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pre-loaded antenna matching (published in Electron #8, #10, 2007) Introduction Resistors in and around antenna systems
usually also provoke resistance around radio-hams as HF-power is a limited
'asset' and if not, restricted by the government. Nevertheless various
antenna systems have been in operation for quite some time that involve
resistors, as in a Beverage antenna (ca 500 Ohm), Rhombic antenna (ca 800
Ohm) and Terminated Folded Loop
antenna (T2FD, 400 - 700 Ohm). Even so most radio-hams are still very
suspicious about antenna resistance and losses around this area. In this
article we will demonstrate that a little loss may be worth considering
especially since this could make radio-life very comfortable. For radio-communication we usually depend on
antenna systems at 'some' position up in the air, fed through 'some'
transmission line by a transmitter somewhere away from the antenna. Broadcast
stations usually transmit on a single frequency, so the antenna and feed
lines will be optimized for this one frequency, showing optimal radiation
characteristics and low loss feed lines. A radio ham likes to operate on many
frequencies and different radio bands, usually without enough 'real estate'
or financial resources for optimized antenna systems on all of these
frequencies. The antenna system therefore is usually a compromise between a
number of antenna and feeding parameters. Let's look at such an antenna
system that often is used on more than one frequency, but is optimized at one
frequency only, in the characteristics of figure 1.
The blue graph is showing the real part of the
impedance of this antenna over frequency while the green graph shows total
impedance, i.e. the vector sum of real and imaginary part of a dipool antenna
of 20 + From the impedance graphs it is clear this
antenna to be designed to operate on 3,6 MHz. as only within the first
rectangle both blue and green line are low. More low positions (but not as
low) may be seen at 11,1 MHz., 18,7
MHz., and 26,1 MHz, unfortunately outside the amateur frequency bands. On all
other frequencies the antenna impedance is (much) higher and always above the
lower red line, representing SWR = 2 as a limiting condition for connecting
this antenna directly to a modern transceiver. This is a pity, as the pink line,
representing antenna gain, is showing a nice 6 dBi at the Connecting the
antenna This nice antenna gain unfortunately is
'consumed' to a large extend by the coaxial feed line when connecting the
high impedance antenna with a high standing wave ratio to the transceiver. To
illustrate this situation the purple line represents the situation when A tuner at the transceiver side will
'translate' the variable and unmatched complex impedances at this side of
the feed line to the 50 Ohm
requirement of the transceiver, but it will not compensate for lost energy. Do not think to get around the feed-line
problem by applying open feeder line. Indeed feed-line loss will be low once
you have learned how to deal with open-line peculiarities around metal roof
trimmings, leading this line to and into the shack. Now you will find high
SWR at the lowest and highest antenna impedances when connecting to
the antenna, compared to using coaxial cable. The antenna tuner now should be
of a more complicated symmetrical design with high(er)
quality components that will be more (voltage) stressed. Also the tuning coil
in the tuner will be of higher inductance, leading to higher loss when not
constructed to the highest standards (very high Q). A practical conclusion may be that 'wild'
antenna impedances should be 'tamed' directly at the antenna to avoid
excessive cable loss. This idea has been worked out further by various
companies that offer remote and automatic antenna tuning units, e.g. Alinco (EDX 2), ICOM (IC AH 2,3,4) en SGC
(SG 211, SG237) . These systems connect directly to the antenna and
handle a large range of impedances, though not necessarily the entire range.
Prices are ranging from € 350,- to over € 1000,-. At this stage one might conclude that the
above antenna may look good, but is either impractical to apply or at too
high an (financial) offer. Alternatives to multiband operation may than be
found in applying a number of mono band dipoles, all cut for a specific
frequency and all connecting to the same balun (lowest impedance carrying
highest current, performing most of the radiation) as a workable way out. As a different solution also specific
multi-band antenna's may be considered, like a Duo-band antenna or Multiband trap
antenna, a G5RV or one of the
'Windom' antenna types by Fritzel (FD3, FD4 etc). All of these examples have been designed to
offer a low enough impedance to connect to the transceiver through standard
coaxial cable, usually requiring a simple and a-symmetric tuner. In this article we will discuss yet an other
way out of the wide impedance range enigma, that will offer other practical
benefits. Antenna transformer If we still would like to employ the 2 x Looking at the impedance 'landscape' of
figure 1, it could be a good idea to bring impedance values of up to about
1000 Ohm within reach of the transceiver. This may be accomplished by
starting from a 1 : 3 voltage transformer,
1 :
The (auto-) transformer in figure 2 exhibits
a windings ratio of n1 : nt,
in our first example 1 : Couple factor should be as close to k = 1, as
possible and stay that way over as wide a frequency range as possible, by
ensuring all windings to see exactly the same flux field. This may be
accomplished by not putting all windings next to each other but spreading
each 'winding' over the entire toroide core circumference, putting the next
winding in between the first and the last winding in between again. Easiest
way to do this is to just keep on winding, like a screw within a screw. The transformer is part of the signal path
but should be invisible herein to not absorb any power. It is easy to
demonstrate this is already pretty much the situation when transformer
impedance is at least four times as high as system impedance; for reference
see 'Ferrite
for HF applications'. To ensure this factor is preserved over the
entire frequency range of interest we best select a ferrite type with a
ferri-magnetic resonance frequency above the highest operating frequency, but
not too high since an inverted relation exists between this ferri-magnetic
resonance and permeability: the higher the resonance frequency, the lower
permeability. Lower permeability means more turns for adequate impedance and
this in turn means high parasitic capacitance, lowering the maximum usable
frequency. Considering this, it comes at no surprise best choice for HF
frequencies is 4C65 ferrite (Ferroxcube, type '61' by MicoMetals)
with a ferri-magnetic resonance frequency at 45
MHz. and permeability μi = When operating in a 50 Ohms environment at
position n1 of the transformer, impedance at this side should
be: 4 x 50 Ohm = 200 Ohm. At a
lowest operating frequency of 2 MHz., the transformers is easily calculated: Zl = ώ . L = 200 = 2 . p . 2 . 106 . L, from
which: L = 16 μH.; and further, L = 16 . 10-6 = n12
. Al = n12 . 170 . 10-9.
from which: n1 = 9,6 (= 10) turns. For the 1 : 3 transformer, nt will be 3 x 10 = 30 turns, of which n1
is the center part. Keep in mind this simple calculation for n1 to
always be valid, whatever the final transformer ratio. Let's look at the behavior of the antenna
system with this transformer from a SWR point of view in figure 3.
The transformer indeed translates the input
range 225 to 900 Ohm to a SWR < 2, giving access to more HF amateur bands
with this antenna ( Looking at antenna impedances, one should be
aware of the nature of this impedance. When regarding figure 1, we find a few
positions where the green and blue curve overlap, meaning the antenna
impedance to have a real value. This phenomenon may be seen around 3,6 MHz.,
7,0 MHz., 11,1 MHz., 14,8 MHz., 18,6 MHz., 22,1 MHz., 26,1 MHz. and 29,6 MHz.
In between curves for R and Z diverge, meaning the antenna impedance to be of
a complex nature. This situation should be kept in mind when we are
discussing Rb in the following
paragraphs. In figure 3, the green 'loading curve' is crossing
the SWR = 2 line at 900 Ohm. As we have seen in figure 1, this value of 900
Ohm is surpassed at some positions of the antenna impedance curve. To
safeguard the transceiver and to keep feed line loss low, these extreme
impedance excursions may be 'swamped' by pre-loading the transformer with a
resistor 'R' in such a way, that the most extreme antenna impedance (say 6000
Ohm; just above the maximum antenna impedance at 7 MHz. in figure 1) in
parallel to this resistor always ensures SWR < 2. Calculations are going
like this: Transforming Rb
to the primary side: Rb' = Rb / n2
Total input load resistance becomes: Rt = R // Rb'
, to rewrite as: R = Rt . Rb / (Rb
- Rt . n2)
formula 1 According to the definition: SWR = Rt / Z0 (or inverse since SWR >
1), we may write: R = Z0
. SWR . Rb / (Rb
- Z0 . SWR . n2)
formula 2 As an example, in a Z0 = 50 Ohm
system, preferred SWR = 2, maximum load resistance Rb
= 6000 Ohm (see figure 1): R = 50 . 2 . 6000 / (6000 - 50 . 2. 9) = 118
Ohm The picture of figure 2 now becomes figure 3:
Load resistor 'R' will dissipate part of the
transmitter power and more so when 'Rb'
is approaching high values. This sounds like wasting energy but should be
compared to the energy that otherwise would have been dissipated in an
un-matched feed line plus tuner, usually without even noticing. It may be
instructive to find out just how much energy will be wasted by calculating
total transferred power to the load. PRb' / PRt
= ή = V2 / Rb' / V2
/ Rt = Rt
/ Rb' We already found: Rt
= R // Rb' en Rb'
= Rb / n2, so we may write: ή
= 1 / (1 + Rb
/ (R . n2))
formula 3 Let's see what is happening to this 'transfer
efficiency' at various load conditions, while plotting the outcome in a
relative way (dB), like in figure 4.
Compared to figure 3 things have really
changed. The green SWR curve is now below the SWR = 2 line, all the way up
tot the maximum antenna load. Although also the lower load value below SWR =
2 has shifted somewhat (285 Ohm) we now have an intrinsically 'safe' system
for any high load value. The impedance range ratio, which was 1 : Everything comes at a price and in this
situation the penalty is 6 dB of transfer loss ( 1 S-point) at 3165 Ohm and a
bit more (8 dB) at the extreme antenna load of 6000 Ohm. The impedance range below 285 Ohm is still
troublesome as this will bring SWR > 2. This situation is acute for this
particular antenna at frequencies below 4,1 MHz. and between 10,8 and 11,5
MHz, 18,2 and 19,1 MHz and between 25,6 and 26,6 MHz. Staying away from these
frequencies should not be too difficult since none of these are inside
radio-amateur band except for the first value. When we also would like to bring frequencies
below 4,1 MHz. into reach (at 3,6 MHz. the original design frequency for this
antenna!), we may repeat the resistor 'trick' by placing a series resistor in
the transformer output of such value that also at the lowest antenna
impedance (of this particular antenna!): SWR < 2. Calculus is simple
again: SWR = Z0 / Rt,
or Rt = Z0 / SWR (now 'reversed' since we are operating on
the 'other side' of SWR = 1) The value for Rt
may again be found from formula 1, so Z0 / SWR = R . Rb
/ (n2 . R + Rb), and this is
reworked into: Rb = Z0 . n2 . R / (SWR . R - Z0) formula
4 As an example we again set: SWR = 2, system
impedance: Z0 = 50 Ohm, transformer is: n = 3 and the value we
found for protection against the highest loading values: R = 118 Ohm, we
find: Rbmin = 50 . 9 . 118 / (2 . 118 - 50) =
285 Ohm. In figure 1 we found lowest relevant antenna
impedance: Zant.min = 50 Ohm. For full
'protection' we now need a series resistor: Rs = Rbmin - Zant.min
= 285 - 50 = 235 Ohm
formula 5 to safeguard our transceiver while keeping
feed line loss low at the same time since SWR < 2 over the entire
impedance range for this particular antenna. Figure 3 will now be changed
into figure 6.
Again we have to forget a 'free lunch', so
figure 4 has been recalculated to show all relevant changes in figure 7.
Figure 7 shows that now we pay the penalty of
additional loss at the low impedance side. When comparing the light blue
curve with the blue graph it shows that at the lowest antenna impedance,
around 8 dB of power (1,3 S-point at the receiving side) is lost to the
series resistor. On the positive side we created an intrinsically 'safe'
antenna matching that will never allow SWR to rise above 2 over the entire
HF-radio band while at the same time will free the operator from retuning the
antenna going from one frequency (band) to the next, which may be good news
to contesters and wide-band system operators (ALE equipment). Up to this moment we have been designing
around an antenna transformer with a 1 : 3 winding / voltage ratio. To
complete the picture, I have calculated other transformers in the range n = 1
to n = 5 to look for better parameters. All transformers have been pre-loaded
such that SWR < 2 at all impedance conditions of the original 2 x
Figure 7 is showing various transformers with
associated loading resistors to fulfill SWR < 2 for all loading conditions
of our 'standard dipole'. Let's look at the extremes first. - The n = 1 graph denominations actually mean
that no transformer has been used but the antenna has been pre-loaded with a
resistor of 102 Ohm. At the extreme high end, SWR is nicely approaching 1 : 2
but at the extreme low impedance end (50 Ohm), SWR is only 1,5. So a single
load resistor of 102 Ohm makes the widest SWR curve! Transfer efficiency is
also highest at 50 Ohm antenna load as compared to all other transformers
below 300 Ohm loading impedance. This nevertheless is not a preferred
situation which may be appreciated when looking at upward 300 Ohm; transfer
is now lower than any other variation, reaching an 'all time low' at the
highest load (6000 Ohm) with a loss of 18 dB (3 S-points). - The highest transformer ratio is 1 : 5 is
showing lowest loss at the high load side with only 4,5 dB at the extreme.
This is what we like to see, but we are sorry to find a 12 dB loss ( 2
S-points) when loaded with 50 Ohm at the
As usual the 'truth' is in between and our
original 1 : 3 transformer is showing a nicely symmetric behavior at both
extreme load conditions with acceptable transfer in between. Practical transformer considerations After our exploration of the design space lets
look at some practical implications. For this I have made several
transformers and have tested under various load conditions. Transformer winding As stated earlier, it is important that all
windings 'see' the same field. Putting all windings next to each other
results in a lower coupling, with flux leakage as a consequence and a
diminished high frequency behavior. Using 4C65 ferrite (or 61 type) in a Some attention has to be paid to the load
resistor. In our design we constantly put this resistor at the transformer
input, but this appears not to be the most efficient position. Best results
have been obtained when 'symmetrically' loading the transformer by having
each winding 'damped' with the same load. In case of the 1 : 3 transformer
this means the load resistor R will be subdivided into three resistors of
equal value but 3x the original value. This subdivision will be different with other transformer
ratios. At low frequencies no difference could be measured at different
loading schemes but at higher frequencies (20 MHz. and above) this better
loading condition was showing up as extended good SWR behavior and power
transfer, up to double the original frequency range. Also keep in mind that power not radiated
from the antenna, is lost in the loading resistors. From figure 7 it may be
appreciated that at the loading edges, around -8 dB of power will be
radiated, which is around 16 % of the input. The rest (84 %) will be
dissipated in the (distributed) load resistor, meaning that the combined
power rating should roughly equal the total power output of the transceiver.
This is especially true for FM mode of operation and to a lesser extent for
SSB and CW. In the latter situation average power is less than half peak
power with relaxed power requirements for these loading resistors. As a
guideline and in case n = 3 and three distributed resistors, each should be
capable of handling about 1/6 total input power. Series resistor With a series resistor in the output circuit,
the above calculations for the power rating of R still are valid since at the
highest antenna impedance hardly any current will flow in the output circuit,
so neither in the output series resistor. At very low antenna impedance
output currents are much higher. At n = 3, R = 118 Ohm, Rb
= 50 Ohm, and Rs = 235 Ohm, total input
resistance now is 25 Ohm of which the transformed value of Rb plus Rs
is 31,7 Ohm. Of total input current, this series connection takes 25 / 31,7 =
79 %, of which Rs takes 235 / 285 = 82
%. In this extreme situation the series resistor Rs
will also take 82 % of 79 % = 65 % of total input power meaning this resistor
should have a power rating of over half total system power in FM mode or just
over one quarter in case of CW or SSB. Furthermore, both the load resistors
and series resistor should be of and induction-free or carbon-composite type
for HF use. A mounting flange for
connecting to a solid metal surface (transformer box) is advisable to conduct
heat away. Transformer rating The step-up transformer may also absorb some
power so let's take a closer look here. In other articles more information on
ferrite loss mechanisms is available and may be checked here. For this material and
core size (4C65 and In our calculations for total transformer
impedance we found 10 turns to be the number in a 50 Ohms environment, which
brings us to: Vmax = Vwdg
x Wind = 24 x 10 = 240 Volt, and this leads to Pmax = Vmax2 / Z0
= 2402 / 50 = 1152 Watt, or more than 1 kW. in a 50 Ohm system. The
transformer therefore will not easily be a limiting factor for pre-loaded
antenna matching. Measuring the transformer At the input of the transformer one side is
grounded as may be seen in figure 3. When measuring transformer
characteristics, one would like to see one of the output leads to be grounded
too, but this should short circuit (part of) the transformer. A way around
this problem is to make two such devices and measure performance in a
back-to-back situation, dividing results over both half's. An alternative
method is to decouple the input from ground by connecting the input to the
generator by means of a choke. The latter is easily constructed by winding
the connecting coax around a ferrite core again, preferably a higher
permeability type to raise series impedance. When applying a A good many different transformer types have
been made in various transformer ratio's. A few of these may be seen in
figure 8.
Some construction details: - left hand transformer has been constructed
on a - middle transformer has been constructed on
a - right hand transformer has been constructed
on a Best performance and widest bandwidth is with
4C65 ferrite. For measurement set up and connection
details, please see above. As an example a transformer measurement is
shown in figure 9 of the n = 3 type, analogue to the left hand transformer in
figure 8. Loading resistors are 330 Ohm, 390 Ohm, 330 Ohm to arrive closest
to 118 Ohm from above calculations. No series resistor has been applied in
this measurement.
Figure 9 is showing transformer is well
behaved over frequency with antenna loading up to the highest value of 5600
Ohm. Bandwidth is very good starting from the calculated lower cut-off
frequency of 2 MHz. to well over 30 MHz., in fact to over 60MHz. when not too extremely loaded. Even
an unloaded transformer will end up around SWR = 2 as may be predicted from
above measurements. Power transfer is equally satisfactory with
less than 0,5 dB difference from theory at 1 MHz. up to well over 30 MHz.,
making this component a good candidate to replace the more common tuning
unit. For this latter test the transformer has been loaded with 600 Ohm, a
value from the middle of the range. Relative behavior using a real antenna The pre-loaded matching unit is to bring down
the large impedance excursions of our typical dipole as in figure 1. For a fair
comparison, we modeled the component (n = 3, including R 118 Ohm and Rs 236 Ohm) in parallel to the real behavior
of the dipole antenna as in figure 1 (real and imaginary values) on all HF
frequencies. This situation does not require the usual antenna tuner, since
SWR < 2. To obtain a fair comparison, the same antenna
has also been modeled while connected to a 1 : 1 balun and
In figure 10 some interesting features may be
observed. - SWR in the situation of balun plus
feed-line plus tuner has been omitted as this is supposed to yield a SWR = 1
situation when the tuner has sufficient range. - SWR of the pre-loaded matcher is showing
the predicted behavior and will stay safely beneath SWR = 2 over the entire
HF frequency range with this antenna. - Total power transfer has now been
calculated as perceived by a receiving station (S-points), with the '0' mark
meaning a perfect power transfer. - The green transfer curve is showing the
'usual' situation with a (lossless) balun to the antenna, - The blue power transfer curve of the
pre-loaded matching transformer is beating the unmatched cable on nearly all
amateur bands except for Mind that the above curves are generated
using a more or less randomly selected antenna system and a pre-loaded
transformer to match antenna behavior over a very wide impedance and
frequency range. Other antenna types over a different frequency range may
yield different results, that may be better or worse. As it happens, the idea of a pre-loaded
matching transformer is not particularly new. In the last quarter of the last
century Maxxcom has put a 'Maxxcom
automatic antenna matcher' on the market which may be connected to 'almost
any' antenna while keeping the transceiver safe at SWR < 1,5, even when
completely shorted or with no antenna connected at all. The behavior over
frequency is very good and may be compared to graphs we already have seen
from comparable transformers in this article. This very safe behavior comes at a price. The
Maxxcom actually is also a pre-loaded matching
transformer, this time designed as n = 2, R = 40 Ohm and Rs
= 800 Ohm. This configuration is eating power away when connected to our
'standard dipole'; At 3,6 MHz power transfer will be - 20 dB (almost 3
S-point) below maximum rising to an optimal transfer of - 13 dB (more than 2
S-point) below maximum when loading into 1000 Ohm. Although not very efficient, this may still
be the component of choice when laymen are left alone with valuable equipment
that may not easily be replaced due to adverse terrain conditions. I found ICOM as a second manufacturer of
pre-loaded matching transformers on the internet. Looking at the specs this
may well be our n = 3 model with resistors to match, as insertion loss is
specified at 6 dB with SWR < 2. Prices for Maxxcom
and ICOM units are around € 300,- Lets look at how to apply the pre-loaded
matching transformer with the tools from this article. A good approach may be to first select a
range of frequencies, communication modes and required communication
distances. From this starting position an effective antenna may be designed
using Eznec or Mmana
as a free and efficient design tool. When starting conditions are satisfied,
next step could be to calculate antenna behavior (impedance) over all
application frequencies, arriving at a comparable graph as in figure 1. Next
step is to determine a transformer ratio, to best bring impedance excursions
within range of the transceiver specifications. As a last step R and Rs may be calculated applying the tools in
this article. When being less 'greedy' than myself in desiring to cover a
very wide frequency range, the final pre-loaded matching transformer may be
even more efficient than the one presented above, while protecting your
receiver from overload conditions on any frequency setting and not having to
tune your antenna ever again. Bob J. van Donselaar, on9cvd@veron.nl |
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