a "T" or an "inverted L" as a horizontal and think that the direction of the antenna will affect the vertically polarised radiation pattern. Although the top of the antenna produces no useful radiation it does greatly increase the efficiency. The loss resistance for the original "T" antenna was calculated to be 19 ohms. If the top were removed the loss resistance would be at least as high.
 

 Radiation resistance with the top

 = 4.03 ohms.

F for a 0.222 vertical (Fig. 7)

= 0.505.

R_R = 98.75 (0.222 x 0.505)²

      = 1.24 ohms.

                 = 0.061  (6.1%)

Compare this with the "T" antenna with an efficiency of 0.208, the improvement with the top section added would be 3.3 times (i.e. 3.3 times the radiated power).

Calculations for the Horizontal Antenna

 The length of one leg of the top

= 42 ft.

= 0.312

 Form factor (Fig. 7) = 0.51

 From equation (11):

R_R = 197.5 (0.312 x 0.51)²
      = 5.0 ohms

 Electrical distance from end of antenna to tuner = 0.222 + 0.312
                                                                             = 0.534.

 Refer to the graph of Fig. 14, the radiation resistance calculated above can also be obtained from the dotted curve (point 1). The resistance at the end of the line can be found by continuing along the graph to electrical distance 0.534. The resistance at this point would be 1.9 ohms-point 2 on Fig. 14. From measurement, the resistance was actually 6.2 ohms. If we take 6.2 ohms at point 0.534 (point 3), this corresponds to a resistance at the centre of 16 ohms (point 4) and an S.W.R.. of 180. If the ground were perfectly conducting the resistance should be (from Fig. 15):

5.0 x 0.093 = 0.465.

Radiation resistance above perfect ground = 0.465 ohm.

Radiation resistance in space = 5.0 ohms.

Actual resistance = 16 ohms.

 The actual effect of a poorly conducting ground is impossible to determine. Is it possible to apply the same method for determining efficiency as for a vertical antenna? That is: efficiency = theoretical radiation resistance / actual resistance.

 In the case being considered,

Efficiency = 0.465 ¸ 16
                 = 0.029 (2.9%).

Comparing the efficiency of the horizontal with that of the vertical, the result is:

0.029 ¸ 0.175 = 0.165.

Distance 30 miles (no surface wave path): horizontal 2 S points better than vertical.
Distance 100 to 150 miles: on some occasions equal, better or worse.
Distance 500 miles: horizontal between 1 and 3 S points down on vertical.

 
Conclusions from Results

1. The efficiency of a vertical antenna for 160 metres is fairly easy to determine.

2. It is suggested that the efficiency of a horizontal antenna can be determined in a similar manner.

3. The results have been cross-checked with results in practice and would appear to be correct.

4. The comparison between the efficiency of the horizontal and the vertical is useful in determining the area in which the horizontal would have advantage over the vertical.

5. In short range work, outside the surface wave area; it is greatly advantageous to have a choice of a vertical or a horizontal antenna. The doublet centre fed, with open wire feed line provides the best answer since it can be used in either configuration.

REFERENCE

1. The use of the terms effective length, form factor and some of the symbols were taken from the "Admiralty Handbook of Wireless Telegraphy," 1938, Sections R1O, R11 and R22. The term effective length is also referred to as radiation length or radiation height.

2. R.S.G.B. Handbook 1968, diagram, Fig. 12.9.

3 Radio Engineers. Handbook, Terman, p. 773.

4 Radiotron Designers Handbook (Forth edition). Reactive component of impedance, p. 903. .

5. Radiotron Designers' Handbook. Conversion from series to parallel impedance, p. 157.