A MORE EFFICIENT MAGNETIC LOOP ANTENNA
Variations on a Theme Continued
Glen E. Gardner, Jr.
For the last five or so years, I have been using a rather different magnetic loop antenna. It was built with improved efficiency in mind, and it has served as a configurable testbed for experimentation. I have withheld most of my comments regarding this antenna because I felt that I did not adequately understand why, and how it was more efficient. Over time I began to understand this antenna a bit better, so now I have decided that it is a good idea to share some of the things that I have learned from using these antennas on a daily basis.
The idea behind this antenna was to use multiple conductors in parallel to reduce the resistance losses in the antenna , and thereby improve the efficiency. At the time I began working with this problematic design, there was no complete model for it. What I found was that not only did multiple parallel conductors increase the efficiency of the antenna, they increased it by quite a lot more than I had initially expected. Also, I learned that there are limits imposed on the benefits of such a configuration and that there were also some surprising changes in the behavior of the antenna when using multiple parallel conductors.
The antenna pictured above is an evolution of the original antenna built with improved efficiency in mind. Tests indicate that this antenna is at the limit for significant improvement in efficiency by adding additional parallel conductors.
The initial design from about 2008 was posted on the internet to encourage others to experiment and to challenge current notions about how a magnetic loop antenna actually works. The web page has details of the construction which are omitted here.
The initial design incorporated two, sometimes three parallel conductors with good results. It was later modified into the present form to allow it to be converted to single , dual, or four parallel conductors for the purpose of experimentation. it also features a more adjustable and configurable coupling arrangement, and can be configured to use an external gamma match or a small, adjustable coupling loop inside the main loop perimeter.
How it works
*For a given magnetic loop antenna, doubling the number of conductors from one to two will typically increase efficiency by about a factor of two. There is a limit, and beyond three or four conductors further increases are small, and may not be worth the bother.
*If the number of parallel conductors is increased, the operating frequency range of the antenna is shifted upwards significantly.
*The maximum potentials appearing across the variable capacitor is reduced significantly in loop antennas with multiple parallel conductors and a high value for K. In some cases a less expensive capacitor with a lower voltage rating can be used with very good results.
*Increases in Q can be large in multiple parallel conductor loops as compared to single conductor loops.
*The impedance of the antenna rises more rapidly as frequency increases in magnetic loop antennas using multiple parallel conductors. Antennas with more than two parallel conductors will likely need an adjustable coupling loop to be usable on all bands... The old "1/5 to 1/6 loop diameter" on all bands is too inaccurate for this antenna.
Some things that are generally known that become even more obvious with parallel conductors in a mag loop are;
*Magnetic loop antennas having a circumference approaching 1/4 wavelength at the operating frequency begin to behave more like a dipole than a magnetic loop, and the conventional models for magnetic loop antennas fail progressively as the circumference approaches 1/4 wavelength.
*For a given area, a circular magnetic loop antenna will be more efficient than a square magnetic loop. You need to make the square ones approximately 26 percent bigger than the round ones to get the same efficiency.
*Large diameter conductors, and low resistance connections are essential to good efficiency in a small transmitting loop.
*Aluminum works well in magnetic loop antennas. Yes, copper is a little better, but in multiple conductor magnetic loop antennas, there may be difficulty getting a copper loop to support its own weight. Structurally, aluminum is a lot better. Just make the conductors bigger. The choice of aluminum alloy can be important. Some aluminum alloys have excessively high resistivity figures, with 6061-T6 alloy having about the lowest resistivity of the commonly available aluminum alloys.
Why is this antenna square ?
Making the antenna square allowed a reconfigurable antenna with bolt-together construction, using off the shelf hardware. The key feature is that that antenna is reconfigurable. With the ability to change the number of parallel loops, and impedance matching schema on the same antenna, it became easy to make comparisons between the configurations so that parallel conductors could be evaluated as a performance enhancement for magnetic loop antennas.
I have no means of measuring the absolute field strength of the magnetic field from a magnetic loop antenna. However I was able to devise a means of making relative field strength measurements using a field strength meter modified to detect the magnetic field emitted by the antenna.
A search coil was made by wrapping about ten turns of 20 gauge enameled copper wire onto a four-inch diameter plastic cap from a shipping tube. An old 1970's vintage SWR meter having the feature of a field strength meter was used to measure the RF voltage output of the coil. The antenna for the field strength meter was removed and one wire of the coil was connected to the threaded post for the field strength antenna and the other was grounded to the metal case of the meter at one of the case screws. The completed instrument was placed about 1 meter away from the magnetic loop with the search coil aligned on the same plane as the magnetic loop antenna. The meter proved to be quite sensitive with power levels less than 1 watt adequate to achieve a full scale reading on the meter. Since the field strength meter measures the RF voltage developed across the coil, relative power changes can easily be expressed as dB=20log(V1/V2).
Testing was a careful, iterative process. The typical procedure is as follows: An initial calibration test of the magnetic loop antenna was made, and the field strength meter adjusted for a half scale reading to set a datum. Once the calibration was done, the desired changes to be tested on the mag loop were made and a measurement was made without any adjustment to the meter. The observed changes were logged in a notebook and the antenna was restored to the calibration configuration. A new measurement of the magnetic field strength was then made to assure that the datum had not changed, and the results written in the notebook. The results were generally good, and the improvised instrument produced consistent and reliable measurements throughout the tests of the antenna.
The antenna was tested as follows;
Tuning: antenna at resonance
loop geometry: square
tuning capacitor: Comet 5-500 pF, 5KV vacuum variable capacitor.
loop circumference: 128 inches (3.2512 meters)
conductor diameter: 7/16 inch (0.0111125 meters)
conductor material: 6061-T6 aluminum alloy
operating bands tested: 40m, 30m, 20m.
feed method: small pickup loop in the corner opposite from the tuning capacitor.
calculated pickup loop area
observed pickup loop area at lowest swr
swr at calculated loop area
relative magnetic field strength
Baseline configuration: single conductor magnetic loop
Second configuration: two conductor magnetic loop, loop spacing was 3.0 inches (0.0762 meters)
Third configuration: four conductor magnetic loop, two turns spaced 3.0 inches, two turns spaced 1.5 inches (0.0381 meter). Average spacing: 0.0508 meters.
Recorded test results were compared to a computer generated numeric model of the loop written in C.
The calculated area of the pickup loop is very sensitive to minor changes in radiation resistance, proximity effect, and skin effect. This makes it a good parameter for gauging the compliance of the actual antenna as compared to the numeric model.
In every case, the calculated pickup loop area was within 10% of the observed value for a 1.1:1 or better SWR.
In every case, adjusting the pickup loop area to the calculated value resulted in a 1.5:1 or better SWR.
For a two conductor loop antenna the measured relative field strength was 3 dB above that of a single conductor loop.
For a four conductor loop antenna the measured relative field strength ranged from 4.0-4.5 dB above that of the single conductor magnetic loop configuration.
Modeling the magnetic loop antenna
There are a number of models for single turn magnetic loop antennas. However there are no models, that this author is aware of, which can model magnetic loop antennas having multiple parallel conductors. Furthermore software to model square magnetic loop antennas is rather uncommon. In this document an attempt is made to offer a simplified model of single conductor magnetic loop antennas as well as magnetic loop antennas with multiple parallel conductors having either square or circular geometries. The model shown here is simplified and lacks rigorous detail for the sake of illustrating the concepts clearly. A reader interested in a more rigorous workup should refer to the literature on this topic.
The basic magnetic loop antenna
There are two basic requirements to make a magnetic loop antenna work.
The first requirement for a magnetic loop antenna is that the antenna must be resonant.
This is usually accomplished by adding a parallel capacitance to cancel the inductive reactance of the loop at the desired frequency.
Once resonance is established the loop effectively becomes a radiator exhibiting a purely resistive impedance composed of the radiation resistance that is defined by the area of the loop, and RF loss resistance, composed of DC resistance and skin effect resistive losses. In the case of magnetic loop antennas having multiple parallel conductors (and in multiple turn magnetic loop antennas) there is additional RF loss resistance due to increased proximity effect.
The second requirement of the magnetic loop is uniform current distribution. This requires that the circumference of the loop be significantly less than 1/4 wavelength at the frequency of interest. As the operating frequency of the loop increases, and approaches 1/4 wavelength , the behavior of the antenna begins to change significantly, behaving less like a magnetic loop antenna and more like a dipole. It is common practice for loop designers to assume that a loop circumference less than 0.20 wavelength satisfies the requirement for uniform current distribution, and many state 0.10 wavelength as a preferred maximum circumference.
Xl=inductive reactance (ohms)
Xc=capacitive reactance (ohms)
μ=permeability of free space. taken as: 4π·10-7
μ0=relative permeability of the loop conductor
Ra=mean inside radius of the loop (meters)
D=mean inside diameter of the loop (meters)
A=area of the loop (meters)
B=area of the small coupling loop
r=mean radius of the loop conductor (meters)
N=the number of parallel conductors.
K=a dimensionless constant K>0,K<=1
CIR=circumference of the loop (meters)
cir=circumference of the conductor (meters)
Rr=radiation resistance (ohms)
Rhf=RF loss resistance from skin effect(ohms)
Rhf2=RF losses from combined skin effect and proximity effect (ohms)
ρ=resistivity of the loop conductor (ohm-meter)
σ=conductivity of the loop conductor=1/ρ (mho)
Z=series impedance of the loop (ohms)
Zin=input impedance applied to small pickup loop (ohms)
Better accuracy in the radiation resistance calculation is obtained if the mean inside diameter of the loop is used to calculate the circumference.
The equation used for inductance here is very commonly used in magnetic loop antennas. It has a long history , and is one of many approximations commonly used to calculate inductance. This author is not well satisfied with this equation as the accuracy of it is frequently poor and the measures required to correct it are sometimes complex and difficult. In the numeric model for the loop antenna, the inside diameter of the loop has been used to define the diameter of the loop. This equation is commonly stated as requiring the loop diameter (and radius) be based on the distance between the centers of the conductors. Since the term is imprecise to begin with it has been left as-is, with the notation that improvement is needed.
The loop is a simple inductor. In its most simple form, the inductance of a single turn loop can be stated as;
For a circular loop(Smith, 2006): L=Ra·μ·μ0·(ln((8·Ra)/r)-2)
For a square loop antenna (Smith, 2006): L=((2·μ·μ0·D)/π)·(ln(D/r)-0.77401)
In the case of multiple parallel loops, the resulting inductance should be divided by N multiplied by the constant, K.
For a circular loop antenna: L=(Ra·μ·μ0·(log((8·Ra)/r)-2))/(N·K)
For a square loop antenna: L=((2·μ·μ0·D)/)·(log(D/r)-0.77401)/(N·K)
The inductive reactance is calculated as: Xl=2·π·f·L
For our purposes, the condition of resonance in a parallel L/C circuit
is defined as Xc=Xl.
To establish resonance a capacitance with an equal reactance can be calculated as: C= 1/(2·π·f·Xc)
Parallel Inductances and the constant K
The parallel conductors in a multiple parallel conductor antenna are individual inductances which exhibit mutual inductance. For the antenna shown here K=0.4 N=4. In antennas with significantly different parameters than the one presented here, it may be necessary to use a different value for the coefficient, K. The value of K used here will be less than 1 and greater than 1/N for antennas with multiple parallel conductors. K is controlled by the spacing between the parallel loops, with wider spacing yielding a higher value for K. Extremely close spacing between the parallel conductors will increase skin effect losses excessively and reduce the maximum usable upper frequency limit for the antenna. In all cases, a spacing of 3 times the conductor diameter between centers will be adequate, and opting for three or four parallel conductors will provide a significantly improved value for K and a higher usable upper frequency limit than one or two conductors. Since a high value of K in loops with multiple parallel conductors results in a larger loop diameter for a given resonant frequency, the efficiency of the antenna can be enhanced significantly. For example; In most cases a four conductor magnetic loop, with one-inch conductors, spaced 3 inches between the conductors, 48 inches wide can be expected to yield an efficiency greater than 90% on the 20 meter band, and nearly 60% on the 40 meter band.
The approximate value for K can be determined by setting the tuning capacitor on the antenna under test to maximum, and observing the resonant frequency. The calculated capacitance is then observed, and K is adjusted for the numeric model until the calculated capacitance is equal to the known maximum capacitance value of the tuning capacitor. Since the distributed capacitance of the antenna is typically small compared to the maximum value of the tuning capacitor, the term can usually be discarded. The reader is advised that adjusting the value of K to bring calculated inductance into agreement with the observed results in a value of K that combines an error correction to the calculated inductance along with the coefficient of inductive coupling. After K has been adjusted, the tuning capacitor can be set to its minimum value, and the resonant frequency observed. The calculated capacitance can then be compared to the known minimum capacitance of the tuning capacitor to arrive at an estimate of distributed capacitance in the antenna.
An important design consideration is that since the equation for radiation resistance has no terms for the diameter of the conductor, it assumes that the conductor is infinitely thin. In reality the conductor has little to do with it, as the radiation resistance is determined from the area inside the loop and the impedance of free space. Additionally, in a magnetic loop antenna, skin effect and proximity effect tend to cause the RF currents to flow along the inside surface of the loop conductors. This means that the calculation of the area for the loop requires that the inside diameter of the loop be used when calculating the area. Alternatively stated, radiation resistance in a magnetic loop antenna is defined by the area confined by the loop.
For a single turn circular magnetic loop antenna, radiation resistance is adequately stated as: Rr=31171·(A2/λ4)
When multiple loops in parallel are considered: Rr=[31171·((N*A2)/λ4)], Which is subtly different from the radiation resistance equation for a single conductor multiple turn magnetic loop antenna: Rr=[31171·((N*A)/λ2)2]. The two equations should not be confused because in the case of a loop with parallel conductors the areas of the individual loops are additive, and radiation resistance of the antenna is directly related to the number of parallel conductors. In the case of a single conductor multiple turn loop the total area inside the loop is directly related to the square of N times the loop diameter and the end result is a radiation resistance which changes directly with N2.
In the interest of clarity it can be stated that for a circular loop with multiple parallel conductors: Rr=[31171·(A2/λ4)]∙N
It is known that the radiation resistance in a circular loop is very close to 1.621 times that of a square loop (Zimmerman, 2006).
For a square loop divide Rr for a circular loop by 1.621.
From observation of the test antenna, and from the software model. It is taken that Rr increases directly with the number of parallel loops.
N=number of parallel loops.
For a square loop with multiple parallel conductors: Rr=[(31171·(A2/λ4))/1.621]∙N
This term is a well known approximation, and is very sensitive to small errors in resistivity and relative permeability for the loop material. If the values for these parameters are in error, the end result is that the efficiency calculation , impedance calculation, and the calculation of the area of the pickup loop will be affected adversely.
Unfortunately, the recent influx of imported, low quality metals into the industry has resulted in many metals having an issue with extreme "out of spec" values for these parameters. Also, even in high quality materials, there is a great deal of variation in the value for resistivity as stated by the manufacturer and you must be careful to use the correct value of resistivity and permeability for the metals that you are using.
resistivity of 6061-T6 aluminum alloy, as used in this antenna
relative permeability of aluminum
conductivity of the aluminum alloy
Because the loops are in parallel, the RF resistance loss decreases as the number of loops increase: Rhf=Ro/N
Glenn Smith (1971) did an exhaustive examination of proximity effect in multiple parallel conductors. To make it simple, if you space the center of the conductors by 3 times the diameter of a single conductor, proximity effect will be minimized to less than 1.2 percent for a small number of parallel conductors (N > 0, N<=2). However, there is a limit, and at around three or four parallel conductors it is no longer possible to adequately compensate for proximity effect, and there is little to gain from adding additional parallel conductors. The model is complex and a suitable simplified equation for proximity effect in a magnetic loop antenna does not yet exist. With this problem in mind an approximation is used here which assumes that proximity effect increases by N cubed as the number of parallel loops is increased. In practice, this is far from being a perfect approximation, but the gross behavior of the approximation is correct, and comparisons of predicted vs measured change in antenna radiation due to a change in N are within 1 dB of predicted values in the test antenna with N=4 (four loops) and are more strongly in agreement at N=2.
The efficiency of a magnetic loop antenna is typically calculated as (Smith, 2006);
This term is not adjusted for the effects of ground or nearby objects. In practical use consideration of external influences on a magnetic loop antenna are installation specific, and not appropriate to this model. With this in mind the calculated efficiency is presented as an estimate of the best possible result obtainable for the antenna. Changes in calculated efficiency proved to be a useful tool. Changes in radiated power from the antenna can be expressed as: dB=10Log(efficiency1/efficiency2), and this measure proved to be useful in comparing calculated results to observed values.
The impedance of the loop can be determined by the well known equation: Z=√(Rr+Rhf2);
Area of the small coupling loop
The area of the coupling loop can be easily calculated using the impedance of the loop
and the impedance of the transmission line. It is a good idea to make the area of the coupling loop adjustable so that a low SWR can be obtained on all of the covered bands.
let B=area of the small coupling loop
let A= area of the loop antenna
Zin=feedline impedance. Here it is assumed to be 50 ohms.
K= A coefficient of coupling (K>0,K<=1)
let B= (A·(Z/√Zin))/K
Since K is typically very close to 1 when the pickup loop is correctly placed, the term can be dropped;
The area of the small coupling loop is sensitive to variations in impedance arising from errors in the following:
errors in the measurement of physical dimensions
incorrect placement of the coupling loop
The sensitivity of this parameter is useful when the software model is compared to the performance of a "live" antenna. In general, if the pickup loop is built with the area specified the VSWR will typically be better than 1.5:1. Such a result should be considered as confirmation of the antenna, and the calculated efficiency can then be taken as a reasonable estimate of antenna efficiency.
Placement of the coupling loop
The coupling loop (sometimes referred to as the small pickup loop) may be placed in one of three locations inside the perimeter of the main loop.
1) 180 degrees away from the main tuning capacitor, near the inside edge of the main loop. In the case of the antenna shown here the pickup loop is located 1.5 inches inside the main loop at the corner opposite of the tuning capacitor.
2) Zero (0) degrees away from the tuning capacitor, near the inside edge of the main loop.
3) In the exact center of the main loop.
Placing the coupling loop outside the perimeter of the main loop will reduce the value of K greatly and require a larger coupling loop. The dimensions rapidly become impractical thus this method is not recommended.
Also, placing the coupling loop inside the main loop at locations other than mentioned here will result in a gross impedance mismatch due to shifted voltage-current phase relationships along the loop perimeter.
Keeping it simple, the best placement for the coupling loop is near the high current, low voltage node of the main loop (180 degrees from the tuning capacitor). Note: It is a good idea to place the tuning capacitor at the top of the main loop, and the coupling loop near the bottom, so that the high impedance presented across the tuning capacitor at parallel resonance is not readily coupled to ground. This will help assure a high Q and make feeding the antenna a bit easier.
Constructing the Coupling Loop
When constructing the small coupling loop, flat, or round conductors may be used. In the case of round conductors, the diameter of the coupling loop is determined from the spacing between the centers of the conductor at opposite sides of the loop. When using thin thin, flat conductors in the coupling loop the inside edge of the loop conductor should be used to determine the dimensions of the loop. In the antenna shown here, an adjustable loop using round vertical posts with a fixed spacing was used, along with horizontal flat metal straps to provide for an easy adjustment of coupling loop area. In this case the width of the coupling loop is determined from the distance between the centers of the vertical posts, and the height of the coupling loop is measured from the inside edges of the flat horizontal straps. Failure to consider this when calculating or adjusting the coupling loop area will result is significant errors.
Using the Software
A link to source code for software suitable for designing your own magnetic loop antennas is provided at the end of this article. Using this software you can design round or square magnetic loop antennas having a single conductor, or multiple parallel conductors.
You will need the following information to use the program:
GEOMETRY: You need to decide if you wish to make a circular or a square magnetic loop. If you are constructing an octagonal loop, assume the loop geometry is circular. The program will prompt for your choice. Simply type "circle" or "square", and press enter.
LOOP CIRCUMFERENCE (meters): The program requires that all physical dimensions be stated in meters. The loop circumference for a square loop is simply circumference=W*4, where "W" is the width of the square loop. For a circular loop, the circumference can be calculated as circumference=2*pi*r, where "r" is the radius of the loop (r= W/2). To convert inches to meters meters=inches*0.0254.
CONDUCTOR DIAMETER (meters): The program requires that all physical dimensions be stated in meters. To convert the conductor diameter to meters: meters=inches*0.0254.
NUMBER OF LOOP CONDUCTORS: This should be a number between 1 and 4. If you enter zero or numbers greater than 4, the results will be invalid.
RESISTIVITY OF LOOP MATERIAL: This is a critical value and you MUST use the correct value for the material you are using for the loop conductor.
for 6061-T6 aluminum: 0.000000037
for pure copper: 0.0000000168
RELATIVE PERMEABILITY OF LOOP MATERIAL: This is a critical value and you MUST use the correct value for the material you are using for the loop conductor.
for 6061-T6 aluminum: 1.000022
for pure copper: 0.999994
LOOP COEFFICIENT OF COUPLING (K): This value should be between 1 and 1/N, where N is the number of parallel conductors in the loop. For a parallel conductor magnetic loop with a spacing between the loops of 3X the conductor diameter (on the centers), K should be greater than 1/N, but less than 1. As a starting point: For four conductors a K of 0.4 is suggested, and for two conductors: 0.9.
LOW FREQUENCY LIMIT (MHz): This parameter is the low-end frequency at which the software is to begin calculating results for. This should be in units of MHz: ie: 3.5 and not 3500000.
HIGH FREQUENCY LIMIT (MHz): This parameter sets the high-end frequency where calculation swill stop.
FREQUENCY STEP (MHz): This parameter sets the interval over which to make calculations.
For an antenna with the following parameters, the output for the 7 MHz and 14 MHz calculations are shown:
Assuming a four foot (3.8302 m) diameter , round loop made of copper, with four one-inch (0.0254 m) diameter conductors.
LOOP TYPE (CIRCLE or SQUARE): circle
LOOP CIRCUMFERENCE(METERS): 3.83023
CONDUCTOR DIAMETER(METERS): 0.0254
NUMBER OF LOOP CONDUCTORS: 4
RESISTIVITY OF LOOP MATERIAL (OHM-METER): 0.0000000168
RELATIVE PERMEABILITY OF LOOP MATERIAL: 0.999994
LOOP COEFFICIENT OF COUPLING (K>=1/N,K<=1): 0.4
LOW FREQUENCY LIMIT (MHz): 3.5
HIGH FREQUENCY LIMIT (MHz): 30
FREQUENCY STEP (MHz): .5
Frequency: 7.000 MHz Rr: 0.0504 ohm
Rhf2: 0.0390 ohm Efficiency: 0.5638
L: 1.8915 uH Xl: 83.1913 ohm C: 273.3 pF
Z: 0.2989 ohm Q: 465.4935
Bandwidth: 15.0378 2:1 SWR Bandwidth: 5.1329 KHz
Pickup loop area: 0.0494 square meters
Frequency: 14.000 MHz Rr: 0.8060 ohm
Rhf2: 0.0552 ohm Efficiency: 0.9360
L: 1.8915 uH Xl: 166.3826 ohm C: 68.4 pF
Z: 0.9280 ohm Q: 96.6104
Bandwidth: 144.9119 2:1 SWR Bandwidth: 49.4633 KHz
Pickup loop area: 0.1532 square meters
The simplified numeric model is in general agreement with the observed behavior of the test antenna. It is possible to increase the efficiency of a small magnetic loop antenna significantly by means of adding multiple parallel loops. The useful limit for parallel conductors appears to be three or four. An increase in radiated RF power of up to 4.5 dB over a single loop of similar dimensions and construction has been noted in testing of the four conductor configuration. In addition, a new equation for calculating the area of the small coupling loop has been presented, and software for modeling the antenna has been provided.
Click HERE to view/download the original source code for the software model.
Click HERE to download the source code for the latest version of the model (lots of improvements!).
Click HERE to see a picture of a two conductor magnetic loop for 50 MHz with fixed tuning.
Links to a few more images...
field strength meter hack for measuring magnetic field strength
details of the small coupling loop
more details of the small coupling loop
tuning cap mounting
rear view of the capacitor mount
one corner of the loop
the pedestal mount
G. S. Smith, "The Proximity Effect in Systems of Parallel Conductors and Small Multiturn Loop Antennas", Office of Naval Research Technical Report 824, 1971.
G. S. Smith,"Loop Antennas",Chapter 5 in J.L. Volakis, "Antenna Engineering Handbook", 2007 .
R. K. Zimmerman , "Uniform Current Dipoles and Loops' , AntenneX Issue No. 108, 2006.