05.pdf

Loop

Antennas

Chapter

A loop antenna is a closed-circuit antenna—that is, one

in which a conductor is formed into one or more turns so its

two ends are close together. Loops can be divided into two

general classes, those in which both the total conductor

length and the maximum linear dimension of a turn are very

small compared with the wavelength, and those in which

both the conductor length and the loop dimensions begin to

be comparable with the wavelength.

A “small” loop can be considered to be simply a rather

large coil, and the current distribution in such a loop is the

same as in a coil. That is, the current has the same phase and

the same amplitude in every part of the loop. To meet this

condition, the total length of conductor in the loop must not

exceed about 0.1

loops side by side with a few inches spacing between them

and applying power between terminal X on one loop and

terminal Y on the other.

Unlike a 1 / 2 -

dipole or a small loop, there is no

direction in which the radiation from a loop of the type shown

in Fig 1 is zero. There is appreciable radiation in the direction

perpendicular to the plane of the loop, as well as to the

“rear”—the opposite direction to the arrows shown. The

front-to-back (F/B) ratio is approximately 4 to 6 dB. The

small size and the shape of the directive pattern result in a

loss of about 1 dB when the field strength in the optimum

direction from such a loop is compared with the field from

a 1 / 2 -

dipole in its optimum direction.

The ratio of the forward radiation to the backward

radiation can be increased, and the field strength likewise

increased at the same time to give a gain of about 1 dB over

a dipole, by using inductive reactances to “load” the sides

joining the front and back of the loop. This is shown in Fig 2 .

The reactances, which should have a value of approximately

360

. Small loops are discussed later in this

chapter, and further in Chapter 14 .

A “large” loop is one in which the current is not the

same either in amplitude or phase in every part of the loop.

This change in current distribution gives rise to entirely

different properties compared with a small loop.

, decrease the current in the sides in which they are

inserted and increase it in the side having terminals. This

increases the directivity and thus increases the efficiency of

the loop as a radiator. Lossy coils can reduce this advantage

greatly.

Ω

Half-Wave Loops

The smallest size of “large” loop generally used is one

having a conductor length of 1 / 2

. The conductor is usually

formed into a square, as shown in Fig 1 , making each side

1 / 8

long. When fed at the center of one side, the current

flows in a closed loop as shown in Fig 1A. The current

distribution is approximately the same as on a 1 / 2 -

One-Wavelength Loops

Loops in which the conductor length is 1

wire, and

so is maximum at the center of the side opposite the terminals

X-Y, and minimum at the terminals themselves. This current

distribution causes the field strength to be maximum in the

plane of the loop and in the direction looking from the low-

current side to the high-current side. If the side opposite the

terminals is opened at the center as shown in Fig 1B (strictly

speaking, it is then no longer a loop because it is no longer a

closed circuit), the direction of current flow remains

unchanged but the maximum current flow occurs at the

terminals. This reverses the direction of maximum radiation.

The radiation resistance at a current antinode (which

is also the resistance at X-Y in Fig 1B) is on the order of

have

. The impedance at the terminals in Fig 1A is a few

thousand ohms. This can be reduced by using two identical

Ω

Fig 1—Half-wave loops, consisting of a single turn

having a total length of 1 / 2 λ .

Loop Antennas

5-1

shown in the drawings. This direction reverses halfway

around the perimeter of the loop, as such reversals always

occur at the junction of each 1 / 2 -

section of wire.

The directional characteristics of loops of this type are

opposite in sense to those of a small loop. That is, the radiation

is maximum perpendicular to the plane of the loop and is

minimum in either direction in the plane containing the loop.

If the three loops shown in Fig 3 are mounted in a vertical

plane with the terminals at the bottom, the radiation is

horizontally polarized. When the terminals are moved to the

center of one vertical side in Fig 3A, or to a side corner in B,

the radiation is vertically polarized. If the terminals are moved

to a side corner in C, the polarization will be diagonal,

containing both vertical and horizontal components.

In contrast to straight-wire antennas, the electrical

length of the circumference of a 1-

Fig 2—Inductive loading in the sides of a 1 / 2 -

loop to

increase the directivity and gain. Maximum radiation or

response is in the plane of the loop, in the direction

shown by the arrow.

loop is shorter than the

actual length. For a loop made of bare #18 wire and operating

at a frequency of 14 MHz, where the ratio of conductor

length to wire diameter is large, the loop will be close to

resonance when

1032

Length

feet

MHz

The radiation resistance of a resonant 1-

loop is

approximately 120

, under these conditions. Since the loop

dimensions are larger than those of a 1 / 2 -

Ω

dipole, the

radiation efficiency is high.

In the direction of maximum radiation (that is,

broadside to the plane of the loop, regardless of the point at

which it is fed) the 1-

Fig 3—At A and B, loops having sides 1 / 4

long, and at

C having sides 1 / 3

The polarization depends on the orientation of the loop

and on the position of the feed point (terminals X-Y)

around the perimeter of the loop.

long (total conductor length 1

loop will show a small gain over a

1 / 2 -

dipole. Theoretically, this gain is about 1 dB, and

measurements have confirmed that it is of this order.

The 1-

loop is more frequently used as an element of

a directive antenna array (the quad and delta-loop antennas

described in Chapter 12 ) than singly, although there is no

reason why it cannot be used alone. In the quad and delta

loop, it is nearly always driven so that the polarization is

horizontal.

different characteristics than 1 / 2 -

loops are shown in Fig 3 . At A and B the sides of the squares

are equal to 1 / 4

loops. Three forms of 1-

, the difference being in the point at which

the terminals are inserted. At C the sides of the triangle are

equal to 1 / 3

. The relative direction of current flow is as

Small Loop Antennas

The electrically small loop antenna has existed in

various forms for many years. Probably the most familiar

form of this antenna is the ferrite loopstick found in portable

AM broadcast-band receivers. Amateur applications of the

small loop include direction finding, low-noise directional

receiving antennas for 1.8 and 3.5 MHz, and small

transmitting antennas. Because the design of transmitting

and receiving loops requires some different considerations,

the two situations are examined separately in this section.

This information was written by Domenic M. Mallozzi,

N1DM.

definition, the loop is considered to be electrically small

when its total conductor length is less than 0.1

—0.085 is

the number used in this section. This size is based on the

fact that the current around the perimeter of the loop must

be in phase. When the winding conductor is more than about

0.085

long, this is no longer true. This constraint results

in a very predictable figure-eight radiation pattern, shown

in Fig 4 .

The simplest loop is a 1-turn untuned loop with a load

connected to a pair of terminals located in the center of one

of the sides, as shown in Fig 5 . How its pattern is developed

is easily pictured if we look at some “snapshots” of the

antenna relative to a signal source. Fig 6 represents a loop

from above, and shows the instantaneous radiated voltage

The Basic Loop

What is and what is not a small loop antenna? By

5-2

Chapter 5

Fig 7—Example of orientation of loop antenna for

maximum response.

wave. Note that points A and B of the loop are receiving the

same instantaneous voltage. This means that no current will

flow through the loop, because there is no current flow

between points of equal potential. A similar analysis of

Fig 7 , with the loop turned 90

Fig 4—Calculated small loop antenna radiation pattern.

from the position represented

in Fig 6, shows that this position of the loop provides maximum

response. Of course, the voltage derived from the passing wave

is small because of the small physical size of the loop. Fig 4

shows the ideal radiation pattern for a small loop.

The voltage across the loop terminals is given by

ANE

cos

(Eq 1)

where

V = voltage across the loop terminals

A = area of loop in square meters

N = number of turns in the loop

E = RF field strength in volts per meter

Fig 5—Simple untuned small loop antenna.

= angle between the plane of the loop and the signal

source (transmitting station)

= wavelength of operation in meters

This equation comes from a term called effective height .

The effective height refers to the height (length) of a vertical

piece of wire above ground that would deliver the same

voltage to the receiver. The equation for effective height is

(Eq 2)

where h is in meters and the other terms are as for Eq 1.

A few minutes with a calculator will show that, with

the constraints previously stated, the loop antenna will have

a very small effective height. This means it will deliver a

relatively small voltage to the receiver, with even a large

transmitted signal.

TUNED LOOPS

We can tune the loop by placing a capacitor across the

antenna terminals. This causes a larger voltage to appear

Fig 6—Example of orientation of loop antenna that

does not respond to a signal source (null in pattern).

Loop Antennas

5-3

across the loop terminals because of the Q of the parallel

resonant circuit that is formed.

The voltage across the loop terminals is now given by

for inductors of common cross-sectional shapes and small

length-to-diameter ratios. (See the Bibliography at the end

of this chapter.) Grover’s equations are shown in Table 1 .

Their use will yield relatively accurate numbers; results

are easily worked out with a scientific calculator or home

computer.

The value of a tuning capacitor for a loop is easy to

calculate from the standard resonance equations. The only

matter to consider before calculating this is the value of

distributed capacitance of the loop winding. This capacitance

shows up between adjacent turns of the coil because of their

slight difference in potential. This causes each turn to appear

as a charge plate. As with all other capacitances, the value

of the distributed capacitance is based on the physical

dimensions of the coil. An exact mathematical analysis of

its value is a complex problem. A simple approximation is

given by Medhurst (see Bibliography ) as

C = HD

ANEQ

cos

(Eq 3)

where Q is the loaded Q of the tuned circuit, and the other

terms are as defined above.

Most amateur loops are of the tuned variety. For this

reason, all comments that follow are based on tuned-loop

antennas, consisting of one or more turns. The tuned-loop

antenna has some particular advantages. For example, it puts

high selectivity up at the “front” of a receiving system, where

it can significantly help factors such as dynamic range.

Loaded Q values of 100 or greater are easy to obtain with

careful loop construction.

Consider a situation where the inherent selectivity of

the loop is helpful. Assume we have a loop with a Q of 100

at 1.805 MHz. We are working a DX station on 1.805 MHz

and are suffering strong interference from a local station

10 kHz away. Switching from a dipole to a small loop will

reduce the strength of the off-frequency signal by 6 dB

(approximately one S unit). This, in effect, increases the

dynamic range of the receiver. In fact, if the off-frequency

station were further off frequency, the attenuation would be

greater.

Another way the loop can help is by using the nulls in

its pattern to null out on-frequency (or slightly off-frequency)

interference. For example, say we are working a DX station

to the north, and just 1 kHz away is another local station

engaged in a contact. The local station is to our west. We

can simply rotate our loop to put its null to the west, and

now the DX station should be readable while the local will

be knocked down by 60 or more dB. This obviously is quite

a noticeable difference. Loop nulls are very sharp and are

generally noticeable only on ground-wave signals (more on

this later).

Of course, this method of nulling will be effective only

if the interfering station and the station being worked are

not in the same direction (or in exact opposite directions)

from our location. If the two stations were on the same line

from our location, both the station being worked and the

undesired station would be nulled out. Luckily the nulls are

very sharp, so as long as the stations are at least 10

(Eq 4)

where

C = distributed capacitance in pF

H = a constant related to the length-to-diameter ratio

of the coil ( Table 2 gives H values for length-to-

diameter ratios used in loop antenna work.)

D = diameter of the winding in cm

Table 1

Inductance Equations for Short Coils

(Loop Antennas)

Triangle:

(

)

1.1547 sN

0.1348 N

(

)

0.006N s

0.65533

(

)

Square:

(

)

1.4142 sN

0.3333 N

(

)

0.008N s

0.37942

(

)

Hexagon:

(

)

2sN

0.1348 N

(

)

0.012N s

0.65533

off axis

(

)

from each other, the loop null will be usable.

A similar use of the nulling capability is to eliminate

local noise interference, such as that from a light dimmer in

a neighbor’s house. Just put the null on the offending light

dimmer, and the noise should disappear.

Now that we have seen some possible uses of the small

loop, let us look at a bit of detail about its design. First, the

loop forms an inductor having a very small ratio of winding

length to diameter. The equations for finding inductance

given in most radio handbooks assume that the inductor coil

is longer than its diameter. However, F. W. Grover of the

US National Bureau of Standards has provided equations

Octagon:

(

)

2.613sN

0.07153 N

(

)

0.016N s

0.75143

(

)

where

N = number of turns

s = side length in cm

l = coil length in cm

Note: In the case of single-turn coils, the diameter of

the conductor should be used for

5-4

Chapter 5

Table 2

Values of the Constant H

for Distributed Capacitance

Length to Diameter

Ratio

0.10

0.96

0.15

0.79

0.20

0.78

0.25

0.64

0.30

0.60

0.35

0.57

0.40

0.54

0.50

1.00

0.46

Fig 8—At A, the loop is unbalanced by capacitance to

its surroundings. At B, the use of an electrostatic

shield overcomes this effect.

Medhurst’s work was with coils of round cross section.

For loops of square cross section the distributed capacitance

is given by Bramslev (see Bibliography ) as

C = 60S

(Eq 5)

where

C = the distributed capacitance in pF

S = the length of the side in meters

If you convert the length in this equation to centimeters,

you will find Bramslev’s equation gives results in the same

order of magnitude as Medhurst’s equation.

This distributed capacitance appears as if it were a

capacitor across the loop terminals. Therefore, when

determining the value of the tuning capacitor, the distributed

capacitance must be subtracted from the total capacitance

required to resonate the loop. The distributed capacitance

also determines the highest frequency at which a particular

loop can be used, because it is the minimum capacitance

obtainable.

Fig 9—Distortion in loop pattern resulting from antenna

effect.

transformer or a balanced input preamplifier. One important

point regarding the shield is that it cannot form a

continuous electrical path around the loop perimeter, or it

will appear as a shorted coil turn. Usually the insulated break

is located opposite the feed point to maintain symmetry.

Another point to be considered is that the shield should be

of a much larger diameter than the loop winding, or it will

lower the Q of the loop.

Various construction techniques have been used in

making shielded loops. Genaille located his loop winding

inside aluminum conduit, while True constructed an

aluminum shield can around his winding. Others have used

pieces of Hardline to form a loop, using the outer conductor

as a shield. DeMaw used flexible coax with the shield broken

at the center of the loop conductor in a multiturn loop for

1.8 MHz. Goldman uses another shielding method for

broadcast receiver loops. His shield is in the form of a barrel

made of hardware cloth, with the loop in its center. (See

Bibliography for above references.) All these methods

provide sufficient shielding to maintain the balance. It is

possible, as Nelson shows, to construct an unshielded loop

Electrostatically Shielded Loops

Over the years, many loop antennas have incorporated

an electrostatic shield. This shield generally takes the form

of a tube around the winding, made of a conductive but

nonmagnetic material (such as copper or aluminum). Its

purpose is to maintain loop balance with respect to ground,

by forcing the capacitance between all portions of the loop

and ground to be identical. This is illustrated in Fig 8 . It is

necessary to maintain electrical loop balance to eliminate

what is referred to as the antenna effect . When the antenna

becomes unbalanced it appears to act partially as a small

vertical antenna. This vertical pattern gets superimposed on

the ideal figure-eight pattern, distorting the pattern and filling

in the nulls. The type of pattern that results is shown in Fig 9 .

Adding the shield has the effect of somewhat reducing

the pickup of the loop, but this loss is generally offset by the

increase in null depth of the loops. Proper balance of the

loop antenna requires that the load on the loop also be

balanced. This is usually accomplished by use of a balun

Loop Antennas

5-5

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