## Reconciling W5QJR’s loop formulas

Ted Hart inspired interest in loops for transmitting applications with his article “Small, high efficiency loop antennas” (Hart 1986).

He included a table of recommended designs, the following is an extract of the table rows relating to an octagonal loop with perimeter=20′ (6.1m). The tube specified was 3/4 copper pipe which has an OD of 22mm. Continue reading Reconciling W5QJR’s loop formulas

## Reconciliation of field strength to efficiency calculator with Boswell’s loop measurements

(Boswell et al 2005) discussed a small transmitting loop (STL) and offered predictions and measurements of performance.

Boswell’s loop is 1m diameter of 22mm diameter copper tube. Above, Fig 6 from Boswell shows his prediction of the field strength of a 100% efficient loop at several distances, and measured field strength. He calculated efficiency from the difference between predicted lossless and measured. Continue reading Reconciliation of field strength to efficiency calculator with Boswell’s loop measurements

## Belrose field strength measurements of his 80m mobile whip

(Belrose 1998) described a mobile antenna system which, to his credit, the author validated its performance by making a series of field strength measurements and calculating radiation efficiency.

It appears that Belrose has assumed the antenna is omni directional for ground wave, though he shows that for higher angle space wave it is not omni directional.

## Belrose’s measurement and calculation Above, Belrose gives a set of measurements of field strength at different distances, and a curve fit from which he takes a value of 101.42dBµV/m at 100m as the basis for his efficiency calculation. Continue reading Belrose field strength measurements of his 80m mobile whip

## On ignoring capacitor losses in Small Transmitting Loops

There are a host of design tools for Small Transmitting Loops, spreadsheets, online calculators and conventional applications you download and run on your PC.

Almost all ignore capacitor loss… and I say almost so that I am not wrong, I have never seen one of these tools that does include capacitor loss.

NEC study of Small Transmitting Loop Q vs frequency contained a graph of the elements of feed point resistance from and NEC-4.2 model for a small loop. Key parameters are:

• Octagonal loop of 20mm copper with area equal to that of a 1m diameter circle, loop perimeter=0.104λ at 10MHz;
• centre height=2m;
• Qcap=2000;
• ground=0.007/17; and
• freq=1-10MHz.

This analysis only extends up to 10MHz, because for perimeter>λ/10, the formulas used by most of these simple calculators are in error for other reasons. Above, the four elements on log scale. Continue reading On ignoring capacitor losses in Small Transmitting Loops

## NEC study of Small Transmitting Loop Q vs frequency

Recent comments elsewhere on the shape of the plot of measured Q from (Austin et al 2014) gave reason to explore the behaviour of Q for a ‘good’ Small Transmitting Loop (STL) using an NEC-4.2 model.

The term Small Transmitting Loop means a loop sufficiently small that there is not a significant departure from smaller loop behaviour. Essentially this is true for perimeter less than about λ/10.

## NEC-4.2 model

Key parameters are:

• Octagonal loop of 20mm copper with area equal to that of a 1m diameter circle, loop perimeter=0.104λ at 10MHz;
• centre height=2m;
• Qcap=2000;
• ground=0.007/17; and
• freq=1-10MHz.

This is a quite practical small transmitting loop with current that is approximately uniform around the loop. Continue reading NEC study of Small Transmitting Loop Q vs frequency

## K4PP’s 1m Small Transmitting Loop

K4PP described his Small Transmitting Loop (STL), including details of its construction and measured VSWR response.

The loop is a 1m diameter circle of 12.7mm dia copper tube with a high Q vacuum cap for tuning. Using a quality capacitor and copper tube, this loop should be as efficient as they come for its size and location. Continue reading K4PP’s 1m Small Transmitting Loop

## Review of Austin et al paper “Loss mechanisms in the electrically small loop antenna”

(Austin et al 2014) made measurements of feed point impedance of a small transmitting loop using a calibrated transformer, and discussed the loss mechanisms. They also extrapolated their measured data to a larger conductor.

Let me focus on their measurements, the loop was:

• a 1m diameter circular loop of 6.3mm copper;
• tuned with a low loss tuning capacitor (ATC chip capacitor);
• at heights of 3m and 6m above ground;
• from 3.3 – 12.8MHz.

They did not report the capacitor loss, but gave some likely range from manufacturer’s data.

They used ground parameters G-0.007, εr=17 at 7MHz for their NEC models.. Above is a reconstruction of the measured data from their Fig 3. They measured Rin to their matching transformer and used calculated inductance (relying on the calibrated matching transformer) to calculate Q at each measurement frequency. Continue reading Review of Austin et al paper “Loss mechanisms in the electrically small loop antenna”

## Dipole mode component of VK5BR’s 1m square loop for 20m

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. Continue reading Dipole mode component of VK5BR’s 1m square loop for 20m

## Dipole mode of Small Transmitting Loop per King

(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

## Calculation of equivalent self capacitance of Small Transmitting Loop – ARRL

In Calculation of equivalent self capacitance of Small Transmitting Loop I mentioned that (Straw 2007), The ARRL Antenna Book 21, gave an expression for equivalent self capacitance of a Small Transmitting Loop of one turn:

C=HD where C is in pF, D in cm, and H comes from a given table of length/diameter ratios from 0.1 to 1.0. ARRL cites (Medhurst 1947) for this expression. Medhurst’s work was for solenoids.

```Values of the Constant H for Distributed Capacitance

Length to
Diameter
Ratio       H
=====       =====
0.10        0.96
0.15        0.79
0.20        0.78
0.25        0.64
0.30        0.60
0.35        0.57
0.40        0.54
0.50        0.50
1.00        0.46```

A 1m diameter loop of 10mm diameter conductor has l/d=0.01, so it is not covered by the table, and you might form the view from the table that H tends to 1.0 or thereabouts as l/d approaches 0, but that is an extrapolation and dangerous. Continue reading Calculation of equivalent self capacitance of Small Transmitting Loop – ARRL