Bootstrap coax traps for antennas
The article is an analysis of an antenna trap where a coil is formed of a length of coax cable, the outer conductor of one coax end is tied to the inner conductor of the other coax end, and the remaining connections (outer at one end and inner at the other) form the terminals for the trap.
There are other configurations using coax cable for antenna traps, so I will call this one a bootstrap configuration to differentiate it from other configurations.
Gary O'Neil, N3GO, described the trap in an article entitled "Trapping the mysteries of trapped antennas" published in Ham Radio, October 1981. In that article he states that he developed the trap as described, which would appear to mean that he claims to have invented the configuration.
The ARRL Antenna Handbook 19th edition, Chapter 7 refers to these traps as W8NX coax traps, which hints a different originator, but it seems W8NX might have written on the subject a decade later than N3GO.
Yet another look!
N3GO's article, and a stream of other articles have attempted to describe how the trap works, and attempt to provide a quantitative analysis of its operation.
None of the articles that I have seen at the time of writing this article (March 2007) consider the coax cable to be a transmission line, and without a convincing argument for why it is not a transmission line, they are suspect.
Coax transmission line properties
Before examining the circuit of the trap, lets us refresh the properties of coax transmission lines.
Practical transmission lines at radio frequencies have an outer conductor that is much thicker than the skin depth. For that reason, the current that flows on the outside of the outer conductor can be quite different to the current that flows on the inside of the outer conductor.
In the normal mode of operation of a coax cable (TEM), there are three currents to consider:
- the current flowing on the outside of the inner conductor;
- the current flowing on the inside of the outer conductor, and which is equal in magnitude to the current flowing on the outside of the inner conductor, but opposite in direction; and
- the current flowing on the outside of the outer conductor.
Bootstrap trap circuit
Figure 1 shows the trap circuit at radio frequencies (ie where skin effect isolates the inner and outer surfaces of the outer conductor).
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Coil
The outer of the outer conductor of the coax forms an inductor, albeit an imperfect inductor, so it can be represented as an inductive reactance in series with a resistance. Practical coils have some self capacitance which would usually be insignificant around the frequency of first trap impedance maximum (resonance), but may become significant at much higher frequencies where a trap is used in a wide range multi-band antenna. A more complete representation is a series inductance and resistance with a small shunt capacitance. The effective coil resistance will usually vary with frequency (a consequence of skin effect ). At frequencies well below the coil's self resonance, the inductor can be considered as a simple series equivalent inductive reactance and resistance. The ratio of the inductive reactance (Xl) to the equivalent series resistance (Rl) is known as the Q of the coil (Ql).
Current loops
Let's designate the current flowing into trap terminal A as I1, and the current flowing out of the inner conductor at the B end of the coil as I2.
The current flowing out of trap terminal B must equal the current flowing into trap terminal A, so it is also I1.
At the A end of the coax outer, a node if formed by the junction of the inner of the coax outer (current=I1), the outer of the coax outer (current=-(I1+I2)), and the inner of end B of the coax (current=I2), the net current being I1-(I1+I2)+I2 which is 0, so Kirchoff's current law is satisfied.
At the B end of the coax outer, a node if formed by the junction of the inner of the coax outer (current=-I2), the outer of the coax outer (current=I1+I2), and the terminal B lead (current=-I1), the net current being -I2+(I1+I2)-I1 which is 0, so Kirchoff's current law is satisfied.
Coax transmission line
Let's designate the voltage between the inner of the coax and the outer of the coax at end A as V1, and the ratio V1/I1 as Z1.
Let's designate the voltage between the inner of the coax and the outer of the coax at end B as V2, and the ratio V2/I2 as Z2.
The transmission line has a complex propagation constant (γ) which (along with the transmission line equations) describes how a traveling wave propagates inside the coax, and a characteristic impedance (Zo) that describes the ratio of V/I in the traveling wave.
It is important to note that V1 may be very different to V2, I1 may be very different to I2, and Z1 may be very different to Z2. Solving the transmission line equations for the specific conditions reveals the relationship.
A worked example
A trap was designed using VE6YP's design tool which appears to embody the formulas that are commonly expressed as describing the resonance of the trap. The design tool give construction details and calculates the inductance and capacitance of the elements and their reactance at resonance, but does not estimate resistance, or impedance at any frequency.
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Fig 2 is the example design from the VE6VP tool. The design was entered into the ON4AA Inductor Calculator to get an estimate of the Q, and a better estimate of the inductance.
| Item | Value |
| Inductance | 3.71μH |
| Coil Q | (2*π*f*L)/(270*f^0.5) |
| Coil equivalent shunt self capacitance | 1.3pF |
Table 1 shows the assumptions made for a more complete model. The assumptions in Table 1 are not based on measurement, they are based on the inductor calculator, they are probably fairly realistic and suitable for demonstrating the analysis. The characteristics of the cable, Belden 8262 (RG58C/U) are as derived from Belden's published specifications, and as used and described in the RF Transmission Line Loss Calculator / Enhanced.
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Fig 3 is a plot of R and X of a trap for four different configurations:
- R1, X1 using the bootstrap configuration described in this article;
- R2, X2 using the same inductor and a shunt ideal fixed capacitor of 176pF to form the trap;
- R3, X3 using the same inductor and the o/c coax stub in shunt with the coil to form the trap; and
- R4, X4 using the same inductor connected to one end of the length of coax, and the trap terminals being the other end of the coax.
Configuration 1 is synonymous with ARRL Antenna Handbook 19th edition, Chapter 7, Fig 20 'High-Z connection'.
Configuration 2 seems consistent with the apparent VE6VP design tool's treatment of the coax (an ideal capacitance proportional to length of the coax). The resonance is displaced due to the different estimate of inductance of the coil.
Configuration 3 treats the coax as an real (ie lossy) o/c stub in shunt with the coil as seems to be done by some analysts.
Configuration 4 is synonymous with ARRL Antenna Handbook 19th edition, Chapter 7, Fig 20 'Low-Z connection'. It is unclear what purpose the ARRL Antenna Handbook author sees for configuration 4, the 'Low-Z connection'.
The above is not to imply endorsement of the content of the referenced ARRL article.
Clearly, they are all different configurations, with quite different characteristics.
The results for configurations 2 and 3 demonstrate that the bootstrap type coax trap is not well approximated by a conventional tank with a fixed ideal capacitor, nor is is well approximated by merely shunting the inductor by a lossy o/c stub. This suggests that all explanations, tools, and models that ignore the fact the coax behaves as a transmission line are flawed.
Links
A trapped dipole for 80m and 40m using bootstrap coax traps
Changes
| Version | Date | Description |
| 1.01 | 14/03/2007 | Initial |
| 1.02 | 14/08/2007 | Worked example revised to include configurations 2 to 4. |
| 1.03 | ||
| 1.04 | ||
| 1.05 |