Small transmitting loops (STL) are very popular with hams, and a fashion is developing for N turn loops. This article lays out some thoughts on a 2 turn STL.
Firstly, to the meaning of “small transmitting loop’. There are a range of definitions used, and they mostly centre around the concept of a size sufficiently small that current is approximately uniform. The issue is about the meaning of sufficiently. Accuracy of estimation of radiation resistance of small transmitting loops sets out a rationale for a single turn loop for criteria that perimeter<λ/10.
This article will compare NEC-4.2 models of loops with the following key parameters:
- 1m diameter (the loop perimeter is 0.07λ);
- 20mm copper conductor;
- frequency is nominally 7.1MHz;
- 16 segments per turn
- when not specified as in free space, the loop centre is 1m above ‘average’ ground (σ=0.005, εr=13);
- the loop is directly fed in the middle, opposite to the tuning capacitor position, cap down;
- pitch is 0.15m.
The model is sensitive to all these parameters.
One turn in free space
Feed point impedance of an untuned single turn loop in free space is 0.0063+j118Ω, from which we deduce Rrfs is 6.3mΩ and apparent inductance is 2.6µH.
Above is a calculation using Calculate small transmitting loop gain from bandwidth measurement.
NEC’s radiation resistance is very close (6.3 vs 6.0) to that for a circular STL (with uniform current) and apparent inductance is very close (2.6 vs 2.5) to that from the basic calculator.
Two turns in free space
Feed point impedance of an untuned two turn loop in free space is 0.0325+j350Ω, from which we deduce Rrfs is 32.5mΩ and apparent inductance is 7.8µH.
Comparing to the single turn loop, Rrfs has increased by a factor of 5.2 times, and apparent inductance by 3.0 times.
Assuming uniform current, you might expect radiation resistance to increase by exactly 4 times due to doubling the length of conductor that carries current, but the uniform current assumption is not valid
Was there negligible flux leakage between turns, the inductance well below the self resonant frequency might be expected to increase by a factor of exactly 4.0 times, but both of those assumptions are invalid.
So, back of the envelope thinking, or extrapolation from calculators intended for single turn STL is not good enough.
Single turn near ground
The radiation efficiency of the tuned single turn loop near ground is 5.2% and its half power bandwidth is 7kHz.
Two turns near ground
The radiation efficiency of the tuned two turn loop near ground is 7.6% (1.6dB better than the single turn) and its half power bandwidth is also 7kHz.
Other key findings / issues
The two turn loop could probably not be tuned an octave higher to 14MHz, is self resonant frequency was very close to 14MHz and it probably is not practical to tune it to the 20m band. As such, it is a physically small loop with restricted multi-band capability.
- Beware of the validity of models depending on assumption of uniform current distribution.
- N turn loops need to be more than proportionately smaller than single turn loops for uniform current distribution.
- Back of the envelope extrapolation from STL calculators is very prone to error for several reasons.
- An NEC-4.2 model of the example loop suggests that a two turn loop may be a little more efficient than a one turn loop of the same size otherwise, and have similar bandwidth.
- It may be a challenge to obtain efficiency greater than 10% over an octave.