Loss in open wire + coax hybrid feed arrangements

I saw a question posed online about the merits of a proposed antenna system which used a hybrid feed arrangment as 15′ (sic) of the feed line needed to be buried.

Above is the poster’s diagram, and his posting lacked some important details so let’s make some assumptions. Lets assume the antenna is at 150′ in height above average ground, and since the dipole is long enough to be usable on 160m, let’s study it at 1.85MHz.

Input impedance of the dipole under that scenario is around 45-j400Ω.

Let’s consider two options:

  • a tuned feeder option (ie open wire line all the way to the ATU); and
  • the hybrid feed arrangement shown.

Let’s get serious and use home made open wire line made from 2mm diameter copper spaced 150mm. The very popular 19strand windowed ladder lines using CCS do not have sufficient copper to give copper like performance, the single core CCS is marginal.

This analysis looks at transmission line losses only, ATU losses are significant and are likely to be different in each scenario as the load presented to the ATU changes.

Tuned feeders

Let us calculate the line loss for the tuned feeder option.

Nominal 600 ohm 2mm/150mm on 160m

Parameters
Conductivity 5.800e+7 S/m
Rel permeability 1.000
Diameter 0.00200 m
Spacing 0.15000 m
Velocity factor 0.975
Loss tangent 1.000e-5
Frequency 1.850 MHz
Twist rate 0 t/m
Length 100.000 m
Zload 45.00-j400.00 Ω
Yload 2.777e-4+j2.469e-3 S
Results
Zo 587.66-j1.45 Ω
Velocity Factor 0.9750
Length 227.85 °, 0.633 λ, 100.0000 m, 3.421e+5 ps
Line Loss (matched) 8.57e-2 dB
Line Loss 0.873 dB
Efficiency 81.79 %
Zin 39.8520+j146.4072 Ω
Yin 0.00173095-j0.00635910 S

0.87dB is quite reasonable given the quite long feed line. Just under 20% of the ATU output power is lost in the transmission line.

Note that the loss on the open wire section is slightly sensitive to the load impedance it sees, so variations in the dipole will affect loss in the coax section to some extent.

Hybrid feed

The loss in the balun in differential mode will be insignificant compared to the coax loss, so I will ignore it.

Lets repeat the analysis above but for the half length open wire line.

Nominal 600 ohm 2mm/150mm on 160m

Parameters
Conductivity 5.800e+7 S/m
Rel permeability 1.000
Diameter 0.00200 m
Spacing 0.15000 m
Velocity factor 0.975
Loss tangent 1.000e-5
Frequency 1.800 MHz
Twist rate 0 t/m
Length 50.000 m
Zload 45.00-j400.00 Ω
Yload 2.777e-4+j2.469e-3 S
Results
Zo 587.68-j1.47 Ω
Velocity Factor 0.9750
Length 110.85 °, 0.308 λ, 50.0000 m, 1.711e+5 ps
Line Loss (matched) 4.23e-2 dB
Line Loss 0.517 dB
Efficiency 88.78 %
Zin 6.222e+2+j2.346e+3 Ω
Yin 1.056e-4-j3.983e-4 S

Not surprisingly, the loss at 0.52dB is a little over half the full length line.

Note that the loss on the open wire section is slightly sensitive to the load impedance it sees, so variations in the dipole will affect loss in the coax section to some extent.

Now lets calculate the loss in the LMR400 with this load.

Parameters
Transmission Line Times Microwave LMR-400
Code LMR-400
Data source Times Microwave
Frequency 1.800 MHz
Length 50.000 m
Zload 6.000e+2+j2.300e+3 Ω
Yload 1.062e-4-j4.071e-4 S
Results
Zo 50.00-j0.70 Ω
Velocity Factor, VF -2 0.850, 1.384
Length 127.16 °, 0.353 λ, 50.0000 m, 1.962e+5 ps
Line Loss (matched) 0.270 dB
Line Loss 9.059 dB
Efficiency 12.42 %
Zin 3.26+j36.21 Ω
Yin 0.002466-j0.027398 S
VSWR(50)in 23.41
Loss model source data frequency range 30.000 MHz – 6000.000 MHz
Correlation coefficient (r) 1.000000

There is an issue with the model’s source data for LMR400 in that it is based on data for 30-6000MHz and to use an extrapolation at 1,8MHz increases uncertainty.

Note that the loss on the coax section is sensitive to the load impedance it sees, so variations in the dipole or open wire section will affect loss in the coax section.

The model suggests that looking into the open wire line section, the loss on the coax section is likely to be around 9.1dB.

(A little aside: The actual VSWR at the load end of the LMR400 is 199, at the source end is 27. If you use one of those calculators or graphs that estimate line loss from VSWR… which VSWR would you use? The calculation reported above uses the load impedance of the section to find line loss having regard for the current and voltage distribution on the line section and the associated conductor and dielectric losses.)

Adding the calculated open wire line loss, we get 9.1+0.52=9.6dB. Over 90% of the ATU output power is lost in the transmission line.

Conclusions

Loss in line sections is sensitive to the load impedance each sees, more so with the coax section, so variations in the configuration will affect losses.

The tuned feeder scenario has transmission line loss around 0.9dB.

The hybrid feeder arrangement has transmission line loss closer to 10dB.

That is a significant cost to enable burial of his feed line.

For the reader

An interesting exercise for the reader is to calculate the loss in an ATU looking into each of the line options. W9CF’s T-Network Tuner Simulator is a good tool to try. (You might need to download the applet and run it locally, and change the setup to use 500pF caps and 50µH inductor.)

Note that the loss in an ATU can be very sensitive to the load impedance it sees, so variations in the dipole and line sections may affect tuner loss.