I mentioned in An NEC-4.2 model of VK5BR’s 1m square loop for 20m that Butler’s ~1m square loop was too large to be considered strictly a Small Transmitting Loop (STL):
Note that the loop is sufficiently large that the current is not uniform around the loop
(Butler 1991) gives a design for a Small Transmitting Loop (STL) for 14MHz and some other bands.
He gives key design data:
Tube Diameter d 0.75 inch Circumference S 12.7 feet Area A = 10 square feet Frequency f = 14.2MHz Power P 100 watts Radiation Resistance Rr = 0.137 ohm Loss Resistance RL = 0.064 ohm Efficiency n = 68% Inductance L = 3.27 micro-henry Q factor = 723 Inductive reactance XL = 291 ohms Bandwidth B = 19.6kHz Distributed capacity Cd = 10.4pF Capacitor potential Vc = 4587V Tuning capacitor Ct = 28pF
The data above appear to ignore some important factors, and estimate some others based on an assumption of uniform current.
Working through these:
- radiation resistance is the free space value and assumes uniform current flow, it is probably wrong;
- loss resistance considers only loop conductor RF resistance (omitting capacitor loss, matching loss, ground loss) and does not adjust it for the non-uniform current distribution and is probably a significant under-estimate;
- (radiation) efficiency depends on the suspect calculated loss resistance;
- inductance is probably wrong, it seems to calculate a circle of the same perimeter, not a square;
- Q factor is probably wrong because of dependencies and the factor 2 in the denominator of the given formula is wrong, (popular, but wrong);
- inductive reactance is probably wrong because of dependencies;
- bandwidth is probably wrong because of dependencies;
- distributed capacity is probably wrong (see Calculation of equivalent self capacitance of Small Transmitting Loop);
- Capacitor potential is probably wrong because of dependencies;
- Tuning capacitor is probably wrong (though not much) because of dependencies;
It is the departure from uniform current that gives rise to a dipole mode in the antenna.
Because these figures depend directly or indirectly on formulae that assume perfectly uniform current (and many are flawed anyway), they will not reveal the dipole mode drive so recourse is taken to an NEC model to estimate the current distribution around the loop.
Running the NEC-4.2 model used for An NEC-4.2 model of VK5BR’s 1m square loop for 20m with 9 segments per side and in free space gives a list of segment currents that can be fairly simply superposed (having regard for amplitude, phase, and time delay) to arrive at total maximum current moment for loop mode and dipole mode:
- loop mode: 0.259*Iin Am; and
- dipole mode: 0.031*Iin Am.
For this 0.18λ perimeter loop, the dipole mode current moment is 18dB below the loop mode… low, but not zero.
Many might regard -18dB as insignificant, but if you were using an STL for the benefit of the deep null that it provides normal to the plane of the loop on receive, the dipole mode dilutes that null.
References / links
- Butler, L. 1991. A Small Transmitting Loop Antenna for 14MHz and 21MHz. http://users.tpg.com.au/ldbutler/HFTXLoop.htm (accessed 07/11/2015).