half-wave ant.



End-fed antenna systems

(Publiced in CQ-CSO, # 1/2, 2007)






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.



Figure 1: Antenna concept



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).  



A little background


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)



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.




Figure 2: Electrical length and load impedance for various types of transmission line, to arrive at 50 Ohm at the output of the line.



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.



Antenna load resistance 'Za'


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.



An example


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 80 m. dipole antenna, but my aim was to be somewhat less dependant on a small army of  'kiteers' for all lifting equipment. An end-fed antenna system than is system of choice as only a single kite will suffice.


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,


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 =  16,3 meter


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 1,73 meter in an identical manner to the above.


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 =  36,16 meter


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 + 36,16 meter = 54,19 meter; and this should not to be too difficult.



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.






The radio station (fore ground) and kite ready for launch. Compare the size of the kite to the (tall!) helper.


The kite line is almost invisible; the white line is part of the pvc-encapsulated, half-wave antenna wire.











The 'lifter' kite is launched, the antenna wire is hanging straight down.








The TV-type transmission line (upper part).

The stub-line is folded back onto the transmission line, being separated from this by means of pieces of foam rubber.  

The last (black) part is a piece of 50 Ohm, RG58 coaxial transmission line leading to the transceiver.





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