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End-fed antenna systems (Publiced in
CQ-CSO, # 1/2, 2007) Introduction End-fed antenna systems have been known and
in use from the beginning of the 20th century radio-era. An early
manifestation is be the famous Zepp antenna, that
has been named after its convenient application as a towing antenna in
balloons and airships (Zeppelin). In these conditions only one antenna
connection is sufficient for operation with no requirements for a 'counter
poise' or ground connection. Furthermore, the terminating impedance was very
convenient for connecting the antenna to transmitters of those days with
vacuum tubes in the 'final'. In our time the concept is still very much
appreciated at VHF and UHF frequencies, where dimensions are small enough to
permit antenna size of 3/4 wavelength (J-pole) and more. The Zepp-, J-pole and G5RV-antenna are part of a family of antenna systems, where the name is applied to the combination of antenna plus feed-line. This feed-line has a fixed length to ensure a smooth transition from a high antenna impedance to a conveniently low value, as required by a contemporary transceiver. The end-fed antenna system therefore usually consists of two or three parts as in figure 1.
Only the first part of the antenna will radiate and usually is half a wavelength long. The half-wavelength is no absolute requirement, but the antenna should be end-fed and show a high impedance value at its operating frequency, so also other 'half-wavelength multiple' designs will do. The radiating part defines all antenna
characteristics and is easily modeled in an antenna design program. Depending
on the required antenna polarization, the radiator will be horizontally or
vertically positioned; the rest of the antenna system should not radiate and
will therefore not contribute to the antenna transmitting or receiving
properties. The second part of the antenna system is the
transmission-line transformer, to translate the high impedance at the antenna
end into a low impedance for connecting to the
transceiver. For this purpose, the length of this line should be somewhat
shorter than half a wavelength and exhibit a characteristic
impedance that is lower than the antenna termination impedance and higher
than the required impedance at the transmitter side. If the latter condition
is satisfied, the 'transformer' is flexible enough to allow a number of
transformer ratio's, although a real impedance at
the antenna input will always be translated into a complex impedance at the
transceiver output of the line. With a careful design however, it is possible
to arrive at SWR between 1,5 and 2,5 and this may be
further brought down to SWR = 1 at the expense of an additional antenna
tuner. Using this antenna tuner, the antenna systems
may be easily applied on more than one (amateur-) frequency, provided these
are harmonically related to satisfy the conditions of high antenna
termination impedance and un-even relation of one-quarter wavelength for the
transformer section. If these conditions are satisfied, one finds a low
enough real and imaginary part at the output of the transformer section to
allow the antenna tuner to perform final matching. With such an antenna system one may operate
at more than one frequency (band), although a really low 'output impedance' will
only be found at the fundamental design frequency. On all other frequency
bands, one has to consider some losses in the connection (line) between the
transceiver and the antenna system (usually 50 Ohm coax), due to high(er) SWR. The transformer section in the antenna system
itself will only show minor loss due to the parallel-line structure and the
relatively short line length (around 1/4 wavelength).
A third characteristic part of this design is
the terminating stub-line, usually of the same characteristic impedance as
the transformer section. This stub-line is very much shorter than 1/4 wavelength
and will therefore be equivalent to an inductive impedance. At careful design
this inductive reactance will compensate nicely for the capacitive reactive
impedance, we found at the end of the transformer section. In this way we
have obtained a perfect transformer to translate any high (and real) antenna
impedance into a low (and real again) impedance of our requirement (e.g. 50
Ohm). Such a stub is a characteristic part of the
J-pole antenna. For practical antenna design, de length of
the transforming line plus the compensating stub comes close to a quarter wavelength. Therefore this entire length is sometimes
called a 'quarter-wavelength transformer', although we have now seen that
this section actually consists of two parts with a different action each. We
will later see that the total length will only in a limiting situation be
exactly one quarter wavelength long. One should also bear in mind this
quarter-wavelength transformer only applies to 'one' operating frequency;
without the stub the antenna could be applied to more frequency (bands). With
the stub the antenna system may only be used at one frequency, but may be
matched to many desirable (and real!) impedances to
directly match other system parts (transmission line, transceiver).
The formula for the impedance we may find at
the end of a transmission line, that is terminated into a real, but high
impedance at the other end is not very easy to handle, but is much
'friendlier' if we consider this line to be lossless. This simplification is allowed because
this section of transmission line is usually short and of an open, symmetric
structure, again a low-loss indicator. The transformation formula is: Zi = R0 (Za
+ j R0 tan φ) / (R0 + j Za
tan φ) where: R0 = characteristic impedance of
the transmission line Za = terminating impedance (in this
case our half-wavelength antenna) φ
= electric length of the transmission line (in degree; 360 degree is a
full wavelength) This formula will yield a complex impedance
for any length: φ, so we better immediately expand Zi
into a circuit of a real part, Rp and an
imaginary part, Xp as in: Rp = R0 ((Za/R0)2
+ (tanφ)2) / (Za/R0
+ (Za/R0) (tanφ)2) and
Xp = -j Ro (((Za/R0)2
+ (tanφ)2) / ((Za/R0)2
tanφ - tanφ) The imaginary part has a minus sign and
therefore behaves as a capacitor. We therefore are allowed to compensate with
a short part of shortened transmission line, which will behave as an
inductor. The length of this line may be easily found in the original formula
for Zi, when setting the terminating
part (Za) at zero (shortened line), as
in: Zi = j R0
tan φ2 = Xk,
with φ2 the electrical
length of the short (and shortened) transmission line. Calculating the transformer section in this
way has now changed into a number of simple steps: - we first calculate
the (electrical) line length: φ, to translate the (high, antenna)
impedance: Za, into the required value
of Rp, usually 50 Ohm. - using: φ, we calculate the capacitive
input value: Xp - using: Xp,
we find the compensating stub: Xk, as
having an equal value but opposite sign from: Xp,
to find φ2, the electrical length of the stub. To
make matters simple, I
calculated figure 2 to directly show relevant numbers without further
calculations. This graph has been made for a desired value of Rp = 50 Ohm. The lightly colored lines
(bottom) represent the (electrical) length, φ, of the transmission line to
translate the high antenna impedance (x -axis) into 50 Ohm. The dark lines
represent the total length of the transformer section including the
compensating stub. The difference between the dark lines and lightly colored
lines is the (electrical) length of the compensating stub. The number tags
represent the characteristic impedance of the transmission line as desired.
In figure 2 we find Za
approaching 90 degree (1/4 lambda) only at the highest values of the load
resistance. This means the so-called 1/4 lambda transformer usually is
somewhat larger than a quarter of a wavelength! Also the higher impedance transmission-lines
take-off more to the right of the graph as the formula in these situations only
starts generating solutions at high load resistances (Za
> 8 kOhm).
This should be kept in mind when selecting the type of transmission line for
this application. The antenna load resistance is an important parameter
of the application, so we better look a bit more carefully into this. Regarding an antenna with a length of exactly
one half wavelength, we find that at each end the
antenna current goes to zero and the voltage to a maximum value. In a first
approximation this means antenna impedance to go to 'infinity' at these
points and that is useful when matching to a shortened piece of transmission
line of exactly 1/4 wavelength long. The short will be 'translated into
infinity' at the other end of the line, nicely matching the 'infinite'
impedance part of the antenna. The ARRL Antenna Handbook is supplying information
on the type of impedances one could expect at the end of a half-wavelength
antenna. Theoretical values are supposed to be in the vicinity of 5000 - 8000
Ohm, depending on other physical antenna parameters and the number of
half-wavelength' that fit the total length. Further on the book informs us
that more realistic values from experiments have been found to be in the area
of 1000 - 5000 Ohm. Modeling half-wave antenna's in EZNEC around
3,6 MHz. will show the 'infinite impedance' values to be around 2500 Ohm and
my own measurements on such antenna's have yielded values between 2700 and
3400 Ohm. A simple method for such measurements consists of setting up a
parallel L-C circuit to resonate at the frequency of interest and measuring
Q-value by means of a delta C method, after which the circuit's equivalent
parallel resistance may be calculated. Thereafter the resonating
half-wavelength antenna is connected (resonating C-value should not have
changed at an electrical antenna length of exactly 1/4 wavelength). Measuring
Q-value again yields the antenna impedance in parallel to the original
equivalent parallel resistance and from these the antenna impedance may be
calculated. Concluding one may deduce that the impedance
value of a half-wave antenna will be between 1000 and 5000 Ohm with a likely
value around 3000 Ohm. This will reflect on the characteristic impedance of
the transmission-line of choice for the transformer line. Let's look at the
formula for Zi again, with φ = 90,
so a transmission line of exactly 1/4 wavelength. The formula resolves into
the simple form: Zi = R02 / Za
, often more familiar as: R0 = √(Za
. Zi) When we desire the output of the transformer
to be at 50 Ohm, and the maximum antenna impedance we have found to be below
5000 Ohm, we calculate: R0 max = √(5000
. 50) = 500 Ohm, or more likely (3500 Ohm): R0 max = √(3500.50)
= 420 Ohm. Again looking at figure 2, we now find that
only the first 30 % at the left side is really interesting. We further notice
that for this type of transformation the transmission line should have a lower characteristic impedance than 450 Ohm, limiting
the selection further when transforming into 50 Ohm at the line output. Background for my interest in this type of
antenna was found in combining radio with kiting, one of my earlier hobbies.
Some big lifter kites were still hanging around and appeared to be promising
as a means for erecting an end-fed antenna for the lower HF-bands. Other
experiments in this area have been reported using three kites to pull-up a
full-size To keep things light and 'transportable' the
antenna was to consist of one half part of twin hook-up wire. For the
transmission line a piece of 300 Ohm TV line was selected since this is of
light weight again and the characteristic impedance will not easily change
during transport or movements in the air by the wind or the kite. The right antenna length for this 3,65 MHz., half-wave antenna was determined connecting the
antenna to a high-output impedance HF generator (low output impedance
generator in series with a very small capacitor) and looking for maximum
voltage. The line should be free of all obstacles as this is a high-impedance
measurement. It appeared that the velocity factor for this (pvc-encapsulated) piece of hook-up wire was 0,88, which is quite a bit lower than expected. The antenna
impedance was measured using the earlier discussed method. With the
characteristic impedance of the transmission line already selected together
with the desired output impedance of 50 Ohm, the rest of the system may now
be calculated. Let's look at the graph at the light blue
colored line for 300 Ohm transmission line. At an antenna impedance of Za ~ 3,5 kOhm,
one finds an electrical length of φ
= 85 degrees. The real line length may now be calculated as: l = (φ / 360) x (c / f) x vf, where: φ = electrical length of the
transmission line f = frequency in use (in this example 3,6 MHz.) c = speed of light vf = transmission line velocity factor (for TV
twin lead: 0,84 by the manufacturer or self measurement) For the kite antenna at 3,65 MHz. this leads
to: l = (85 / 360) x (3 .
108 / 3,65 . 106) x 0,84 = In figure 2 we next find total transmission
line length (dark-blue line, 300 Ohm) at a load of Za
~ 3,5 kOhm to be 94
degrees. The piece of shortened transmission line now becomes: 94 - 85 = 9
degrees. This leads to a physical length of In an analogue way the half-wave antenna wire
(vf = 0,88) will become: l = (180 / 360) x (3 .
108 / 3,65 . 106) x 0,88 =
With the antenna connected directly to the
kite and the total length of antenna plus transmission line to be free of the
ground, the minimal flying height of the kite should be 16,3 + 1,73 +
The experiment At the end of this story we may find a few
photographs of the experiments to verify calculations. Since the total weight
of antenna plus feeder will 'put some weight in the scales', the kite should
not be too small. Luckily a 'heavy lifter' was available in a parallel hobby
to do the job, so we only had to wait for the selected range of wind speeds
to perform the experiments.
Concluding Mind that this kiting antenna has been tuned
by means of the stub line to operate on the desired frequency of 3,65 MHz. and so will function perfectly at and somewhat
around this frequency. For wide-band usage on more (un-even harmonically
related frequency bands, one should omit the stub line and connect directly
to an antenna tuner. This makes no difference to the above calculations. Bob J. van Donselaar
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