Losses in yagi antenna elements at 413 MHz

(May 2 2006)

When simulating yagi antennas with NEC2, NEC4 or OMNEC one typically uses the bulk conductivity of the element material as one of the input parameters to the simulation program. This is well justified for new (uncorroded) elements that are mounted on a non-conducting boom tube but it is not self-evident that a real antenna that has been used for several years will have as small losses as predicted by the simulations.

There are several mechanisms by which element losses may increase above the values computed by the modelling software.
  • Reduced surface conductivity due to corrosion.
  • Ohmic losses due to Eddy currents in the boom tube or other conducting materials near the element center.
  • Magnetic losses in washers, screws and other magnetic materials near the element center.
  • Dielectric losses in surface coatings used to prevent corrosion.
  • Dielectric losses in plastic plugs at the element tips.

Element losses are particularly important at the highest frequencies where yagi antennas are used for space communication because the sky temperature is very low. Very low system noise temperatures may be reached and a small loss in the antenna would therefore give a much larger loss in receiver S/N because besides loss of signal the ohmic losses would increase the system noise temperature since the losses would occur at room temperature. The lowest sky temperature at 500 MHz is around 15 K and modern low noise amplifiers may also have a noise temperature of 15 K. The antenna is not perfect so some noise will be picked up through sidelobes. This might add another 15 K. The ohmic losses could be 5% which would add another 15 K (5% of 290K.) If the ohmic losses are increased by 25% due to ageing or some other effect, the antenna losses would become 7.5%. The loss in gain would be 0.1 dB only, but the contribution to the system noise would increase from 15 K to 19 K which would change the noise temperature from 60 K to 64 K, causing the noise floor to increase by 0.3 dB for a loss of S/N of 0.4 dB.

A yagi that is optimised for maximum gain might have 10% ohmic losses and would be more sensitive to increased element losses. The signal would loose 0.2 dB for a 25% increase of the ohmic losses but the noise temperature would go from 75K to 82.5K causing the noise floor to increase by 0.4 dB for a total S/N loss of 0.6 dB.

In order to get an idea of the magnitude of the additional element losses that might be introudced by the phenomena listed above we have measured the Q-value of rods inside a cavity with dimensions 0.7m x 0.3m x 0.3m, see figure 1. The elements were hung in thin polyethylene bands at the center of the box and RF energy was loosely coupled to the ends of the elements from coaxial connectors in the box wall having a small wire to give some capacitive coupling. This way the cavity with connectors and an element forms a coaxial filter and the insertion loss was set to be 40 dB or more in order to have a negligible influence on the Q-value from loading by the signal source or detector. (A network analyzer was used for both.)

Figure 1. The 0.7m x 0.3m x 0.3m box with the lid off showing a 10 mm element in position for measuremeny of the Q-value.

Losses due to corrosion

One series of measurements was made on three different corroded elements and a new one. Figure 2 shows what the elements look like.

Figure 2. Four elements used to measure the effects of corrosion. From top: First, new element from alloy 6063-T6 with epoxy filled polyamide element holder and non-magnetic stainless screw. Second(CO1), element used 20 years near Stockholm. Third,(CO2), element from start of regular TV in Sweden. Made from folded sheet metal, about 50 years old. Fourth,(CO3), element used on the chimney of a house that was heated with a gas burner for 10 years, then with an oil burner for 5 years. The element 38 years old but has been kept indoors the latest 25 years. The alloy is SM 5050-18, bought from Svenska Metallverken in 1967. Nowadays known as SS 4007 or 1050A.

Since one of elements is from an old antenna it is not known what alloy it is made from. Resistivities are available for 5050 alloys but what 5050-18 means is unknown to us. It is easy however to measure the bulk resistivity from the resistance, length and weight under the assumption that all the aluminium rods have the same density 2.69 g/cm3. The resistance was measured with a DC current of about 20 A applied at the ends of a rod and with a millivoltmeter connected to two points a few cm away from the ends. The results are shown in table 1.

Element Total  Weight Area Current Voltage Res.   Dist.  Resis-    Diam   Q-value 
        length                           (milli-  for U  tivity           in box  
         (mm)   (g)   (mm2)  (A)    (mV)  ohms)   (mm)   (ohm-cm)  (mm) 
 New     310.8 26.10  31.22 22.64   6.55 0.2893    278   3.25E-8    10      8250  
 CO1     307.1 22.72  27.50 23.57   8.05 0.3415    275   3.41E-8    10      7900
 CO2     307.4 17.44  21.09 24.38  10.21 0.4188    273   3.74E-8    9.6     5576  
 CO3     310.2 18.21  21.82 23.76   9.54 0.4015    276   3.17E-8     8      5926
Table 1. Evaluation of bulk resistivity of old elements and observed Q-values. (The new element without element holder.)

The new element was made from alloy 6063-T6 and according to manufacturer specifications the resistivity should be 3.30E-6 to 3.50 ohm-cm for extruded tubes. Cast material (heat sinks) from 6063-T6 has higher resistivity, typically 5.3E-6 ohm-cm.

Directly from the Q-values we see that two of the corroded elements have much higher losses than the new element. The Q-values observed with elements in a box are affected by the losses of the box and not only the losses of the element itself. For an evaluation of the magnitude of the losses due to corrosion, see below.

Losses due to protective coatings

Losses due to corrosion might be neglected in good locations but corrosion may be much faster in industrial areas or near salt water and therefore it might be a good idea to protect the surface with some kind of coating. Anodization is the obvious choice for aluminium so we have measured the Q-value of several anodized elements with oxide thicknesses 15u and 30u. We also checked the Q-value for painted elements (100u powder coating, polyester, Interpon 610 from Akso Nobel, product code MW701D Silver, RAL9007.)

Typical values are shown in table 2.

                Q-value for element inside box.
Coating       diam=10mm     diam=6mm     diam=4mm        
 None           8250          5480        4070 
Oxide 15u       7825          5315        3908
Oxide 30u       7663          5145        3748
Paint 100u       6272          3846        3026
Table 2. Q-values inside box for different coatings on aluminium.

Anodization with 15u has a small but clearly visible influence on the element losses. The effect is similar to using an unprotected aluminium surface for 20 years in a good environment. The values in table 2 are typical values that do not take small variations of diameters into account. For a detailed evaluation of losses due to surface coatings, see below.

Losses due to mounting materials and boom tube

Elements can be mounted through the boom tube with isolators or in contact with the boom tube. Elements in contact with the boom tube should have be in very good metallic contact because of the low impedances and very high currents that cause small contact resistances to give high losses. For metallic contact welding is preferred.

Elements that are mounted through the boom tube with isolators can be kept in place with Starlock washers as illustrated in figure 3.

Figure 3. Isolated through hole mounting with Starlock washers.

With isolated through-hole mounting there are Eddy currents in the boom tube that lead to a reduced Q-value. The Starlock washers are made from magnetic stainless steel and add magnetic losses.

When elements are mounted on top of the boom tube in metallic contact or at a small separation from it on an insulator losses also occur. Table 3 shows Q-values for elements mounted on short boom tubes measured in the 0.7m x 0.3m x 0.3m box. The boom tube used for table 3 was a 25x25 mm tube with quadratic cross section.

                  Q-value for element on boom tube inside box.
Mounting on boom         diam=10mm     diam=6mm     diam=4mm        
 None                     8250          5480        4070 
Through, glued.           5700          4525        3295
Through, Starlock.        3250          2875        2120
9mm above, polyamide      6650          4407         - 
Table 3. Q-values inside box for different mounting methods. New aluminium elements without surface coating on 25mm x 25mm quadratic boom. The "polyamide" mounting block is visible in figure 2.

Through-hole mounting with Starlock washers gives rise to severe losses on 413 MHz. Such mounting is also not compatible with anodized elements. Mounting elements at some distance from the boom tube even on a material with poor RF properties (and excellent mechanical properties) is much better for losses and compatible with anodized elements. When a 10 mm element is mounted through the boom tube one has to drill a 12 mm hole while the plastic block is well secured through a 4 mm hole. This allows the use of a slightly thinner boom tube which reduces Eddy current losses and wind load. The total losses due to surface coating and mounting to the boom tube can be expressed as an effective resistivity and included in the optimization procedure for yagi antennas.

The next paragraph describes how we extract the effective resistivities from the measurements described above.

Converting Q-values inside a box to effective resistivities

It is not self evident how to estimate how the losses of the box affect the observed Q-values, and therefore we have measured the Q-value of elements made from copper, aluminium and brass with several different diameters inside the 0.7m x 0.3m x 0.3m box. Some of these elements were also measured in a smaller box, 0.5 m x 0.3 m x 0.3 m which produces somewhat lower Q-values.

The losses of an element is proportional to the square root of the resistivity and inversely proportional to the diameter. The measurements are made at the same frequency and therefore the element lengths are slightly different depending on the element diameters and it is not self evident in what way the small differences in length affect the losses. Neither in free space, nor inside a box.

The losses of the box will affect the Q-value more for an element with high Q than for one with low Q. The coupling between the box and the element depends on the element diameter in a way that we do not know how to compute from theory. Without any good theoretical justification we adopted a simple model for the Q-value of an element in either of the two boxes. The model and our measured data can be found in this C-program qvbox.c (17452 bytes) The program gives us Q-values that match observations reasonably well and it expresses the losses of an element as its effective resistivity. Having copper, aluminium and brass elements with known resistivities among the measured data that the model is fitted to inside two different boxes gives us some confidence in the reliability of the results despite the lack of theory for the model. Table 4 shows a printout from qvbox.c. The reference elements 0 to 20 are fitted with a RMS error in the Q-value of 96 (QTbox-Qexp) Without any change of the model the resistivities of the other elements are fitted to make the model give the correct Q-values. The procedure is not quite correct because the degradation of Q due to the influence of a boom tube can not be represented by a resistivity that is the same for all diameters. The effect of a boom tube is slightly more harmful on thick elements than indicated by the resistivities that come out from the model.

no    material   alloy  diam  le     QTfree   QTbox   rat  Qfree     Qexp
 0 Cu, massive    5011  3.98 320.73   6723    5589  1.203    6884    5723
 1 Cu, massive    5011  5.95 315.28  10050    7627  1.318   10202    7743
 2 Cu, massive    5011  7.97 310.61  13462    9379  1.435   13414    9345
 3 Cu, massive    5011  9.94 307.53  16790   10830  1.550   16743   10800
 4 Al, massive    6082  3.88 320.62   4738    3981  1.190    4856    4081
 5 Al, massive    6082  5.95 315.24   7250    5582  1.299    7144    5500
 6 Al, tube       6063  8.14 309.92  10242    7207  1.421   10157    7147
 7 Al, tube       6063 10.07 307.16  12676    8312  1.525   12689    8320
 8 Al, tube       6063 15.93 297.43  20049   10897  1.840   20608   11200
 9 Brass                5.04 317.43   4136    3464  1.194    4223    3537
10 Brass               14.95 299.71  12254    7715  1.588   12013    7563
11 Al, tube       6063 10.14 307.19  12758    8346  1.529   12521    8191
12 Al, tube       6063  9.98 307.16  12557    8261  1.520   12388    8150
13 Al, tube       6063 10.07 307.13  12664    8306  1.525   12646    8295
14 Al, massive    6082  3.90 320.70   4750    3990  1.191    4878    4097
15 Al, massive    6082  5.95 315.25   7256    5585  1.299    7106    5470
16 Cu, massive    5011 10.00 307.59  16891   10871  1.554   16749   10780
17 Al, massive    6082  4.00 320.70   4878    4078  1.196    4820    4030
18 Al, massive    6082  6.00 315.25   7317    5621  1.302    7140    5485
19 Al, tube       6063 10.00 307.19  12582    8272  1.521   12645    8313
20 Al, tube       6063 10.00 307.13  12582    8272  1.521   12701    8350
21 Al, elox 15 um      10.11 307.19  11825    7845  1.507   11794    7825
22 Al, elox 15 um       3.88 320.67   4540    3828  1.186    4635    3908
23 Al, elox 15 um       5.89 315.15   6898    5347  1.290    6857    5315
24 Al, elox 30 um      10.14 307.08  11462    7647  1.499   11486    7663
25 Al, elox 30 um       3.88 320.48   4392    3712  1.183    4434    3748
26 Al, elox 30 um       5.91 315.14   6675    5194  1.285    6612    5145
27 Al, Paint 100 um    10.07 306.06   8601    6112  1.407    8826    6272
28 Al, Paint 100 um     3.91 317.78   3338    2894  1.153    3490    3026
29 Al, Paint 100 um     6.04 312.72   5161    4157  1.241    4774    3846
30 CO1(corroded Al)     9.86 307.10  11868    7900  1.502   11868    7900
31 CO2(corroded Al)     9.60 307.40   7614    5576  1.366    7614    5576
32 CO3(corroded Al)     8.03 310.20   8087    5926  1.365    8087    5926
33 Thru boom, glue      4.00 325.56   3456    2983  1.159    3818    3295
34 Thru boom, glue      6.00 320.85   5184    4175  1.242    5619    4525
35 Thru boom, glue     10.00 313.46   8641    6137  1.408    8025    5700
36 Thru boom, Starlock  4.00 326.27   1863    1703  1.094    2319    2120
37 Thru boom, Starlock  6.00 320.85   2794    2447  1.142    3282    2875
38 Thru boom, Starlock 10.00 313.58   4657    3763  1.238    4022    3250
39 Above boom           6.00 319.77   5668    4505  1.258    5545    4407
40 Above boom          10.00 311.04   9447    6577  1.436    9553    6651
Table 4. Q-values inside a box and associated Q-values of the element itself. The Q-values inside the box (QTbox) are fitted to measurements.

The result of the fitting procedure is that a high Q element like a 16 mm diameter aluminium tube has a Q-value inside the box that is 1.84 times lower than the Q-value of the element itself due to the losses of the box. An ordinary element such as a 6 mm aluminium rod is a factor 1.299 lower while a lossy element like a 5 mm brass rod has a Q-value that is reduced by only a factor of 1.194 by the box. The factors depend slightly on the diameters.

The resistivities associated with table 4 are listed in table 5.

Element type          Resistivity
Cu, massive (5011)        1.72
Al, massive (6082)        3.3
Al, tube    (6063)        3.1
Brass                     7.3
Al, elox 15 um            3.6
Al, elox 30 um            3.8
Al, Paint 100 um          6.7 
CO1(corroded Al)          3.4
CO2(corroded Al)          7.8
CO3(corroded Al)          4.8
Thru boom, glue           6.6
Thru boom, Starlock      22.6 
Above boom                5.5
Table 5. Losses of elements expressed as resistivities.

An inspection of table 5 shows that mounting an element above the boom increases the losses by about 30% for a gain loss in the order of 0.1 dB and a S/N loss in the order of 0.5 dB in a low noise system. (Losses are proportional to the square root of the resistivity.) Insulated through-hole mounting with Starlock washers increases the losses by a factor of 2.6 with an associated gain loss in the order of 1 dB for a low loss yagi design. If one feeds 1 kW of 432 MHz power into a through hole mounted yagi with Starlock washers one should expect the boom tube to become warm because it would be heated from the washers by several hundred watts. An antenna with the elements above the boom tube - even if they are directly on the tube in electrical contact should remain cold.

Anodizing with 15u changes the intrinsic Q of a 10 mm element to 11794 from a typical value around 12700 which means that the losses of the element have increased by 7%.

The investigation presented on this page allows the following conclusions for the design of antennas in the 400 to 500 MHz region:
  • Use a resistivity of 6.3 ohm-cm for aluminium in modelling and evaluation of antenna properties when 15u anodized elements are used with a mounting like the one shown in figure 2. (See note below)
  • Do not use Starlock washers.
  • Glass-fibre boom tubes might help to make antennas with very low noise temperatures.
Note: The mounting method degrades the resistivity from from 3.1 (6063) to 5.1 on new aluminium. Anodizing gives a further increase of the losses by a factor of 3.6/3.1 times (=1.16) to 5.9. The alloy could be 6082 which might increase the losses by 3.3/3.1 times (=1.06) to an effective resistivity of 6.3.