Category: Small Transmitting Loops

(Revised 12/11/2015)

Small Transmitting Loops (STL) are loops with approximately uniform current around the loop.

(King 1969) gives us expressions for an equivalent circuit of the ‘loop mode’ and ‘dipole mode’, it consists of parallel branches for each mode of series R and X:

• R0: radiation resistance of loop mode;
• X0: reactance of loop mode;
• R1: radiation resistance of dipole mode; and
• X1: reactance of loop mode.

Plotting these and the combined total Rt and Zt for a 1m diameter (perimeter p=3.14m) lossless circular loop of 20mm diameter conductor from 2-30MHz in free space gives an insight into their relative magnitudes at different frequencies. Continue reading Dipole mode of Small Transmitting Loop per King

(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. Continue reading An NEC-4.2 model of VK5BR’s 1m square loop for 20m

The meaning of the terms efficiency and radiation resistance are often critical to understanding written work on antennas, yet different authors use them differently, often without declaring their intended meaning.

Mike Underhill (G3LHZ) is an enthusiastic proponent of Small Transmitting Loops and in his slide presentation (Underhill 2006) challenges the proposition that their efficiency is low.

The line taken broadly is to introduce his own interpretation of efficiency and to challenge by experimental evidence other views on expected efficiency. Continue reading Underhill on Small Transmitting Loop efficiency

(Dodd 2010) describe a small transmitting loop (STL) and gave some meaningful performance measurements. It is rare to see such measurements and he is to be congratulated.

The loop is an octagon of perimeter 4.7m which at 14.2MHz is 0.224λ so although many will consider it meets the requirements of an STL, the common formula for radiation resistance Rr of a STL fail for perimeter above about 0.1λ (see Accuracy of estimation of radiation resistance of small transmitting loops).

Dodd gives calculations of one of the many simple loop calculators which gives Rr as 0.422Ω, it is probably closer to 160% of that value. This is an important quantity as it has direct bearing on calculated efficiency.

Dodd’s NEC model should have used a better figure for Rr, but it seems unlikely that the structural losses were fully included and its bandwidth prediction will be impaired.

Above is Dodd’s measurement of antenna VSWR at 20m. This is most useful as it allows estimation of the half power bandwidth of the antenna. In this case, the antenna is not perfectly matched at its centre frequency, the residual VSWR is 1.07. The graph allows scaling off the VSWR=2 bandwidth as approximately 42kHz.
Continue reading Review of G3LDO STL (Radcom Sep 2010)

Several correspondents have asked about the application of Calculate small transmitting loop gain from bandwidth measurement to the helically loaded small transmitting loop.

The helically loaded small transmitting loop appears to be the invention of K8NDS and is described at Stealth Antennas for the Radio Amateur and (K8NDS nd). It may not be a novel idea as it was analysed at (Maclean 1978).

Without getting too much involved in the inventor’s specious arguments which attribute magic properties to his antenna, this article focusses on whether / why the calculator will or will not provide valid results for the antenna.

At Stealth Antennas for the Radio Amateur he makes the statement

A solid copper tube “Magnetic Loop” exhibits a certain inductance per foot of the total circumference of the antenna.

The statement seems to belie a basic understanding of inductance, the inductance of a given conductor formed into a single turn loop is not simply perimeter multiplied by some constant “inductance per foot”. Continue reading Helical loading and Calculate small transmitting loop gain from bandwidth measurement

Over recent weeks, I have run literally hundreds of thousands of NEC models of small transmitting loops (STL) over real ground. The objective was to try to discover some simple methods for initial design of a STL, particularly an estimate of ground loss of STL mounted near natural ground. Continue reading A method for initial ground loss estimates for an STL

Continue reading NEC-4 vs NEC-2 on a low small transmitting loop

A simple formula exists for calculation of radiation resistance of a small transmitting loop in free space. The derivation is in most good antenna text books.

The expression depends on an assumption that current around the loop is uniform, so the question is what is the acceptable limit for loop size.

NEC might provide some guidance. A series of NEC-4 models of a octagonal loop of thin lossless wire in free space was constructed with varying perimeter. Perimeter shown is that of a circle of the same area.

Above is a comparison of the two methods of estimation of Rr. To the extent that we trust NEC-4, the graph indicates that error in the simple formula grows quickly for loop perimeter greater than 0.1λ. (The results using NEC-2 are visually identical.)

Many authors set the criteria for a small loop to perimeter<0.3λ, but it is clear that current is not sufficiently uniform for perimeter>0.1λ for estimation of Rr as 31149*(A/λ^2)^2 to 0.1pu error or better.

This article documents a series of NEC-2 models at 7.2MHz of a lossless small transmitting loop near ground for the insight that they might provide about underlying loss mechanisms.

Key model details:

• lossless conductor 25mm diameter;
• octagon of sides 403mm, has same enclosed area as a 1m diameter circle;
• three ground types;
• height varies from 1.5-10m to centre of loop.

Impedance elements discussed in this article are referred to the main loop. Continue reading Small transmitting loop – ground loss relationship to radiation resistance