Where does the HF power go
(published in Electron # 4, 2006)
are reporting on signal strength as perceived by the S-meter. A long
discussion could be held on S-meter calibration but on average these S-meters
are showing about the same mark when a signal is received around S-9 on the
Next to 'conditions' the antenna system could make quite a difference as far as antenna efficiency is concerned and angle of radiation, whether azimuth and / or elevation. Many antenna books have been written on this subject and at the internet some well documented sites are being maintained on this subject.
Even the best antenna however will not be very helpful with the rest of the system between transceiver and antenna not optimized for high efficiency. Many radio-amateurs unfortunately are only vaguely familiar with loss mechanisms in this area. Furthermore many articles in radio-magazines are dealing with aspects of individual constituents (tuner, balun, transmission-line, antenna) but are rarely concerned with the complete system and the interaction between individual system parts. It therefore seems useful to take a look at output-system aspects in a more integral way.
In this chapter we
will model the complete system from transceiver up to the perceived
(relative) power at the receiving station. We will try to find out how much
power will be lost in a high efficient antenna system, where this loss is
concentrated and what is happening when the same system is not so optimally
matched anymore. To set figures into perspective for this exercise we take
the basic station to be capable of delivering 100 Watt into 50 Ohm. The
(transistorized) transceiver should see SWR < 2 to generate full power,
and therefore should be connected to a tuner to correct non-matching
situations. The system should be able to operate on all HF amateur
frequencies, starting at the
Usually an antenna for the lower HF amateur frequencies is the 'hardest' component because of size for a resonant type. We will take the antenna in this article to be resonant at 3,65 MHz. When using one of the antenna design program's e.g. Mmana (free), the antenna will look something like:
above average ground type (ε = 5, conduction = 13 mS).
This antenna will behave like table 1.
Table 1: Example
The antenna indeed is living up to expectations with almost perfect SWR at the design frequency and with band-width is 140 kHz. between SWR = 2 frequencies. In between these SWR positions the antenna may be applied without an antenna tuner.
Note: The antenna input impedance is a complex number (except at the exact design frequency) so all calculations have to be dealing with these complex numbers, including SWR.
The antenna in our example has a symmetrical structure that we like to keep that way. To feed the antenna we may select a symmetrical or an a-symmetrical feed-line. We will start-off this example with the a-symmetrical type, so we will have to make a transition from a symmetrical to an a-symmetrical system, e.g. with a balun. More on this last subject may be found in a dedicated chapter on these components.
A balun should make the balance to un-balance transition without further being 'visible' in the system. This 'invisibility' will be ensured with balun impedance at least four times the system impedance:
Xl = 4 x 50 Ohm = 200 Ohm. This should already been ensured at the lowest operating frequency (3,5 MHz.), so
L = 200 / ω = 9,1 μH.
n = √(9,1 / 0,17) = 7,3 (8).
When constructing this balun as a trifilar flux-transformer, we need four trifilar turns since the antenna and the feed-line will be connected across two windings in series each. Although one sometimes comes across many more turns for these transformers (at 4C65 ferrite), 'more is less' in this situation since parasitic capacitance is increasing with each additional turn, decreasing maximum usable frequency for this balun.
Best 1 : 1 balun however is the sleeve-choke type, consisting of 8 turns of transmission-line on the same toroide.
Even a well-designed balun will not be ideal and will 'consume' some power when connected to the antenna. We will take this power-loss into account in our total picture. Again calculations will be of a complex nature.
In our example
design, the antenna plus balun is situated at ten meter above ground, so we
need some feed-line to connect to the transceiver in the shack. In this
example we will first selected the well known RG58 type of coaxial
transmission-line (Belden 8259), with a loss of 2,76 dB per
Before arriving at the transceiver, a tuner will translate line impedance to the required 50 Ohm resistive value, the transceiver needs to generate full power. For this component, a simple L-type tuner has been selected as low-component count usually also means low loss. In this example, the tuning inductor will be in the series branch and is showing a quality factor, Q = 200. This L-type will also perform as a low-pass filter, which may be useful to suppress undesired harmonics.
Depending on the type (value) of the line impedance, the tuning capacitor will be at the line side or at the transceiver side. In our example-tuner a high Q-factor has been selected which is not an impossible when constructing with a large enough wire diameter and not too small inductor dimensions. Nevertheless, some power will be dissipated in this component as well and we will take this into account.
With the complete antenna system designed as in our example system, let's find out how this will behave on the amateur frequency band it has been designed for, as in figure 1.
In figure 1 we find the red curve representing the bare antenna as a result of the antenna design program. This antenna is behaving as required, resonating at 3,65 MHz. and showing a band-width of 140 kHz. between SWR=2 points.
When connecting the balun (green curve), the compound system has been shifted by 20 kHz. to the lower frequency side. Connecting the transmission line (blue curve), the curve is somewhat shifted again and has increased bandwidth to 145 kHz. between SWR = 2 points. When designing the antenna at one particular operating frequency, we will have to take these small frequency shifts into account.
In our design
example we also connected an antenna tuner, so the 140 kHz. usable band-with
between SWR = 2 positions is not relevant anymore since we are capable of
matching the antenna across the entire
Table 2: Tuner for
In table 2 we see this tuner may be constructed with run-of-the-mill components, except maybe for the high capacitor values below 3560 kHz. although this may be accomplished by adding fixed capacitors.
Note: The '*' sign indicates the capacitor the be connected at the transceiver side; otherwise the capacitor is connected at the line-side of the tuner.
Again we find some power left behind in the tuner. This power is in a first approximation related to inductor loss (Q-value) and therefore it pays to apply high quality parts. With all components known, we may put all loss in perspective in figure 2.
We are happy to
find most of the input power is radiated at the antenna and only little power
is dissipated in other parts of the system. It is remarkable that despite
low-loss transmission-line (2,76 dB /
Figure 2 is also showing we designed a well behaved antenna system with high overall efficiency.
Since we are
satisfied with our antenna system at the
With this statement
we are approaching the motive for this article. Many amateurs in
Table 3. Non matched system
Table 3 is showing
behavior and loss figures for the well designed, 3,6 MHz. antenna system (red
number), now operating at the
balun in parallel to the antenna, will bring the real-part of total impedance
down but will leave SWR at a very high value since the imaginary part is
still quite high. Further more the balun impedance (Z = 477 Ohm) will be too
low compared to the antenna impedance (Z = 5600 Ohm) to perform its balancing
function. The balun was not designed for this high impedance and will now
consume just under 1 Watt, as compared to almost 0 Watt at
The transmission-line that is now totally unmatched, will transform the high input impedance to a (very) low value and to our enjoy we find SWR is down considerably. This however is related to very high cable loss with 84 Watt of available HF power (100 W.) to be turned into heat along this line. At the tuner side we hardly will notice anything unusual as the transceiver will show SWR = 1 when the tuner is set to: L = 2,08 μH. and C = 898 pF. Tuner loss is not unreasonable either with only 1,8 Watt burned internally.
After all system loss along the way, the antenna will radiate only 13,3 Watt of HF power since this un-matched antenna situation is turning 86,7 % of available power into heat. Our communication partner at the other end will notice signal strength at the S-meter to be down by over 1,5 S-point as compared to our neighbor with a well designed, low-loss station. Relative S points may be defined at: (10 log(Pmax/Pactueel))/6. The diminished signal report may be regarded as acceptable (some signal is better than not being able to operate at all), but any signal loss will be too much at adverse communication conditions like high QRM or at a DX pile-up.
The high loss
Figure 3 is telling us the dipole antenna system designed for 3,65 MHz. is doing very well at this frequency with most of the input power going into the antenna (red). At all other HF amateur bands, SWR is high with low antenna power as a consequence. At all but 3,65 MHz. most of available power is lost in the feed-line (blue), with total loss of one S-point or more at the receiving station.
Balun loss (green), limited to 4 Watt maximum, is within safe limits in this example antenna system because of high cable loss.
Why high cable loss?
It may be difficult to imagine why this relative
short stretch of feed-line is generating these high loss figures, since cable
specifications show 2,76 dB /
Total cable loss is somewhat mystified when in cable transfer function but we may gain some insight from the models (just for insight) in figure 4 and 5.
Figure 4: Transmission-line with reflected power
In figure 4a we find a transmission-line that terminated into its characteristic impedance. All energy from the generator is transported to the terminator and only very mildly absorbed by the line. No energy is reflected back.
In figure 4b we find the same situation, this time (very) uncharacteristically terminated. Part of the energy will be reflected at the load and will travel back to the generator, as in:
ρ = Er / Ef
ρ (rho) = reflection coefficient (complex)
Ef = forward energy
Er = reflected energy
With the bare generator being a voltage source, the transmission-line again is terminated uncharacteristically and again power will be reflected.
Note. The generator in our example system is our transceiver. This transceiver is designed to deliver full power when terminated into a 50 Ohm resistive load and is protected to cut back on system power when terminated into a different load to safeguard the active elements in the output. The specified termination resistance however is not related in any way to the 'output impedance' of this transceiver. An article discussing this situation in more details may be found here.
We may be more familiar with the 'SWR' terminology and of course 'SWR' and 'ρ' are related, as in:
| ρ| = (SWR - 1) / (SWR + 1) (vertical lines to denote absolute value)
With SWR = 10, ρ = 0,82 meaning that 82 % of power will be reflected. In above tables we found much higher SWR not to be unlikely. The energy will be reflected back and forward and this will go on until finally all energy has been burned. The transmission-line will therefore be passed a number of times, each time consuming a little energy. The larger the mismatch at the terminator, the larger the portion of energy that will travel up and down and the more times the transmission-line will be traversed (model!).
An other model to visualize the loss mechanisms in un-characteristically terminated transmission-lines, may be found in the SWR definition, as in figure 5.
Figure 5: More loss by higher voltage and current
In figure 5a we again find a generator, a transmission-line and an end-user to terminate the line. The transmission-line has been terminated characteristically so noting is reflected and the voltage and current on the line is constant and equal at the generator and the load (minus a little resistive loss in the cable).
In figure 5b the line is un-characteristically terminated and part of the voltage and current will be reflected. This reflected signal will add to (or subtracted from) the incoming signal so a fixed wave pattern will be building up at the transmission-line. The peak and valleys of this voltage may be directly measured at the cable as the (Voltage) Standing Wave Ratio. This means the voltage at some position at the transmission-line may be much higher than originally envisaged, generating much higher de-electric loss than in situation 'a'. In particular situations this locally higher voltage may even generate a flash-over at below maximum (power) ratings for a well terminated transmission-line.
The identical situation also applies to currents along the transmission line, with local currents to be much higher than average. This is not just a model but will indeed be the practical situation making the transmission-line prone to local hot-spots and even melting of the central conductor at a system power below maximum rating of the well-terminated situation.
What cable loss is acceptable?
To get an idea about what SWR to allow, we
could say to be not very concerned up to a level where the receiving station
is receiving us with a signal strength of 0,5 S-points below optimum. This
situation will arise when half of the available transmitter power is 'lost'
somewhere along the antenna system. Next we calculate maximum SWR at each
frequency for RG58 cable (2,76 dB/
Note these SWR figures to be measured directly at the reflecting side (at the antenna). At the input side SWR will be much lower at half or less the value at the antenna. We may therefore easily under-estimate the bad situation.
In figure 6 and when applying RG58 type of transmission-line, we may allow quite high SWR before cable loss will become excessive (SWR > 50) at frequencies below 3 MHz. Between 3 and 20 MHz. we better ensure SWR < 10 and above 20 MHz. we better be very careful with any type of mismatch as cable loss quickly leads to unacceptable loss of radiated power.
In the previous section we found
transmission-line loss to be 'amplified' when SWR is high because of
non-characteristic line termination. This may lead us to lower
transmission-line loss as a way-out. To test this idea I changed the RG58 for
lower-loss RG213 (Belden 8267) exhibiting 1,194 dB /
Table 4: Power
distribution when applying
When comparing table 4 to figure 3, we find this better transmission-line is doing some good. Since SWR did not change, we still loose quite some power that will manifest itself as a loss of around 1 S-point at the site of the receiver of our signals when compared to an optimal situation.
In table 4 it is also clear we have to look again to our balun, that is loaded above its rated maximum power of 4 W. at several amateur frequencies. At least a double amount of ferrite is to be applied.
Although we have been
applying a better type of transmission-line, cable loss still is high because
of high cable mismatch. As a side step it may be useful to look at a system
that is designed to deliberately avoid (high) mismatch at a number of amateur
frequencies. This antenna may be found at "Multiband trap antenna" and
is consisting of a dipole at 2 x
In this design, the
antenna is coupled through a 1 : 2,25 transformer to ensure SWR < 4
throughout amateur HF frequency bands of 80, 40, 20, 15 and
For the analysis in table 5, I set the balun to be a 1 : 1 type as in the earlier examples for a more direct view to the influence of the well behaved antenna.
Table 5. Power distribution in 'multiband trap antenna'.
In table 5 we find
the system to indeed show a high efficiency at the design frequencies (red numbers)
and low loss figures at the receiving side of a few tenth of an S-point.
Applying the design transformer of 1 :
efficiency is low at the non-design HF-bands, 10, 17 and
It is interesting to look what is happening at high loss situations: at 10,125 MHz. we find at the tuner SWR = 14,1 while at the antenna this is 72,7! Something analogue may be discovered at the other non-design bands: 18,118 MHz.: SWRin is 9,5 with SWRout at 57,6 and at 24,940 MHz.: SWRin is 8,3 with SWRout is 48,9. The lower SWR at the tuner position is no guarantee the system is operating at high efficiency!
Although a transformer is to be applied, the balun will also do an acceptable job with no particular requirements other than specified earlier, since power dissipation is always below 4 Watt, even at the non-design bands.
To my surprise some power is lost in the trap inductors in spite of the relatively high Q, set at 150. This is indicating high Q to be a prerequisite for an efficient (trap) antenna. This also is an indication to be careful when applying 'coaxial traps' to an antenna since these components are exhibiting a relatively low Q-factor because of distributed trap capacitance.
In the early radio-days,
coaxial transmission-lines where not yet readily available so antennas where
connected through single wire or symmetrical lines. This latter type of line
is not very helpful at lowering high SWR but line-loss of well maintained lines may be very low
indeed at 0,104 dB /
To find-out what
this type of line may bring, I calculated the same antenna as in our first
system, this time connected through
Table 6. Power
distribution in dipole antenna designed for
In this antenna
system SWR is still high, since the antenna is the original
Note 1. This calculation is based on system loss in the contributing parts as mentioned. The low transmission-line loss however is valid for a well kept line that connects the antenna to the tuner in a straight line. This may be somewhat difficult in practice since the transmission-line may be strengthened mechanically by special wall-fixes, through-wall connection system and in-house suspension until connecting to the tuner. The electro-magnetic field in this type of transmission-line however is protruding a little beyond the line so everything supporting this will somehow influence field transmission and will induce some additional loss.
Furthermore, nature will also have its way with an open line. Garden debris like fallen leafs, branches etc may become stuck between the two conductors and the wall, as may be insect- / bird-nests, algae, moss etc. Also weather conditions like rain and snow will have some influence making this low-loss line not so very low loss anymore without regular maintenance. This does not apply to coaxial transmission-line that is more a set-and-forget type of material with considerably lower maintenance requirements, especially when 'vulcanizing' connectors.
As a last exercise
I modeled a system with the original
Table 7. Power distribution
in dipole for
At the dipole
section we find SWR re 600 Ohm to be quite high as in the section before.
This is also showing we should be very careful when connecting a 'random' balun at the end of an a-symmetrical tuner to connect to a symmetrical feed-line. Usually the balun impedance is much too low to perform adequate balancing at the high impedance levels as found at this position after high antenna impedances have being transformed by high-impedance feed-lines. Therefore it is quite remarkable one sometimes may come across a carbonyl (low permeability material) balun build into an a-symmetrical tuner to allow for a symmetrical tuner output. It is quite puzzling what type of applications the manufacturer may have had in mind to this extend.
Taking above considerations into account, this last system set-up may be the system of choice to obtain a high efficient antenna system for all HF amateur frequencies, starting at 3,5 MHz. Even the a-symmetric tuner is quite unremarkable with series inductor 18 μH > L > 0,6 μH and parallel capacitor 280 pF < C < 15 pF, which is not extreme at these frequencies. Keep in mind that again we are dealing with high impedances at the tuner with high(er) voltages across system components than usual.
All in all we have
to compare this open-line fed system with the 2 x
At the end of our little discussions we may come to a few basis conclusions:
Coaxial feed-line: For high efficient antenna systems coaxial feed-lines may be applied with resonant, low impedance antenna's. This will yield low SWR at the transmission-line connecting the antenna and the transceiver (tuner). To this extend, 50 Ohm transmission-lines are no better than 75 Ohm cables and may be applied whichever is more convenient. Examples of resonant antenna systems are: monoband dipoles or monoband verticals, cluster of monoband dipoles at a single balun (cat-whisker antenna) and a multiband trap dipole.
Pro coax: easy handling, leading indoors, along walls, along metal drainage pipes etc, usually UV resistant and simple baluns.
Con coax: see pro 'balanced line'
Balanced feed-lines: For high efficient 'random impedance', usually non-resonant antenna systems. Although SWR will still be high, very-low line loss will not 'amplify' cable loss to un-acceptable values.
Pro balanced feed-lines: low loss, simple home-made construction.
Con balanced lines: see pro-coax and also high voltages at feed-line, balun and tuner, already at relatively low power.
In general when designing multi-band, complexity of the antenna system (more tuned antenna's, constructing traps) is to be traded against complexity of the feed system (handling balanced wires) and tuners (symmetrical tuners, complicated balun)
Whatever your design, it is always important to calculated the entire antenna system at all operational frequencies to selected adequate components in order to avoid unpleasant surprises like loss of power (bad report) , flash-over (tuner, transmission-line) or burned components (balun).
Bob J. van Donselaar