impedance of small loop antena

[neazoi]

Hello,
I know that the impedance of large loop antenas for HF is about 200 ohms, so they can be matched to a unbalanced line using a 4:1 balun.

But what should I expect the impedance of a small loop antenna (magnetic) to be in general?
Any references on this would be useful.

 

[vfone]

The impedance of a small loop antenna (circumference << λ/2) is hard to be defined by a formula, but is good to know that the impedance always is very inductive.
So, the impedance looks like and inductance in series with a resistor (loss resistance).

 

[neazoi]

The impedance of a small loop antenna (circumference << λ/2) is hard to be defined by a formula, but is good to know that the impedance always is very inductive.
So, the impedance looks like and inductance in series with a resistor (loss resistance).

Is it generally expected to be much lower than 50 ohms or much larger (for a single turn loop)?

 

[FvM]

As a < λ/4 line is working as a short with some inductance, it should be quite obvious that an electrical small loop antenna has Z << 50 ohm.

The loop impedance is comprised of loop inductance, skin and proximity effect loss resistance and radiation resistance.

A derivation can be e.g. found in the loop antenna chapter of Ballanis, Antenna Theory (and probably most profound antenna text books). Some calculations also in this TI application note https://e2e.ti.com/support/low_power_rf/w/design_notes/an003-srd-antennas.aspx

 

[vfone]

Yeah, I know this app note from TI (actually from former Norwegian Chipcon).
There is an impedance equation for small loops at page 8, which never came even closer to real life measurements.
Generally for small antennas (compared to the wavelength), just using simple equations it's hard to predict their impedance and also the radiated performance.
Better is to do an EM simulation, or real life measurements.

 

[FvM]

There is an impedance equation for small loops at page 8, which never came even closer to real life measurements.

The same expression for the radiation resistance of a circular loop is derived from basic EM equations in Balanis 3rd edition p238, thus I assume that it's correct. Technically, there's no reason why the raditation resistance should depend on other parameters than the relative size related to wavelength. Loss resistance terms in contrast depend on several design parameters.

 

[WimRFP]

The formulas for calculating the increase in resistance due to radiation for small single turn loops have reasonable to good accuracy, as long as the loop is electrically small. If not, the actual resistance due to radiation increases.

The total resistance (I mean Re(Z)) is the sum of the radiation resistance and the ohmic loss resistance. Ohmic loss is the dominant factor in electrically small loops. If you feed the loop in a way that there will be common mode current at the feed line, then the formulas go wrong as the formulas only consider the radiation from a uniformly distributed current in the loop.

For finding Im(Z), you can use the standard formulas for inductance.