# Introduction

This article explores a theoretical model for the losses of an 80m / 40m trapped inverted V dipole antenna system using a bootstrap coax trap.

This article does not examine the pattern of the antenna, essentially as it is a low Inverted V dipole, it will have a nearly omni-directional pattern and with a relatively high main lobe.

# A system view

Components of an antenna system interact with each other in a complex way, and it is important to analyse the entire antenna system (radiator, earth, transmission line, balun, ATU etc) to obtain a correct understanding of how the system works overall.

# The model

• inverted V dipole with traps
• ideal balun;
• feed line
• ATU

The following describes the model used. Results will vary for different configurations.

## Inverted V dipole with traps

### Inverted V Dipole

The dipole is in the Inverted V configuration, centre at 11m height, and two legs each of 15.6m length to a height of 3.5m. The wire is 2mm diameter HDC, and the traps are located at 6.4m from each end.

Figure 1 shows the dipole configuration, including current distribution at 7.1MHz.

### Bootstrap coax traps

Figure 2 shows the configuration of a bootstrap coax trap. The connections are critical to the analysis and design, and the term 'bootstrap coax trap' is used to describe the particular configuration.

The trap is designed for resonance at approximately 6MHz. Whilst that might seem to disagree with some explanations of how traps work, they do not need to be resonant at one of the operating frequencies, and in fact there are good reasons for avoiding operation at trap resonance. Most explanations of these traps in handbooks, journals, websites etc ignore the fact that the transmission line is a transmission line, and are seriously flawed for that reason.

Figure 2a shows the prototype coax trap before cross connection of the ends. It is 10 turns of medium grade RG58C/U type cable close wound on a 50mm PVC pipe, and served with a layer of PVC electrical tape to hold the winding stable during measurements. I would advise against the serving for a real antenna trap, it will retain water which will degrade trap performance.

Fig 3 shows the input data to ON4AA's inductor calculator. It can be seen that the trap consists of exactly 10 turns of RG-58C/U coax cable, close wound on a 50mm diameter former. The inner conductor of one end of the cable is connected to the outer conductor of the other end of the cable, and the remaining conductors are the trap terminals.

Fig 4 is the results of the coil design tool. The calculator overestimates the Q because of the braided outer conductor in the coax cable, and may slightly underestimate the stray capacitance as a result of not considering the dielectric constant of the cable jacket.

Measurements of the inductor formed by the outer surface of the outer conductor of the coil of coax by VK2KRB over 4 to 12MHz suggest that the best simple equivalent circuit is 3.44μH of inductance in series with R, and 6pF of equivalent shunt stray capacitance. R=0.2517*(\$f/1e6)^0.6914.

This model for R is different to the traditional model that R∝f^0.5, as calculated by the ON4AA calculator above. It would seem that the braided tinned copper conductor is quite different to a round copper conductor of the same diameter.

 Item Value Coil inductance 3.44μH Coil R 0.2517*(\$f/1e6)^0.6914Ω Coil parallel stray capacitance 6.0pF

Table 1 sets out the key coil parameters used in the model.

The essential purpose of the traps is to cause a relatively low VSWR on the coax feed line at frequencies of interest.

## Ideal balun

An ideal balun is included in the model. A good balun designed for a nominal 50Ω load at the frequencies used should perform sufficiently well to ignore its imperfection.

## Feed line

The feed line is 20m of RG213. Due to the narrow bandwidth on 80m and the attendant rise in line loss as VSWR increases away from the centre frequency, low loss feed line should be used.

Impedance transformation and loss due to the feed line are modelled using the techniques described in RF Transmission Line Loss Calculator .

## ATU

The model uses an L Tuner with practical Q values for practical least tuner loss. Other tuner configurations (such as the popular T Tuner) will usually exhibit higher loss. Many commercial T Tuners use small variable capacitors, and with extreme loads encountered at low frequencies will deliver worse losses than shown here for the L Tuner.

The antenna could be used without an ATU, but one is recommended for achievement of rated transmitter power and slight extension of usable bandwidth, albeit at the expense of a small loss. ATUs are a source of loss, but that is not to say that the loss isn't affordable, or might not be more than offset by improved transmitter performance.

Note that the internal automatic ATU found in many modern transceivers are typically not as efficient on the lowest bands, and you might expect 0.5dB to 1dB more loss on 80m that shown in this article.

# Analysis

## 80m band

Fig 5 shows the VSWR over the 80m band at the load end of the feed line. VSWR at the tx end of the line will be a little less due to line loss.

VSWR is of itself, is not as important as the loss that it causes on the feed line.

Fig 6 shows the antenna system losses in and around the 80m band.

The component labeled 'Dipole' loss includes the loss in the dipole wire and the traps.

Note that although the Dipole loss at 3.64MHz is 1.05dB, only 0.81dB of that is due to loss in both traps, the remaining 0.20dB is due to wire loss. Of greater concern is the loss in the feed line, a loss that increases rapidly away from 3.64MHz. This narrow bandwidth is typical of a shortened / loaded antenna.

Trap losses cannot be estimated in isolation of the antenna system. Firstly, the trap was to be characterised at a given frequency, the trap inserted as a segment load in an NEC model, and the trap loss calculated from the trap impedance and the current flowing in the antenna segment containing the trap.

Trap loss can be calculated from the NEC results. Taking the attached NEC model output 3.64MHz, input power at the feed point is 1.02540E-02W, current in a trap segment is 1.5672E-02A and the resistance component of trap impedance is 6.6680E+00Ω, so power lost in each trap is I^2R/2 (current in NEC is amplitude, not RMS) which is 8.18e-4W which is 8% of the input power at the dipole centre, 16% for both traps. There was also about 3% of the input power at the feed point lost as heat in the dipole conductors. By comparison, conventional LC traps of similar characteristic would have around one sixth of the loss of the bootstrap coax traps.

Note that ATU losses are barely visible on the graph, and are insignificant.

Being essentially a loaded antenna, the bandwidth is less than a full size dipole, and the manifestation is that the feed point impedance rises quickly away from resonance, causing higher VSWR on the feed line, resulting in increased feed line loss.

Fig 7 demonstrates how poor performance is adjacent to the design frequency. It is important when implementing such an antenna to adjust the length of the legs and position of the traps to ensure that the best performance is at the desired operating frequency.

Antenna bandwidth is often described as a frequency range for  give maximum feed point VSWR, which is rather meaningless from a system perspective.

A better, system oriented perspective, is to form a view about the minimum acceptable efficiency and then determine the system bandwidth that meets or exceeds the acceptable minimum efficiency. Let us call this Acceptable Bandwidth.

Fig 7 shows the relationship between bandwidth and efficiency of the antenna system on 80m. For example, if one was prepared to accept 60% as minimum system efficiency, the acceptable bandwidth would be around 0.32MHz.

The acceptable bandwidth concept properly matches a user's expectation with performance, and provides the mechanism to evaluate alternative configurations such as lower loss feed line.

## 40m band

Fig 8 shows the VSWR over the 80m band at the load end of the feed line. VSWR at the tx end of the line will be a little less due to line loss.

Fig 9 shows the antenna system losses in and around the 40m band.

Note that many designs would make the trap resonant at 7.1MHz for convenience in explanation, but at the expense of efficiency. Modelled trap losses are much worse if the trap was shortened to be resonant at 7.1MHz and operating voltage is higher.

Note that ATU losses are barely visible on the graph, and are insignificant.

Bandwidth is much better than on 80m, and losses should be quite acceptable across the whole 40m band.

Again, it is important  when implementing such an antenna to adjust the length of the legs and position of the traps to ensure that the best performance is at the desired operating frequency.

# Conclusions

• Components of an antenna system interact with each other in a complex way, and it is important to analyse the entire antenna system (radiator, earth, transmission line, balun, ATU etc) to obtain a correct understanding of how the system works overall.
• Traps do not need to be resonant at one of the operating frequencies, and in fact there are good reasons for avoiding operation at trap resonance.
• Focus is often on the trap Q or trap losses, but that is not necessarily an issue.
• Narrow bandwidth results in feed point impedance that changes rapidly either side of resonance, which drives higher feed line loss off resonance.
• The bandwidth of the antenna system has little to do with trap Q.
• Operation of the bootstrap coax trap is explained by the behavior of the coax cable as a transmission line, explanations that pretend otherwise are flawed.
• ATU losses (for a quality ATU) are insignificant.