I was doing some research about the relation between wavelength and antenna size and shape. I was mostly interested in 15KHz rf range.

Based on my research I found the following:

  • A squarish shape antenna is the best sender/receiver
  • Wavelength of the 15Khz frequency is around 14990 meter

A simple antenna with half the wavelength of signal can send/receive this frequency but it can be altered to smaller size by using thin wire wrapped around a ferrite object. (Same method used in AM antenna design).

Now, let say if I use the wire gauge 26 ( with 0.4mm / 0.0159 inch diameter), how many wire turns (loops) is required for a 50mm (~ 20 inch) square shape antenna to send/receive this 15Khz signal?

  • $\begingroup$ As @glenn-w9iq correctly stated, "A squarish shape antenna is the best sender/receiver" is an incorrect statement. However, I would like to know where you read that. Do you have a link you can share with us to that page? $\endgroup$ Jan 2, 2018 at 3:24
  • $\begingroup$ also: have a look at this page: sites.google.com/site/sub9khz/transmitters $\endgroup$ Jan 2, 2018 at 14:30
  • $\begingroup$ @Mike Waters, I need something mobile that I can carry with me and the singnal should penetrate the ground for up to 7m depth so I think its the best practical design for vlf and elf frequencies is square shape antenna because the wavelength is too wide and making other types of antenna is not feasible. $\endgroup$
    – Samk80
    Jan 2, 2018 at 21:52
  • $\begingroup$ @Optionparty, interesting. It operares at the frequency 15Khz too which is suitable for my project but I already have a kit. If I have to design a circuit for a metal detector, where is the best place to start? $\endgroup$
    – Samk80
    Jan 2, 2018 at 21:56
  • $\begingroup$ This is the kit adrianandgenese.com/blogger/2012/07/13/… $\endgroup$
    – Samk80
    Jan 2, 2018 at 22:01

1 Answer 1


A squarish shape antenna is the best sender/receiver

There is no practical basis for this assertion.

Wavelength of the 15Khz [SIC] frequency is around 14990 meter [SIC]

The formula for the reasonable approximation of wavelength is

$$\lambda (in\space meters) = \frac{300}{Frequency\space in\space MHz} \tag 1$$

Since 15 kHz is 0.015 MHz, it has a wavelength of ~20,000 meters.

When a loop antenna is constructed with a loop circumference that is less than 1/10 wavelength, it is classified as a small loop antenna. When designing these types of antennas, one of the most important factors to which the engineer must pay attention is the efficiency. Small loop antennas have very low radiation resistance which gives rise to an inefficient antenna.

Antenna efficiency is defined as:

$$efficiency = \frac{R_r}{R_r+R_l} \tag 2$$

where Rr is the radiation resistance and Rl is the RF resistive losses of the antenna and any losses in the core material.

You can see from equation 2 that as the radiation resistance is reduced, for a given resistive loss, the efficiency drops precipitously.

The radiation resistance of a multi-turn loop antenna that is wound around a high permeability material, such as ferrite or iron powder, is given as:

$$R_r=197n^2\mu_{er}^2\left(\frac{C}{\lambda}\right)^4 \tag 3$$

where C is the circumference of the loops in meters, n is the number of turns of wire and $\mu_{er}$ is the effective relative permeability of the material around which the loops are wound. If the loops are air wound, simply set $\mu$er to 1.

You can see from equation 3 that for a given core material, as the number of turns are increased, the radiation resistance goes up according to the number of turns squared.

The approximate RF resistance of the loop antenna is given as:

$$R_l=n*C*R_{wire} \tag 4$$

where Rwire is the RF resistance of the wire in ohms/meter. The RF resistance of 26 gauge (AWG) copper wire at 15 kHz is 1.265 ohms/meter.

The gain of the small loop antenna is given as:

$$G=1.5*n*efficiency \tag 5$$

Armed with these formulas, you can calculate all of the parameters for any proposed 15 kHz small loop antenna. What you will find is that very small antennas such as you suggest will be very low gain antennas due to low efficiency. Whether or not such an antenna is adequate for your application depends on many other factors such as receiver sensitivity, transmitter power, distance, etc.

  • $\begingroup$ thank you so much for such a comprehensive and detaild response, although I'm not very familiar with most terminologies used in formulas here but I'll dig more to completely understand each one of them. $\endgroup$
    – Samk80
    Jan 1, 2018 at 23:16
  • $\begingroup$ I'm going to build a PI metal detector soon. I have the schematic design and the kit but I don't have any particular antenna after I build this kit, so I'm thinking of designing one. The signal should penetrate up to 30m depth max so I was thinking this type of antenna is a good example for my project. I hope I'm on the right track. $\endgroup$
    – Samk80
    Jan 1, 2018 at 23:23
  • 1
    $\begingroup$ It's easy to build a receive antenna for VLF. In spite of the losses, the noise floor is high enough that losses almost don't matter. But they certainly do if you intend to transmit on a small antenna. $\endgroup$ Jan 2, 2018 at 3:20

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