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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 = R02 Za (1 + (tanφ)2)
/ (R02 + (Za tanφ)2)
and Xp
= -j R0 (R02 – Za2 )tanφ) / (R02 + (Za
tanφ)2) The imaginary part has a minus sign and
therefore behaves as a capacitor. We are allowed to compensate with a short
piece 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 may be
performed in a small number of simple steps: - we first calculate the (electrical) line
length: φ, to change the (antenna) impedance: Za,
into the 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 lines represent the
(electrical) length, φ, of the
transmission line to translate the high antenna impedance (x -axis) into 50
Ohm. Next, calculate the length of the compensating stub to compensate for
the reactive part at the end of the transforming line. This compensating stub
line is shortened at the end and is the complement at the intersection of the
graph and the antenna impedance to the top of the figure (90 degrees), again
measured in electrical degrees, with 360 degrees equal to a full wavelength.
Mind the velocity factor of the line. .
In figure 2 we find the summation of the
transforming transmission line and the stub line is always equal to 90
degrees. Together these lines are forming the ¼ lambda
transformer 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 one of the
antenna simulation programs around 3,6 MHz. will
show the 'infinite impedance' values to be around 2500 to 3500 Ohm and my own
measurements on such antennas have found values between 2000 and 3500 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. When calculating antenna impedances with one of the
antenna simulation programs the following values are showing on various HF
amateur bands: f (MHz) impedance
1,85 3477
3,65 3211
7,10 2781
10,1 2895 14,125 2570 18,10 2582 21,225 2442 24,95 2485 28,5 2222 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 half at the left side is more 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 ~ 3,2 kOhm, one finds an electrical length of
φ = 47 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 = (47 / 360) x (3 . 108 / 3,65 .
106) x 0,84 = 9,01 meters In figure 2 , going from the interception of
the blue line and 3200 Ohm up to the top of the graph at 90 degrees, we again
find for the shortened stub line an electrical length of 43 degrees, leading
again to a length of 8,25meters. 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 9,01 + 8.25 + 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, on9cvd@veron.nl
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