Lumped Component Antenna

Antenna Lumped Components.

For further article reference, please refer to the website url link:

http://www.radiohamtech.com/A%20useful%20guide%20to%20Lumped%20Antenna%20Components%20and%20field%20designs%20and%20matching;%20draft%20version%20star%20date%2014-10-2015;%20marconi%20version%20;%20mid%20morning.pdf

This study started off with a question I posed myself “Alastair GW0AJU” to Dr Tim Davies GW4ADL at Swansea University around 1998, the question being what is the equivalent inductance of a long length of a piece of wire used for a long wire antenna. Should and if the wire length inductance could be calculated, would it be possible to substitute an wound coil inductance component for a section of wire in a long wire antenna.

The inductance of a wire length can be found by the impedance equation used for co-axial cable, Zo = SQR(L/C), if the capacitance per metre is 120pF/m for UR67 cable, then the inductance per metre is 300nH/m. In any type of RF cable, only the capacitance alters for the intended impedance, as the inductance or a length of wire would otherwise remain the same value, here at 300nH/m. A wound coil of inductance, say 3uH, would be equal to 10metres of wire length and therefore reduce a 80metre ¼ wave section in physical length by 10 metres, or by 20metres of physical length with a 6uH wound coil inductance.

A 20metre equivalent coil inductance equates to 1/4 wavelength at 80metre band, subsequently a "top band or 160metre" 1/4 wave section wire has a length of 40metres, or an equivalent coil of 12uH inductance. To trim the impedance loading of the 12uH antenna coil, a trimming capacitor to ground could be used, the connection made at the point between the antenna coil connection to the RF cable, and from here to ground the trimming capacitance. I would suggest a capacitance equal to the accumulated capacitance of 40metres of RF cable, thus so a capacitance of 40metres * 120pF/m would equate to 4800pF, or 4.8nF, the characteristic impedance of the lumped antenna design would thus be 50ohms.

If I recall correctly, as 1998 is some time ago, this technique was used later in the week by Tim GW4ADL to make a 1 metre overall length 10m dia-pole, by using the would coil inductance to offset the pyhsical length. The same could be used to reduce the overall height of a vertical antenna, the coil inductance would then in any case concentrate some the current lobe to the coil, the current lobe at the wound coil equal to the overall current lobe found in the same physical length of long wire.

Lately this goto me thinking, how does a Auto ATU work, and how does the designer calculate the design inductance and capacitance needed for the over Auto ATU design. I thumbed around my books and internet and found as I recalled an equation, Beta = w*SQR(L*C), w = 2*pi*frequency. By writing a BBC Basic for windows program, I investigated the equation, and I found by fixing the value of Beta to say 25 in value, and with a long wire of 15metre in length, an inductance of 4·5uH, either correctly or wrongly found from 1MHz to 30MHz, the matching capacitance varied from 3·5nH to 39pF. I am assuming that the matching current is contained within the Beta value of the equation, hence the complex impedance found within the long wire inductance and matching capacitance. The recalculate signal velocity, the propagation velocity was also rather interesting to find. The BBC Basic for windows program is listed below for all to try. Programs supplied as text file in “MS notepad” for windows. The Panular inductor is a flat circular spiral inductor, which can be made a tiny none rotating “NATO AWAC’s antenna” for aircraft, and so also ship use and mobile etc.

Below are three BBC Basic language computer programs for experimenting with lumped component antenna designs. Many Ham Radio antenna designs use various lengths of radial legs to match the antenna to many bands of the HF spectrum, or even for VHF/UHF band. By winding each half of the dia-pole radiator leg or 1/4 wave length section, that is half a dia-pole antenna, a compact design of multi-band lumped component dia-pole can be made. By using a series of 1/4 wave sections, wound as a coil or a panular/pancake inductors, the impedance match of the overall antenna can be made successful over the designed or desired band plan of operation. By using this method of lumped component antenna design, it would account for the small wing or fin style of antenna used on aircraft in aviation circles. Similarly, an HF antenna design can be derived and subsequently constructed. With care, a microwave band antenna design could be perhaps realised.

REM calculation of single layer air cored inductor diameter

ANSWER = 0

ANSWERS =0

UP = 0

upper =0

REM d = diameter of coil in inches

d = 6

REM z = length of coil in inches

z = 6

REM inductance of coil in uH

ind = 10

UP = ((18*d) + (40*z)) * ind

ANSWER = SQR(UP/d^2)

REM PRINT " by diameter = "ANSWER" turns"

REM raduis calculation

r = d/2

l=z

upper = ((9*r)+(10*l)) * ind

answers = SQR(upper/r^2)

PRINT "for inductance of = ";ind"uH"

PRINT "Coil diameter = ";d" inches";" or ";d*25.4;"mm"

PRINT "Coil length = ";z" inches";" or ";z*25.4;"mm"

PRINT "by diameter = "ANSWER" turns"

PRINT "calculation check by radius = "answers" turns"

REM calculation of pancake style inductor

ANSWER = 0

UP = 0

REM r = radius of coil in inches

r = 1.5

REM w = width of windings

w = 0.05

REM inductance of coil in uH

ind = 100

REM calculation of inductance

UP = ((8*r) + (11*w)) * ind

ANSWER = SQR(UP/r^2)

PRINT "for inductance of = ";ind"uH"

PRINT "Coil radius = ";r" inches";" or = ";r*25.4;"mm"

PRINT "Coil width of track = ";w" inches";" or = ";w*25.4;"mm"

PRINT "number of track turns = "ANSWER" turns"

Short physical length antenna by using inductive loads

The first place of call for this article is the co-axil cable characteristics, in this case RG8 RF co-axil cable.

The above diagram shows the two of the classic component items of the cable, these are the distributive inductance and capacitance components of the co-axil cable. I have found that the RG8 co-axil cable has been specified in to different ways, these the distributive components detailed by their value as per foot or per metre of physical measurement. This occurrence we will return to later on in the article.

When designing or calculating aerial or antenna designs, I have often wondered to how exactly does one calculate the inductance of a length of wire. In other words, what is the inductance of a ¼ wave section of a 20m dipole? Well it has now occurred to me that this answer is buried within the calculations of the impedance “Zo” of a co-axil cable, equation 1, the impedance and capacitance is given for the RG8 cable within its listed spec’s, namely Zo = 52 ohms, C = 100pF/m.

Zo = sqr (L/C) ….. Equation 1

From this equation I have calculated that the inductance is 290nH/m, thus so for a ¼ wave section of a 20m dipole, equates to an inductance of 1·45uH for the 5m length of wire section. I order to reduce the physical length of the ¼ wave section to a 1metre physical length of wire, an inductor may be placed in line with the ¼ wave section from the centre feed point of the ½ wave dipole. An inductance value of 4*290nH equates to 1160nH, equal to 4metres of wire of the ¼ wave section of the dipole, thus then only 1 metre of wire would need be used. An inductance value placed on both ¼ wave sections of the ½ wave dipole would then result of a 20m ½ wave dipole being just 2metres in physical length.

However the velocity factor of the antenna radiating elements would need to be taken into account, the 1 metre physical length of wire would then be trimmed to impedance match the wires velocity factor. The inductance value component would result within a both a current and voltage signal bubble appearing along the physical length of the now inductance loaded ½ wave dipole. The diagram below a double ended loaded antenna, illustrates this approach; the centre capacitance component value would be equal to the unit length of the distributive capacitance, 100pF.

Another approach would be to emulate the characteristic impedance of the co-axil cable within the antenna that is to say that, the radiating section of the signal wire of the antenna would be an inductance component, an inductance value to suit the wavelength of the radio frequency in use.

We will firstly consider the ¼ wave vertical antenna, diagram below.

The inductance is the resonant antenna inductance “wire” section, while the capacitance is there to impedance connect to the co-axil cable, for an RG8 cable, then the value is 100pF.

At 14MHz on the 20metre band, the capacitance reactance of the 100pF at 14MHz equates to the best part of 114 ohms. For the antenna to resonant as a tuned circuit, the inductance reactance would also be 114 ohms, but in complex numbers form, XC = -j (114 ohms), while XL = +j (114 ohms), while the co-axil impedance would remain as Zo = 52 ohms. From the inductance reactance value of 114 ohms, the inductance component value equates to 1300nH, or 1·3uH. The inductor of 1·3uH, would need to be physically spread over or stretched over a 1 metre physical length, that is to say the 1·3uH inductor would be 1 metre in length. This would simulate the distributive components of the co-axil now as the antenna assembly.

Now here comes another interesting bit, the RG8 co-axil cable is not only specified as unit per metre, but also as units per foot “12 inches or per every 30cm”. The component values are thus 87nH/ft. of inductance, and 30pF/ft. of capacitance.

Repeating the above calculations of the capacitance value of 30pF, it’s component reactance at 14MHz, Xc = -j(379 ohms), while XL=+j(379 ohms). The inductance for XL equates to as 4·3uH, an inductance inductor of a physical length of 30cm of a value of 4·3uH. For the double ended loaded antenna, each loading inductor would be half the calculated value, and the complex conjugate would then be half the calculated value per each end of the double ended load antenna, thus equates to +j(190 ohms), thus 2·15uH of inductance, the physical overall length of the double ended loaded antenna would then be only 2 feet, or 60cm overall.

By re-calculating the component values for 80metre band, this antenna too can be only 2 feet for a loaded ½ wave dipole, or 2metres, or even 1 foot tall for a ¼ wave vertical equivalents or perhaps 1 metre tall.

Too dream or too hypothesise.

The calculation of impedance of magnitude and angles.

Too hypothesise is to understand the Pythagoras theorem, the Hypotenuse, the opposites side over the adjacent side, to give the length or angle of the hypotheses. This is an understanding that brings about and hypothesises, such that a known degree of facts or events can lead to a thought based on a problem, in this case the Pythagorean Theorem. The diagram below of Pythagoras shows the basic understanding of angles in a right angled triangle.

http://en.wikipedia.org/wiki/Pythagorean_theorem

Later on this understanding can be taken further as the child or student begins to explore into engineering, either as a profession or as a hobby. I am leading here to complex numbers, used for radio communications for impedance matching of radio antennas as well as tuned circuit impedance input and output circuit matching. This is used for both the profession of radio communications engineering and the hobby of Ham Radio “Amateur Radio”.

http://en.wikipedia.org/wiki/Complex_number

http://en.wikiversity.org/wiki/Electrical_impedance

The "-iy" or otherwise known as "-jy", is a capacitive load, while the "+iy" or "+jy" is an inductive loading. By using polar to rectangular conversion, the impedance and angle of the load, such as 5020 degrees, is a 50ohm impedance to an angle of 20degrees and hence inductive, while a 50-20 degrees is a 50ohm impedance to a minus 20 degree angle, thus is capacitive, which maybe a dry solder joint on an R.F. connection joint. As the "-jy" reactance is known, by relating to the frequency of the carrier signal, the component capacitance value maybe calculated, similarly, the inductance can be equally calculated for the positive angle of the polar co-ordinates.

So how do we get the complex impedance in the beginning, the below diagrams show such a measuring instruments, a “voltage standing wave ratio” (Vswr) sensor.

The subject of impedance measurement of antenna's, i.e. aerial's, is the Voltage standing wave ratio measurement. The load impedance "ZL" is the first to find, from this the fraction value or the "row" value is found. This will determine if the load impedance is greater or lower than the object impedance "Zo", the row value then negative in magnitude if the "ZL" value is less than the “Zo” design value, and positive magnitude if "ZL" is greater than "Zo".

Should the row value be positive, then the resultant vector "+r" angle, would indicate an inductive loading, or an antenna with too a high impedance. Example, if "ZL" = 52ohms, then the vector angle is +15 degrees, while if "ZL" is 48 ohms, then the angle is -16 degrees, indicating a too lower impedance and a capacitive loading. These vector angles are relative to the 50ohms design impedance, thus the magnitude value of a polar rectangular equation.

"50 (angle of +15 degrees)": thus an inductive reactance

"50 (angle of -16 degrees)": thus a capacitive reactance

By altering the "Zo" equation to find the reactance component, the inductive "XL" or capacitive "Xc" reactance can be found. Whether the inductive or capacitive value is calculated, will be determined by the magnitude vector value, be positive or negative rotating around the X axis, will then determine the component type reactance value. the calculation of the angle equation, the y/x will change the sign of the resultant vector. If the impedance is high, i.e. 52ohms thus inductive, then the equation is x/y, while for 48ohms thus capacitive, then equation is y/x. This alteration changes the sign of the resultant vector, from +15 degrees to -16 degrees using this process.

For ZL = 52ohms, the inductive reactance is 14ohms reactance: at a frequency of 14MHz, XL = 161nH or "50 (angle of +15 degrees)"

For ZL = 48ohms, the capacitive reactance is 14ohms reactance: at a frequency of 14MHz, Xc = 812pF or "50 (angle of -16 degrees)"

http://en.wikiversity.org/wiki/Electrical_impedance

http://en.wikipedia.org/wiki/Complex_number