Note: None of the problems below occur when
the loop is on a band where the actual antenna is a full wave or larger.
The primary radiating area of a half wave loop is about 1/8th wavelength. We are
essentially endloading a 1/8th wave long dipole when we use a 40 meter full
wave loop on 80 meters.
On 40 meters a full wave loop is like
endloading two 1/4 wave long dipoles, so there is a full halfwave of total
radiating area and efficiency is high. Folding the antenna into a square kills
80meter efficiency because the square is small, the sides outofphase, and so
only one side (the feedpoint side) radiates. One little mistake by adding a
small amount of resistance and efficiency falls into single digits.
In a recent QRZ thread, it became apparent some transmission line
calculations in models are not accurate. This actually is true for many
transmission line calculators, not just those in modeling programs. The poor
transmission line loss calculators are reinforced by articles that contain bad
measurements, like a
2009
article on ladder line loss.
Let’s look at a few 40meter horizontal loops with an open circuit loop as a
reference, and compare it to others loaded by a 1/4 wave transmission
line stub. We can also see how builtin transmission line calculators compare to a
known good feed line loss calculator. One of the best calculators I’ve found is at VK1OD
http://vk1od.net/calc/tl/tllc.php
What makes a smaller loop so difficult to tune correctly?
Radiation occurs from charge acceleration. This means we must
have current flowing over linear (in line) spatial distance without something
else nearby opposing that radiation with an opposing current. When a loop is
full size, it has two areas that can freely couple to space:
Section 1 is the feedpoint, and all areas of section 1 can
radiate. Sections 2 and 4 have opposing currents inside each section, and with
each other. They almost cannot radiate at all.
A fullwave loop looks like two 1/4 wave long dipoles fed in
phase (currents support each other in radiating) while the sides suppress most
radiation.
At half frequency, where the loop is 1/2 wave perimeter, all
sides fight against each other. This means the antenna needs more current to
radiate the same power, which also means radiation resistance has greatly
decreased. The antenna needs much more current and more voltage to radiate.
When we try to “load” this loop, we can only move the current
maximum around. We cannot change the phase relationship. Without adding sections
or protrusions that carry common mode currents, we can only change where the
maximum and minimum of current and voltage occurs.
With no loads the loop is resonant, but current maximum is in
the middle of the side diametrically opposite the feedpoint. Feedpoint
resistance is terribly high, many thousands of ohms. If we only have a
moderately high feedpoint resistance with a closed 1/2 wave loop, the antenna
has high loss.
If we open the loop exactly opposite the feedpoint, the loop
behaves like a bent dipole. There is very high voltage across the gap, and much
higher than normal currents at the feedpoint.
The feedpoint now has highest current and lowest voltage,
making it a low impedance. Most radiation comes from the short area in wire 1,
only 1/8th wavelength long. Sides 2 and 4 tend to cancel each other because they
have the same currents flowing opposing directions. Side 3 has very little
current and as such cannot usefully contribute to radiation.
We essentially have a 1/8th wave long dipole, and have no real
way to make it better without extending the middle of sides 2 and 4 further
apart without shortening sides 1 and 2! In other words to increase
radiation resistance, the loop has to be
made spatially larger.
If we have a loop like this with a high feedpoint resistance,
over 1020 ohms, the antenna has very high loss.
Reference loop, 40meter full wave loop 36feet high over
medium soil, opened opposite feedpoint to make reasonable feed impedance on 80
meters. The
problem with relayswitching the loop open is, with only 100 watts, relay
contact voltage is 5000 volts peak. High voltage and high
current is a direct result of having a small radiating area (folding the antenna
in a square).
EZNEC+ ver. 5.0
Horiz loop 10/12/2010 6:57:25 AM
————— SOURCE DATA —————
Frequency = 3.55 MHz
Source 1 Voltage = 71.7 V at 81.97 deg.
Current = 1 A at 0.0 deg.
Impedance = 10.01 + J 71 ohms
Power = 10.01 watts
SWR (50 ohm system) = 15.197 (75 ohm system) = 14.267
Overall Efficiency 43.7% 
Stub decoupled loop (phosphor bronze) using real open wire
line 3 inch spacing #18 AWG
stub is modeled as two parallel conductors
EZNEC+ ver. 5.0
Horiz loop 10/12/2010 7:38:36 AM
————— SOURCE DATA —————
Frequency = 3.51 MHz
Source 1 Voltage = 49.99 V at 0.57 deg.
Current = 1 A at 0.0 deg.
Impedance = 49.99 + J 0.4946 ohms
Power = 49.99 watts
SWR (50 ohm system) = 1.010 (75 ohm system) = 1.500
Overall Efficiency 8.6% 
(Efficiency a few percent higher using copper)
SWR plot of stubswitched loop. Resonant frequency 3.510 MHz
3.5 MHz using built intransmission line loss calculator with
values for Wireman 551 450ohm line:
EZNEC+ ver. 5.0
Horiz loop 10/11/2010 9:30:06 PM
————— SOURCE DATA —————
Frequency = 3.55 MHz
Source 1 Voltage = 56.99 V at 9.09 deg.
Current = 1.777 A at 0.0 deg.
Impedance = 31.67 – J 5.07 ohms
Power = 100 watts
SWR (50 ohm system) = 1.605 (75 ohm system) = 2.381
Overall Efficiency 15%

3.5 MHz Wireman 450ohm ladder line using VK1OD calculator values
inserted as a load:
Parameters 

Transmission Line 
Wireman 551 
Code 
W551 
Data source 
Wireman / N7WS 
Frequency 
3.550 MHz 
Length 
0.250 wl 
Zload 
1.000e7+j0.000e+0 Ω 
Yload 
1.000e+7+j0.000e+0 S 
Results 

Zo 
400.00j1.63 Ω 
Velocity Factor, VF^{ 2} 
0.903, 1.227 
Length 
90.00 °, 0.250 λ, 19.056 m 
Line Loss (matched) 
6.11e2 dB 
Line Loss 
74.492 dB 
Efficiency 
0.00 % 
Zin 
5.687e+4j2.324e+2 Ω 
EZNEC+ ver. 5.0
Horiz loop 10/11/2010 9:42:32 PM
————— SOURCE DATA —————
Frequency = 3.55 MHz
Source 1 Voltage = 150.3 V at 16.42 deg.
Current = 0.6938 A at 0.0 deg.
Impedance = 207.8 + J 61.23 ohms
Power = 100 watts
SWR (50 ohm system) = 4.536 (75 ohm system) = 3.043
Overall Efficiency 2.2% 
There is 8.1 dB difference between the built in transmission line calculator
and the external more accurate VK1OD calculator.
Look like not much problem on higher bands, except SWR bandwidth:
14 MHz with transmission line in EZnec
EZNEC+ ver. 5.0
Horiz loop 10/11/2010 9:15:06 PM
————— SOURCE DATA —————
Frequency = 14.1 MHz
Source 1 Voltage = 171.2 V at 1.4 deg.
Current = 0.5842 A at 0.0 deg.
Impedance = 293 – J 7.164 ohms
Power = 100 watts
SWR (50 ohm system) = 5.863 (75 ohm system) = 3.909
Antenna system efficiency 74.8%

VK1OD RF Transmission Line Loss Calculator 14 MHz
Parameters 

Transmission Line 
Wireman 551 
Code 
W551 
Data source 
Wireman / N7WS 
Frequency 
14.100 MHz 
Length 
1.000 wl 
Zload 
1.000e7+j0.000e+0 Ω 
Yload 
1.000e+7+j0.000e+0 S 
Results 

Zo 
400.00j0.78 Ω 
Velocity Factor, VF^{ 2} 
0.903, 1.227 
Length 
360.00 °, 1.000 λ, 19.191 m 
Line Loss (matched) 
0.128 dB 
Line Loss 
77.703 dB 
Efficiency 
0.00 % 
Zin 
5.89j0.01 Ω 
Yin 
0.169760+j0.000332 S 
VSWR(50)in 
8.49 
Loss model source data frequency range 
50.000 MHz – 100.000 MHz 
Correlation coefficient (r) 
1.000000 
Simulation using VK1OD calculator
Horiz loop 10/11/2010 8:35:59 PM
————— LOAD DATA —————
Frequency = 14.1 MHz
Load 1 Voltage = 3.405 V at 1.32 deg.
Current = 0.5771 A at 1.32 deg.
Impedance = 5.9 + J 0 ohms
Power = 1.965 watts
Total applied power = 100 watts
Total load power = 1.965 watts
Total load loss = 0.086 dB

