How do I calculate low frequency loop antenna?

[Amish_Fighter_Pilot]

I need tx and receive antennas for my project and I want to make loops, but I have no idea how to calculate them. Can anyone recommend a good educational resource that can help me determine conductor size, loop diameter, and number of turns? I'm using the 500Hz to 500KHz range so I know it won't all be one antenna. Thanks

[A.Z.]

check if these

https://miguelvaca.github.io/vk3cpu/magloop.html

https://miguelvaca.github.io/vk3cpu/magloop_equations.html

may be useful for your purposes

[geggi1]

For these frequencies its more like resonant coil you will require.

[radiolistener]

To calculate and build a magnetic loop antenna, start by forming a loop from a piece of wire or conductive tubing. Measure the loop’s inductance, then add a capacitor in parallel that resonates with the inductance at your desired frequency. Technically this is LC circuit. The resonant frequency is given by:

  f = 1 / (2*pi*sqrt(L*C))

Larger loop diameters generally improve signal strength due to increased radiation efficiency and better coupling.

After that, you’ll need to match the antenna to your feedline (typically a coaxial cable). A gamma match is a practical and commonly used method for this purpose. I recommend using a NanoVNA for precise tuning, as calculated parameters often don't yield optimal results without fine adjustment.

[Andy Chee]

Transmitting loops can be difficult to make work. Basically you want DC resistance of the loop to be as low as possible.

See here for some construction hints.

https://web.archive.org/web/20201218104218/http://members.iinet.net.au/~sadler@netspace.net.au/tmla.html

https://youtube.com/watch?v=sd83z_X5XGQ

[Amish_Fighter_Pilot]

Thanks for all the replies! I will look over your links and try to figure it out!

[radiolistener]

Transmitting loops can be difficult to make work. Basically you want DC resistance of the loop to be as low as possible.

No, it transmit the same effective as receive. Regarding to DC resistance, it doesn't matters for transmitter, because it transmit with AC current, not DC. If you properly matched impedance at transmitting frequency, it will works ok.

The main limitation of magnetic loop antennas for transmission, as with dipole antennas, is that shortening the antenna increases the required Q-factor for efficient radiation. Since the Q-factor is inversely proportional to bandwidth (Q = 1/BW), this results in a narrower operational bandwidth.

Thus, a physically shortened antenna operates over a narrower frequency range. However, it is important to note that this is a general characteristic of all resonant antennas and applies equally to dipoles and other types. In this regard, a magnetic loop is the same as a half-wavelength dipole of comparable size. Also it requires very high voltage capacitor for frequency tuning.

It is also important to note that electrically small antennas, due to their high Q-factor, generate extremely high field intensities in their near field, often exceeding safety limits by a significant margin. Therefore, compact antennas - regardless of type, whether dipole, magnetic loop, or others, can pose a potential health hazard when used with transmitter.

Thus, while large full-size antennas are bulky, they are generally safe for health and present significantly fewer noise issues for radio reception than small-size antennas.

PS: I also often used this kind of match for TX in my experiments (see left picture), it also works good and can be easy tuned:

[fourfathom]

[...]
After that, you’ll need to match the antenna to your feedline (typically a coaxial cable). A gamma match is a practical and commonly used method for this purpose.

The OP did mention "number of turns", so the matching techniques used in single-turn loops may not apply (but I suppose you could consider a tap on a multiturn as a sort of gamma match).  Of course the typical multi-turn resonant loop is usually going to be a really poor transmit antenna because of losses.

[Andy Chee]

Transmitting loops can be difficult to make work. Basically you want DC resistance of the loop to be as low as possible.

No, it transmit the same effective as receive. Regarding to DC resistance, it doesn't matters for transmitter, because it transmit with AC current, not DC. If you properly matched impedance at transmitting frequency, it will works ok.

The main limitation of magnetic loop antennas for transmission, as with dipole antennas, is that shortening the antenna increases the required Q-factor for efficient radiation. Since the Q-factor is inversely proportional to bandwidth (Q = 1/BW), this results in a narrower operational bandwidth.

Loop resistance affects Q.  If you have high loop resistance the Q will be lowered, turning the antenna into a dummy load, rather than a radiator.

https://en.wikipedia.org/wiki/Radiation_resistance

Please note, R_rad + R_loss

High loop resistance will increase R_loss turning the antenna into a dummy load.

No amount of impedance matching will reduce R_loss

R_rad is dependent on antenna length relative to wavelength.  For a loop, this means making the antenna longer i.e. multi-turn loop 

Increasing R_rad is good.  Increasing R_loss is bad.

[radiolistener]

Loop resistance affects Q.  If you have high loop resistance the Q will be lowered, turning the antenna into a dummy load, rather than a radiator.

Yes, but the same principle applies to any resonant antenna - including dipoles, Yagi-Uda arrays, and others. This is not unique to magnetic loops. Higher conductor (loop or element) resistance reduces the Q-factor and increases Ohmic (thermal) losses, which in turn reduces radiation efficiency. In the worst case, the antenna acts more like a dummy load than a radiator.

If you consider where the power fed into an antenna can go, there are only two destinations: radiated electromagnetic energy and thermal losses. These thermal losses are directly determined by the resistance of the conductors used in the antenna. The rest of the power must be radiated - it cannot simply disappear. This is a fundamental consequence of energy conservation.

Moreover, regardless of antenna type, if two antennas have similar physical size and resonant frequency, they will tend to have similar Q-factors and similar thermal losses - assuming similar materials and construction. This is because the radiation resistance and conductor resistance scale in predictable ways with geometry and frequency. So it's not about the type of antenna, it's about the physical constraints and quality of construction.

Therefore, reducing conductor resistance (e.g., using thicker wire, better materials, or soldered joints) improves efficiency in all antenna types, not just magnetic loops.

However, on the other hand, excessively high Q-factor is not always beneficial, as it can result in an overly narrow antenna bandwidth, which may be unacceptable in some cases. Therefore, it may sometimes be necessary to intentionally use conductors with worse conductivity in order to reduce the Q-factor and broaden the antenna bandwidth, even at the expense of efficiency.

That's why Q-factor more than 2000 is not practical for small antennas. For 500 kHz carrier Q-factor of 2000 leads to just 250 Hz bandwidth which is too small for common applications, even for CW.

[Wallace Gasiewicz]

I built and used a mag loop.  Radio is correct.  A small loop has very bad Radiation resistance, so the ohmic resistance must be kept very low.  A good mag loop has high Q and is very sharp in it's tuning otherwise it is not a good radiator. Even solder joints are not good. Usually silver solder or welding of some sort is used on the radiating loop part.   The radiation resistance is mostly a function of surface area of the loop, so bigger pipe is better.  The tuning capacitor must be able to stand several thousands or even tens of thousands of volts. Usually a vacuum variable capacitor.  These things are very expensive  There are several web sites with calculators for mag loops that take in consideration the size of the loop. the size of the pipe and the tuning cap.
You would need a huge mag loop for low freq.  A coil does not really work since most of the RF is contained around the coil, so these antennas are not used for transmitting, although they have been used for Rx for 100 years..  I think that someone made a mag  loop for 80 meters that had two loops.  It won the ARRL award for antenna design that year.     
At lower frequencies a large loop (not a mag loop) would be  far more practical, .

[Xena E]

A receiving loop for very low frequencies the problem is its inductance requires a lot of turns of wire or a huge area.

One way to overcome that is to use inductance transformation, so that loops of a reasonable size can be used at low frequencies.

The construction of the transformer obviously has to follow good RF practice, and the transformation of inductance follows the square law, ie., the ratio of inductance is the square of the turns ratio...

Tuning of the loop in this case is done on the receiver side of the transformer.

X

[Amish_Fighter_Pilot]

[...]
After that, you’ll need to match the antenna to your feedline (typically a coaxial cable). A gamma match is a practical and commonly used method for this purpose.

The OP did mention "number of turns", so the matching techniques used in single-turn loops may not apply (but I suppose you could consider a tap on a multiturn as a sort of gamma match).  Of course the typical multi-turn resonant loop is usually going to be a really poor transmit antenna because of losses.

I just want to be clear that I am not trying to transmit more than a few feet. It's a sort of RF material analysis system, but my current plan for it is a "interference as sound" art project. So poor transmission is totally acceptable!

[Amish_Fighter_Pilot]

A receiving loop for very low frequencies the problem is its inductance requires a lot of turns of wire or a huge area.

One way to overcome that is to use inductance transformation, so that loops of a reasonable size can be used at low frequencies.

The construction of the transformer obviously has to follow good RF practice, and the transformation of inductance follows the square law, ie., the ratio of inductance is the square of the turns ratio...

Tuning of the loop in this case is done on the receiver side of the transformer.

X

I'm new to this stuff so I am just learning what a balun is in radio parlance. Am I correct in assuming I will need to create a balun for every antenna that I build for this system?

Edit: I forgot to mention that my antennas will connect to an AD831 mixer module with 50ohm sma connections

[Andy Chee]

I just want to be clear that I am not trying to transmit more than a few feet. It's a sort of RF material analysis system, but my current plan for it is a "interference as sound" art project. So poor transmission is totally acceptable!

Unfortunately being unclear is extremely common, and can lead to unrelated discussion.

Are you trying to construct something like an induction heater?

Also, please elaborate on “interference as sound”. Do you want to manipulate radio white noise and convert it to audio?

Please include as much big picture detail as you can.  As a newbie, it’s understandable you may not be familiar with terminology or techniques. That’s why details are important.

[Amish_Fighter_Pilot]

Unfortunately being unclear is extremely common, and can lead to unrelated discussion.

Are you trying to construct something like an induction heater?

Also, please elaborate on “interference as sound”. Do you want to manipulate radio white noise and convert it to audio?

Please include as much big picture detail as you can.  As a newbie, it’s understandable you may not be familiar with terminology or techniques. That’s why details are important.

That is a great suggestion. I have a lot of ideas for this system as it is basically a multi-function signal send and receive system. An induction heater would be a good use for it if I can pair it with a bigger amp like the OP541. I could easily change a couple accessories around and this can be anything from an AM radio to a low frequency navigation system. The sound sampling stuff is for fun. I don't know all of what I intend to do with all of this, but I'm having fun and it is better than spending money on something like alcohol or gambling. Mostly I will be listening to a beat frequency and then saving any fun sounds that come out of causing phase and frequency distortions with various sorts of interference.