6-Band HF Center-Loaded Off-Center-Fed Dipole

# Design Goals

Like many fellow radio amateurs, I own a fairly standard shortwave radio station consisting out of a good quality HF transceiver driving a 1kW tube power amplifier.

I never chose to spend money on a kW-rated (balanced) antenna-tuner since *the adjustable pi-network of the output filter-tank of my power amplifier allows me to tune out VSWRs of up to 3÷1.* The goal that I set out was *to design an HF antenna, with a VSWR of 3÷1 or less over the full bandwidth of as many amateur radio HF bands as possible, with a preference for the low- and the non-WARC bands.* This design goal has been achived with a new kind of antenna;

## The Center-Loaded Off-Center-Fed Dipole Antenna (CL-OCFD)

In order not to tease your curiosity any further, you will find an EZNEC-calculated VSWR-graph of the antenna below. *This is an antenna that works without a tuner over the entire bandwidth of the 80, 40, 30, 20, 15 and 10m-band, simply by adjusting the output-tank of your tube power amplifier. (If you have a transistor amplifier as a final stage, you definitely will need an antenna-tuner though.)* In such, this antenna is the first single-wire antenna described in literature offering these capabilities.

# Working Principle of the OCF Dipole Antenna

When offsetting the feed position of a dipole antenna away from its center, at some point, *similar magnitudes of feed impedance may be encountered for the fundamental resonant frequency and a number of harmonic resonant frequencies of the dipole.*

This is possible because a standing wave is present along the dipole which, in the span of a quarter wavelength, causes the feed impedance to change from an (almost) infinite value at the antenna-ends to the value of the radiation resistance at that respective frequency.

By consequence, the optimal feed point will have a higher impedance than the center feed impedance at the fundamental frequency (73Ω in free space for an infinitesimal thin wire). An *impedance-transforming balun* will be necessary to match the optimal (balanced) feed impedance to that of the (unbalanced) coaxial feed cable.

# Broadband Effect at the Fundamental Frequency:

Full 80m-Band Coverage

Operating a center-fed dipole over the entire 80m-band turns out to be particularly challenging. With 8.2% relative bandwidth the 80m-band (3.5-3.8MHz) is exceptionally broad. Cumbersome cage dipoles or load switching arrrangements deliver only partially satisfactory results that are easily outperformed by the OCF dipole^{[1]}.

*Offsetting the feed position of a dipole antenna, will result in a lower Q-factor and hence a broader working bandwidth, especially at the fundamental frequency.*

This is due to the fact that when offsetting the feed position away from the center, the resistive part of the feed impedance will increase more rapidly than the reactive (imaginary) part, thus effectively lowering the Q-factor of the antenna at the feed point. In a sense, the antenna will be loaded in a different way by the off-set feeding.

*The effect is most pronounced at the fundamental frequency. This is a first reason why it pays of to build your OCF dipole with 80m as the fundamental wavelength, and not for example 160m.* A second reason will be given in the section about center-loading.

# Resonant Lengths

*We always have been told that the HF amateur radio bands are harmonics of the 80m-band. But is this really the case?*

Let's investigate by determining for every band's center frequency, f_{c}, the harmonic resonant length of a *0.8mm soft-PVC-insulated 4mm² copper wire at 16.75m (55ft) height above a typical city lot (σ = 1mS/m; ε _{r} = 5). Bare copper wire at higher heights and above better ground would yield longer lengths,* but this does not matter for the validity of the reasoning that will follow.

## Even Harmonics

For a reason that will become evident in a brief moment, we will look at the even and odd harmonics in seperate groups, starting with the even harmonics.

What we immediately notice is that the lower band-edges, are exactly harmonical, being integer multiples of 7.000MHz. All even harmonic bands also have similar relative bandwidths; higher harmonic bands become proportionally wider. The geometric *center frequencies of the even harmonic bands are therefore also more or less harmonical and their resonant lengths almost equal.* (Note: The FM-portion of the 10m-band has been temporarily disregarded.) This is reflected in a low value for the standard deviation(st.dev.) of the resonant lengths. *In conclusion, it must be relatively easy to design an off-center-fed dipole for this set of even harmonics,* provided we find a feed position with comparable feed impedances for all of these frequencies.

In this example, the geometric mean (as opposed to the arithmetic mean) of the even harmonic resonant lengths is 40.66m, *corresponding to a seventh harmonic frequency of 24.912MHz.*

band (m) | f_{l} (MHz) | f_{u} (MHz) | f_{c} (MHz) | harmonic | length (m) | Δ (m) |

40 | 7.000 | 7.200 | 7.099 | 2 | 40.52 | -0.14 |

20 | 14.000 | 14.350 | 14.174 | 4 | 40.75 | 0.09 |

15 | 21.000 | 21.450 | 21.224 | 6 | 40.87 | 0.22 |

10 | 28.000 | 29.200 | 28.594 | 8 | 40.49 | -0.17 |

geometric mean | 40.66 | |||||

st.dev. | 0.16 |

## Odd Harmonics

band (m) | f_{l} (MHz) | f_{u} (MHz) | f_{c} (MHz) | harmonic | length (m) | X_{CL} (Ω) |

80 | 3.500 | 3.800 | 3.647 | 1 | 38.68 | -j91 |

30 | 10.100 | 10.150 | 10.125 | 3 | 42.76 | +j241 |

17 | 18.068 | 18.168 | 18.118 | 5 | 39.89 | -j153 |

12 | 24.890 | 24.990 | 24.940 | 7 | 40.61 | -j12 |

geometric mean | 40.46 | |||||

st.dev. | 1.48 |

Let us continue and have a look at the odd harmonics. The whole story is completely different now; Eventhough 3.500MHz is exactly one half of 7.000MHz, *the resonant length of the 80m-band is, at its geometric center frequency, much shorter than that of the even harmonic bands.* This is due to the fact that 80m is the band with the broadest relative bandwidth (8.2%), easily surpassing the 5.9% of the entire 10m-band (28.000-29.700MHz).

*30m is equally problematic,* being not even a real harmonic. *Its resonant length is much longer than the mean* of 40.66m for the even harmonics.

*Finally, we see that 17 and 12m that behave very well.* The resonant length of the 12m-band actually nearly coincides with the mean resonant length of the even harmonic bands.

Remember the problems that occurred with the OCF antennas discussed in the previous literature survey? This id no longer a suprise as above tables reveal that the *non-harmonic frequency bands are the underlying cause for the partial 80m coverage and the complete absence of 30m-band coverage.*

*Below diagram shows the current distribution along an antenna wire for its first eight harmonic resonances. The current distributions of the even harmonics are plotted above the wire, those of the odd harmonics below.*

*Do you notice anything special?*

At least, I do. It may seem trivial, but *all even harmonics have (almost) zero current at the center of the antenna, whereas all odd harmonics experience a current maximum at this location.*

Zero current for the even harmonics at the center, implies that *I can literally do what I want at the center of the antenna without upsetting the even harmonics. I can even cut the antenna in two!* As a matter of fact, this is precisely what we are going to do!

Perhaps, it is unfortunate that the wavelengths of the 80m and 30m-bands are respectively too short and too long to be true harmonics of the other bands. However, luck did strike upon seeing that *both problematic bands happen to be odd harmonics.* Please note that this statement does not hold when considering a double-sized OCFD with 160m as the fundamental frequency. *This antenna design is therefore not scalable!*

What remains to be done now, is to cut the antenna in half and insert a center-loading network in series. This network will need to add the necessary center loading reactances X_{CL} (see table on previous page) in order to render the antenna resonant at the odd harmonics. As has been mentioned before, resonance makes matching at multiple frequencies a lot easier.

# The Center-Loading Network

## Five Resonant Bands

Let's start easy. When we have a 40.66m long wire hanging in our garden, at least we would like it to be also perfectly resonant on the 80m-band. The tableon the previous page told us that the wire is too long for resonance at 80m and that *a capacitive reactance of -j91.3Ω would need to be placed in series at the center of the antenna. At 3.647MHz this corresponds to a capacitor of 478pF, say 470pF.*

However, by placing this capacitor at the center, we will upset all other odd harmonic resonances, i.e. 30, 17 and 12m.

## Six Resonant Bands

Now let us try to regain an additional odd harmonic, apart from 80m. For some, but not all odd harmonics, this can be done by *loading the center of the antenna with a series LC network* (see table below).

f (MHz) | X_{CL} (Ω) | odd bands | C_{ser} | |||

3.647 | -j91.3 | 80m | 478pF | L_{ser} | f_{res} (MHz) | X_{L,f} (Ω) |

10.125 | +j241 | 80 & 30m | 213pF | 4.95µH | 4.900 | +j314.7 |

18.118 | -j153 | 80 & 17m | 692pF | no solution | ||

24.940 | -j11.8 | 80 & 12m | 477pF | 10.1nH | 72.486 | +j1.58 |

**For example: ***The antenna will be resonant at 80 & 30m, as well as all even harmonics, by placing a 213pF, say 220pF capacitor in series with a 4.95µH inductor at the center of the antenna.*

## What about more bands?

Yeah, right. Let me disappoint you by saying that things are not as easy as adding just one additional reactive element in series or parallel to obtain yet another band. Although, *theoretically it is possible* to devise a passive network that makes the antenna resonant on all odd harmonic bands. However, such a network will be *far from practical* to have it hanging along a wire. Moreover, *it remains to be seen whether a low VSWR feed point can be found that accommodates all these bands* (see next page). Nonetheless, the challenge is there for the taker!

As mentioned before, *it is not posssible to scale this antenna to a longer 160m-version.* Would one try to do so, the problematic 80m-band would become an even harmonic and hence impossible to be influenced by center-loading the antenna.

The 6m-band (50-52MHz) is the 14th harmonic of the 80m band. Being such a high harmonic, *it becomes prohibitively difficult to pin point a low-VSWR 6m-band feeding offset.*

## No Resonant Traps

Please, do allow me to tackle some anticipated critisism. Uninformed spirits may argue that the two-element network of this antenna be a resonant trap adding significant loss.

This is clearly not the case. *The two-element center-loading network is not resonant at any of the amateur bands and is therefore not acting as a trap. It is strictly a loading network,* adding relatively little reactance. As such, it does not contribute more loss than any other loading inductor commonly employed in the very best of commercial and home-made low-band yagi designs.

## Mechanical Construction

The mechanical construction of my center-loading network is based on a plastic corrugated end-insulator of the type MFJ-16H02 or, equivalently, TELEX^{®} hy-gain^{®} PN 801439, Order No. 156.

# Optimal Feed Offset & Input Impedance

Now that the antenna can be made resonant on six bands, *a «sweet spot» needs to be found for which the VSWR with a given feed impedance is low on all six bands.* In order to determine this ideal feed offset, VSWR graphs at difference feed impedances are plotted for all frequency bands and all possible offset percentages and then compared. *This will be done for the 6-band version of the CL-OCFD which includes 30m.* Note that 0% offset corresponds to the open end of the antenna, 50% to the middle of the dipole.

## 200Ω Source

When this is done *for a feed impedance of 200Ω (first graph), we notice that the VSWR on all bands drops below 2÷1 at 28.9% offset.*

This is how the *6-band* ON4AA CL-OCFD will look like:

The same optimal offset equally applies to the *5-band version* of the CL-OCFD*without the 30m-band coverage:*

## 150Ω Source

Feeding the antenna from a *150Ω source* yields two «sweet spots»: the very same 28.9% and *a more interesting 19.8% offset.* With 19.8% offset, the VSWR will be slightly higher than 2÷1 at the band centres of only two bands; 20 & 15m. *However, when the antenna is frequency swept over the entirety of these bands, it becomes evident that the VSWR exceeds 3÷1 at the band edges* (see next section). Another drawback is that 150Ω baluns are difficult to locate.

## 100Ω Source

However, feeding the antenna from a *100Ω source is not interesting* since the VSWR on several bands will be above 3÷1.

## 300Ω Source

*Neither is feeding the antenna from a 300Ω source interesting* since the VSWR on all bands will be generally higher than with the 200Ω feed impedance.

## Conclusion

150Ω produces unacceptable high VSWR ratios at the band edges of the 20 and 15m bands. Only 200Ω feeding produces practicable results. Therefore, *a feed impedance of 200Ω and a feed offset of 28.9% are kept as the results of this design exercise.*

## About Rendering these Graphs

Here is an interesting fact: Every line on every graph has been drawn on the basis of 98 datapoints. One datapoint is, as a matter of fact, a complete antenna analysis. In other words, six times 98, that is, 588 NEC2 runs were necessary to draw one graph. In 2002, the only way I could obtain such a graph was by undertaking the monastic task of running EZNEC 98 times and manually copying 1176 numbers —because input impedances are complex numbers— onto a spreadsheet.

Only since recently, this task can be automated thanks to 4nec2, an excellent antenna modelling interface for NEC2 that, amongst a host of other things, allows to sweep any arbitrary antenna variable. Furthermore, 4nec2 is freeware. Thank you for that, Arie Voors!

## Model

The 4nec2 input file for the ON4AA-200 CL-OCFD antenna over good RF ground (σ = 10mS/m; ε_{r} = 14) can be downloaded here. It requires 4nec2 version 5.7.0 or higher.

## Ground Characteristics

Above graphs were produced with the antenna over city ground (σ = 1mS/m; ε_{r} = 5) in the near field. Running the model with different ground characteristics demonstrated that *the VSWR of the antenna is almost not influenced by the RF properties of the ground.*

*Radiation Patterns*

The 72 power gain patterns in dBi were obtained with *4nec2 over good RF ground (σ = 10mS/m; ε*_{r}= 14).## Discussion

Focussing on the lower bands, *the most interesting radiation patterns are obtained with an antenna height of about 16.76m (55ft):*

- On 80m, the pattern combines maximum gain in the zenith for
__N__ear-__V__ertical__I__ncidence__S__kywave (NVIS) short-haul communications with still enough broadside gain at 30° elevation for long-haul DX contacts. - On 40m, a take-off angle of 34° is sufficiently low to enable reliable long-distance (DX) contacts in all directions except for two broadside nulls.
- 30m is actually the main reason for the above statement, with only at this height the surpression of a useless zenithal lobe.

It is also interesting to see how *nulls in certain directions on one band are covered by increased gain lobes on the next harmonic band.* This holds true for all six bands. So, one may conclude that *the antenna offers spatial diversity through its frequency diversity.* Careful selection of operating time and frequency, taking into account available propagation modes, will put you in contact with any place on the globe. This is quite a lot for such a simple, yet very effective, broadband trapless antenna!

A final warning: As for with any antenna, *be very careful about placing it in the vicinity of other resonant metallic structures (especially antennas)* since this may severely upset the desired radiation patterns.

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