Design and Impedance Matching

of a

Magnetic Loop Antenna

Keith Greiner

Updated August 23, 2023

This is a description of a magnetic loop antenna project that includes the steps needed to create two versions of a system having one large loop and one small loop.  The first system uses a small loop made from three turns of number 12 stranded wire.  After the first system is completed, there is a description and steps needed to construct a modification that uses a small loop made of coaxial cable. The projects are an application of the MFJ-259D antenna analyzer, an MFJ grid dip meter, an MFJ-16010 antenna tuner, an AM broadcast band stop filter (after the tuner), a Ham-it-Up upconverter, a Nooelec SDR, Gqrx software, the online Smith Chart tool at https://www.will-kelsey.com/smith_chart/, and variable capacitors manufactured by the Oren Elliott company.   

There are five sections: 

1) Discussion of the Project, 

2) Summary of the Steps for the First Design, 

3) An Improved Small Loop, 

4) Steps to Build the Improved Magnetic Loop, and

5) Radiation Pattern

1) Discussion of the Project

A magnetic loop antenna is one of a general type of loop antennas.  It has a radiation pattern that is along the plane of the loop, with a null at a right angle to the plane of the loop.  The typical magnetic loop has a larger loop, capacitors, and a smaller loop.  Together, I am calling the two loops and the associated capacitors as an antenna "system."  In this system, the larger loop has a perimeter that is very small compared to the operating wavelength.  It may have one or two (ie: not very many) large turns of a low resistance conductor and a large capacitor.  This example has one loop and a large capacitor.  Together, the loop and capacitor combination form a parallel resonant tank circuit.  In this example project the larger loop has a circumference of about 78 inches, which is about 2.4% of the wavelength of 3.6 Mhz and about 4.8% of  7.1 Mhz. 

The first design shown here, is like a parallel tuned circuit that has a capacitor and inductor connected in parallel.  A small, three-turn loop transfers energy to, or from, another circuit.  Some authors may call that smaller loop, the pick-up loop, or maybe the primary, or maybe the secondary (depending on one's perspecitve), or maybe the coupling loop,  but I have decided to simply refer to it as the smaller loop.  So we have a large loop and a small loop where the large loop is part of the capacitor/inductor tank circuit. The small loop is just referred to as the "small loop."  The method of using a small loop to connect external circuitry to a larger loop inductor is used in oscillators, amplifiers, baluns, variometers, and antennas connected to transmitters and receivers. The first design shown here in Section 2 was created as an antenna for receiving.  In Section 3 the smaller loop is made of coaxial cable which makes it a better system for receiving and transmitting. 

The following image shows an LTSpice simulation that can help us understand how the magnetic loop operates.  Here we have a band-pass filter that uses a parallel tank circuit having a large capacitor in parallel with a one-loop inductor.  The capacitor is set to 260 pf and the inductor is set to 0.5 uH.  The output at Out_2 has an inductance of 0.01 uH connected to a 50 ohm load. To make the circuit work in LTSpice, I added a one ohm resistor and a 300 pf capacitor that connect in series with the sine wave signal source.  If this simulation were a true magnetic loop antenna, it would not include the 1 ohm resistor or the 300 pf capacitor.  It would include only the section outlined in a light dotted line box.  

The simulation can be analyzed using a frequency sweep that shows how the tank circuit component values affect the voltage and current seen at Out_2.   The LTspice model shows a sharp voltage peak of resonance around 7 mHz.  By changing the internal resistance of the parallel inductor or capacitor, one can see how the sharpness of the resonance changes.  If the internal resistance is low, or near zero, the peak will be sharp.  If the internal resistance is increased, the peak will be broader.  It you begin with the circuit as shown, and add one ohm of series resistance to the inductor component, you'll see a nice broadening of the resonance curve and a reduction in the dB values in the left-hand Y-axis of the LTspice display.  After the project is completed, one can see the peak in the spectrum view of the SDR.  Changing the resistance allows an analyst to simulate the wire size used in the magnetic loop.  Experiments with magnetic loops indicate that larger diameter conductors in the loop have lower resistance, a sharper resonance and a higher Q.  I found that in some cases, I’m ok with a higher resistance loop (ie: smaller wire size) when I want the system to have a broad peak at the point of resonance.  The broader bandpass, however, has a lower efficiency. 

For the project to be successful, all the pieces need to work together.  The magnetic loop antenna must first resonate at the desired frequency, and then it's impedance must be matched to the transmission line.  In the system that uses an upconverter for receiving, the transmission line impedance needs to be matched to the input of the upconverter.  The upconverter is connected to a Nooelec software defined radio (SDR) and ultimately to a computer running the Gqrx software.  The system design is shown below.  In order to ensure that the upconverter sees a 50 ohm load, I use the MFJ-16010 tuner.  With that, the receiver can see an impedance of 50 ohms, and an SWR of 1:1.  The operator can change the settings on the tank circuit capacitor or the MFJ tuner and watch the frequency peak move up and down the dial. Be careful, however, becase a very very small physical change in the tuning capacitor can result in a big frequency change in the dial, and it is possible to not see the change. 

The magnetic loop antenna is constructed of ¼-inch flexible copper tubing.  The tubing is repurposed and was once used to connect water to a refrigerator ice-maker.  The loop has a diameter of about 25 inches and a circumference of about 78 inches.  It’s a bit irregular.   The main loop is open at the bottom where it is connected, in parallel, with three variable capacitors that have a maximum of 835 pf.     Originally, there were two Oren Elliott 73-1-12-53W capacitors that each have a range of 30 to 245 pf, and one junk-box capacitor that has a range from 19 to 345 pf.   Later, I replaced the junk-box capacitor with another Oren Elliott 73-1-12-53W.  So now, there are three identical high voltage variable capacitors.  I added a switch in series with one of the capacitors so it can inserted or removed from the circuit. For 40 meters, one of the three capacitors is removed because the circuit needs only two of the capacitors.

At the top of the magnetic loop is a smaller (pick-up) loop that has three turns of number 12 stranded copper wire.  The turns in the smaller loop are in the oval shape shown below, with about 17 inches closely aligned to the magnetic loop.  I formed the small loop on top of a drawing on a piece of foam board to keep it with the correct curvature shape, and mounted the pick-up coil and foam board to the main loop.  This small loop replaces one that was a perfect circle.  This design operates better than the perfect circle design. From the pick-up loop there is a 36-inch run of twisted-pair, going to Test Point A.

At Test Point A, there is a small coil of five turns that is used to insert the grid dip meter.  To set the resonance I connected the two twisted pair wires and inserted a grid dip meter via that miniature loop at the test point. The grid dip meter was used to adjust the capacitors so the system resonated a 3.6 Mhz. Be careful, here, because the resonant point is very narrow, and if you turn the grid dip meter dial too rapidly, you may never find it.  The same is true if you change one of the capacitors to change the resonant frequency.  Next, the connections were changed so the test point coil was not across the test point but was in series with the small loop.  This is where the MFJ-259D was connected: at Test Point A.

With the MFJ-259D connected, the resonance was confirmed and the impedance was found to have an R value of 83 and an X value of 65, with an SWR of 2.9.  When tuning the MFJ-259D I found that the X value increased at frequencies above and below, 3.60 Mhz.  That is, the X value increased when the VFO dial was turned in both directions away from 3.60 Mhz. That observation confirmed that the system was resonant at 3.60 Mhz.  Adjusting the capacitors that are part of the magnetic loop antenna (as the parallel tank circuit) resulted in changes to the resonant frequency seen by the MFJ-259D as well as the R and X values.  Testing at point A at 3.6 Mhz, the antenna analyzer showed the following.

The values of R and X were entered onto the Smith Chart tool, and the tool plotted point DP1 as shown in this image. DP1 stands for “data point number 1.”  I added a larger text to this image to make the data point labels more visible here.   

Near the center of the chart there is a green circle that marks the outer bounds of an area where the SWR would be 1.5 or less.  By using the tool to simulate the connection and by experimentally adding and removing resistance values I was able to see how various values of resistance might result in data points closer the center of the chart.  DP2 is one of those points just outside the 1.5 SWR circle and was found by adding a 100-ohm resistor in parallel to the loop antenna.   

Next, and again using the online tool, I tried adding several values of capacitance in parallel with the resistor and the antenna, and stopped when a value of 220 pf placed DP3 inside the 1.5 SWR circle.  That combination of 100-ohm resistor and 220 pf capacitor obtained an R = 50 and X = 9.  Other resistance and capacitance values could bring the location of DP3 closer to the center, but I was limited by the resistor and capacitor values that are in my collection. So, 100 ohms resistance and 220 pf will do the job.  Based on the Smith Chart tool, it looks like ideal values of R = 80 and Xc = 177 (250 pf) would put a data point almost exactly at the middle. 

Applying the Smith Chart model, and after inserting the resistor and capacitor into the circuit, I checked the SWR and observed a value of 1.2 using the MFJ-259D.  After making some minor adjustments to the connections and generally moving things around, the SWR moved to 1.4.  with R = 72 and X = 4.  By verifying the meter readings using the formula; Z = (R2 + X2)0.5 , it was found that the system Z was 72.1 ohms and the SWR = 72.1/50 = 1.44.  Readjusting the main capacitor, I was able to get the SWR to 1.1.    

The numbers jump around a bit on the MFJ-259D, so at one instant the SWR could be 1.44 and another instant it could be 1.3, 1.2, or 1.1.  That is an acceptable range because there are many things that can change just a little bit and affect the readings. Among those are physical items around the antenna, the temporary connections in the wires, slight movement of the capacitors, and a slight tendency for the instrument’s oscillator to be affected by surrounding conditions.  I concluded the SWR was adequately within the 1.5 SWR circle.  

I think it is important to remember that instability of the readings is to be expected.  Grid dip oscillators are known to be unstable but helpful.  As one moves around the wires and makes seemingly minor adjustments to the location and the connections, the values of R, X, and SWR reported by the MFJ-259D will change. I am expecting that the values will settle down somewhat after I make the connections and the physical structure of the circuit more permanent. 

The magnetic loop antenna was connected to the up-converter via a junk box, 34-foot, RG6U (75-ohms).  I alternately adjusted the tuner inductance and capacitance, and the antenna capacitor and found a minimum SWR of 1.5 to 1, with the tuner inductance setting at J, and capacitance setting 10, which is the maximum.   At this point, the MFJ-259D readings were; R = 75 and X = 0 (varying between 0 and 8). Calculating the SWR using Z = (R2 + X2)0.5  , it was found that the system Z was between 75 and 75.4 for an SWR of somewhere between = 1.5 and 1.51.  That’s well within the range that was need.  By adjusting the three variable capacitors I was able to use the SDR to tune from CHU 3.33 Mhz. to WWV 5.0 Mhz. and on to WWVB10.0 Mhz.  Clearly, the magnetic loop antenna functioned well on both the 80-meter and 40-meter bands.       

2) Summary of Steps for the First Design

These steps were used to for the example shown above.  They should be applicable to a broader range of antenna designs and frequencies.  

Following are the steps that were used to set up this system.

1. 1. 1. Design and construct the antenna.

      2. Use the MFJ grid dip meter to adjust the antenna to the desired frequency.

      3. Use the MFJ-259D to confirm the frequency, make fine-tuning adjustments, and determine the R, X, and SWR values.

      4. Use the Smith Chart tool to find a combination of inductance, capacitance, and resistance that will provide a 1:1 match at the antenna with R = 50, X = 0 and SWR = 1:1 or as close as possible.  

      5. Use the Smith Chart findings to adjust the circuit.

      6. Use the MFJ-259D to confirm that the Smith Chart findings are working.

      7. Connect the antenna to a coaxial cable, and the tuner, and use the MFJ-259-D to adjust the inductance, capacitance, and antenna to a minimum SWR on the receiver side of the tuner.  In this case, that’s about the same as the inductance of the coaxial cable.

      8. Remove the MFJ-259D and connect the output of the tuner to the AM Broadcast band-stop filter.

      9. Connect from the Band-stop filter to the up-converter.

      10. Connect the up-converter to the SDR.

      11. Connect the SDR to the computer.

      12. Set up the SDR program as needed, keeping in mind that the upconverter shifts signals up by 125 Mhz. so the 80-meter ham band begins at 128.5 Mhz. on the display.  

3) An improved Small Loop, and Then an Even More Improved Small Loop

The small loop shown above consists of three loops of  number 12 wire, and a 35-inch twisted pair of wires connected to an MFJ  tuner.  However, In the literature of magnetic loop antennas, you will find that the smaller loops are constructed with a modification of coaxial cable.  Several coaxial-based designs may be found.  I selected the design shown here because of its simplicity. It is a small loop of coaxial cable with the center conductor attached to the shield at the point where the incoming coaxial cable forms the oval.  The use of an oval shape is a departure from what I've seen in the literature.  Virtually all the loops I've seen in the literature have a small loop that is a perfect circle.  I found that the oval has a better connection with the point of greatest current in the larger loop. So this design uses an oval.   

On the left we have a diagram of the oval and on the right is a close-up of the point where the oval is completed.  

Notice how, the coaxial cable forms an oval having a length of about 8” and a height of about 3" and a circumference of 20.5”.  It is not a circle.  The oval design allows the loop to lay alongside the top of the larger loop.  That’s the location with the greatest amount of current.  The current maximum is opposite the capacitors and is at the top for two reasons; 1) having the high current point at the top raises that point away from the ground, and 2) the size of the three high-voltage variable capacitors makes it impractical to suspend them at the top of the supporting pole. 

In this design, the coaxial cable arrives from below and circles around in a clockwise direction (from this perspective).  At the point where the cable completes the oval, the inner conductor is connected to the outer shield of the incoming cable, and the outer shield on the right side of the loop is left unconnected.  This connection is shown in the enlarged diagram on the right and in the images below.

Because it is difficult to form a good electrical connection with the aluminum shield in today’s coaxial cable, my first attempt at this design used the manufacturer-installed end connectors on the coaxial and a Female-to-Female type-F splice connector shown in the image shown below.  This worked well for awhile, and was most successful for receiving.  However, when I used it for transmitting, I found that the connections were of poor quality and lowered the output signal.  I still got a good SWR, but moments after turning on the transmitter at, say 50 watts, the output dropped to something less than 10 watts.  It appears the entergy was been used up in bad connections.  I opened up one of the sealed manufacturer-installed connectors and found that the connecdtion was made by compressing an outer metal ring, without first having removed the outer, black, insulation from the cable.  It's no wonder that with time and usage it became a high resistance point in the system. 

Still, maybe you will want to try this as a quick and easy loop for receiving.  For that reason, I'm showing the construction of the coaxial loop as I first constructed it.  Later, I will show an improvement. 

First is an image of the parts before they are assembled using the manufacturer-installed connectors.

Below is an image of the completed smaller loop after it was attached at the top of the larger loop. Notice the point of connection at the center bottom, and the shape of the loop.  The design is to be a oval, but as a practical matter, when using the original connecttors that were installed by the manufacture of the coax, it's not an exact, perfect, oval.  However, it works.  Would it work better if it were a perfect oval?  Yes.  Perhaps a future analysis will compare this loop with one that has a perfect oval, and still another with a perfect circle.  

Now lets look at the redesign of the coaxial loop.   This still uses the design where the inner conductor is connected to the outer conductor after a loop as shown above.  The difference is in the type of connection to the outer loop.

Here are the steps.

1. I located the place where the inner conductor was to be connected to the outer conductor, and removed an inch of the outer black insullation.

2. I then cut one inch of 5/8" flexible copper tubing, and then slit the tubing along it's axis to form a tube with an open side.  

3. I slipped the tubing over the coaxial cable and positioned it over the place where the outer insulation had been removed.

4. I carefully tightened the copper tubing around the coax so that one side overlapped the other  in a tight wrap.  

5. See the photo below.

6. Next I used part of a 208 Copper Offset Tongue Lug, Southwire type OLG2-8CQ2.  The original lug is on the left and the modified lug is on the right. I removed the tab, and coated one side with solder, to make the later connection easier. 

7. Next I made the loop and soldered the center conductor to the outer flat side of the lug.  The following image shows the set up for soldering.  Having the solder already applied to the lug and the center conductor made the process easier, although there was an issue with having enough heat to make the solder joint perfect without melting the insulation around the center conductor and without melting the insulation inside the cable.  Here is the setup prior to the soldering.

8. The final assembly looks like this, viewed from the non-solder side.  In this image, to the left, opposite the tightening screw, I've convered the open portion of the coaxial cable with black electrical tape.

9. Tighten the screw to form a secure electrical connection and mount the loop in the same position and shape as the previous loop, and enjoy the success of improved reception and transmitting.  the consistent behavior of the new design during transmit reinforces the observation that the previous problems were with the Type-F connectors as described above.

Compared to the very first, original loop that had three turns of number 12 wire, the coax loops contributed to a reduction in RF noise and a broader tuning range.  The example shown above had three capacitors connected in parallel with the loop, and tuned to the 80-meter amateur radio band.  By removing one of the capacitors and using the MFJ tuner, the system tunes with a 1:1 SWR on 40-meters.  When used with a 200 mW WSPR beacon, and with the antenna at ground level, the signal was spotted throughout North America. When the system is used with a transmitter, do not touch any part of the large loop and capacitor tank circuit.

4) Steps to Build the Improved Magnetic Loop

In Section 2, I showed the steps I took to create the first magnetic loop antenna of this project.  With the improved small loop in place, I made the following list of steps that could get you directly to the improved antenna. 

1. 1. 1. Create a large loop having a diameter of about 25 inches and a circumference of about 3.14 * the diameter.  Use a large stiff wire or a small flexible copper pipe with at least a ¼ inch diameter.  You could also use flexible copper with a diameter of 5/8, some other workable size.  Remember that the larger the diameter of the pipe, the lower the resistance and the higher the Q.

      2. Mount the large loop on a vertical pole or other non-conductive stand so the open part is at the bottom.  

      3. Firmly mount one or more variable capacitors at the bottom.  I now use up to three Oren Elliott 73-1-12-53W capacitors connected in parallel with plastic knobs on each tuning shaft.  The plastic knobs minimize the effect of your touch on the frequency. I put a switch on one of the capacitors so it can be removed from the circuit. I tried using a junk capacitor from an old radio, but it was so sensitive to miniscule adjustments that it was very difficult to find the point of resonance.   Do not touch any part of the pipe or capacitors while the system is in operation. Each 73-1-12-53W capacitor has a range from 30 pf to 245 pf and a voltage rating of 3,500.

      4. Create a smaller loop using the revised 8-inch by 3-inch design and parts described above, and with about a 10-foot coax between the smaller loop and the MFJ tuner.

      5.  You will likely need to use an appropriate adapter to connect what is likely a Type-F cable connector to the PL259 on the tuner. 

      6. Check the frequency using a grid dip meter or the MFJ-259D and make sure the capacitor/large loop circuit is tuned to an appropriate frequency.  

      7. Using the MFJ-259D, recheck the impedance and adjust accordingly.

      8. Using an appropriate connecter, make the connection from the tuner to the upconverter.  

      9. Connect the upconverter to the SDR, and then to the computer with Gqrx installed. 

      10. Be sure to set the Gqrx settings to the correct configuration needed to make it work with the RTL-SDR.

      11. Start, and run, and enjoy.

      12. Of course, there can be a a few thousand things that go wrong.  I've tried to account for everything you need to know, but undoubtedly there will be steps that are not included here.  So, if this doesn’t work, it is an opportunity problem-solve and find a workable solution.

5) Radiation Pattern

The theory of magnetic loop antennas suggests that the design emits in a figure-eight radiation pattern with the primary lobe running in the plain of the loop.  That’s the direction where the electrical field is the greatest.  The magnetic field is at right angles to the loop and is the direction of minimal radiation.  The image presented below shows a drawing and labels that describe the direction of radiation.  The loop likes like a straight line because when viewed from above, that's what one would see.  In practice, it can difficult to measure the actual radiation pattern unless one sets up a controlled experiment.  

Directional beam antennas are another matter. For a beam antenna, with a precise forward pattern, one can detect the pattern fairly easily during normal operation because the operator can see changes in a received signal strength when the beam is rotated.  

With this magnetic loop in operation, I expected to see directionality in WSPR reports, either from the absence of reports from the direction of the magnetic field, or from differences in signal strength from receiving stations along the direction of the plain of the loop vs. at right angles to the plain of the loop.  

So far, there has been no indication of directionality of this antenna.  More research is planned and a future update is likely. 

(c) 2023 by Keith Greiner

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