Understanding the Gieskieng (Lab Notes)
Introduction
Last month (antenneX January 2002 online issue #57) I described an unusual antenna called a Gieskieng antenna, which is purported to be an average of 2 dB better than a dipole at long ranges. This month I will describe my understanding of how the antenna works. I was surprised to find that it can be easily tuned to a low frequency -7.7 MHz for a 7.32-meter long antenna. It is easily made out of a piece of twin lead with one end shorted and the other end left open. Connection to the cable is roughly 0.18 wavelength from one end — it is symmetrical in that it seems to work equally well when the connection point is offset from either the open or the short! The amount of offset determines how much inductance or capacitance is needed between one side of the twin lead and the drive cable center conductor to tune it to resonance.
Tools for the Trade
Much of the explanation involves a Smith Chart. I will discuss the usage verbally without going into much theory of the Smith Chart. The Gieskieng antenna can be thought of in several ways: It is a quarter-wave resonator tapped part way up its length at a 50-ohm point like the J pole bottom half, except it is not necessarily a quarter wave. Or, it is an exercise in combining the admittances of a shorted and open transmission line connected in parallel, then converted into impedance that is wired in series with an L or C reactance and tuned to resonance. I prefer the last description, which follows below. I finish with a custom-made Microsoft Excel spreadsheet calculator that computes all the values for any size antenna at any frequency.

The initial point in figuring out how this antenna worked was a result of the open wire version made last month. It didn’t work at the “design frequency” but matched very well at the third harmonic of the design frequency (Table 1). Where it was matched, the distance from the open end to the drive connection was 0.614 wavelength, and on to the shorted end was another 0.178 wavelength. I had a scrap length of twin lead 7.3 meters long. The length 0.614 wavelength is equivalent to 0.114 wavelength past a half wave and the Smith Chart repeats itself every half wave. Therefore, a connection point was made by stripping the insulation on the wires at the location:
0.114/(0.114+0.178) * 7.3 =2.85m,
….or 2.85 meters from the open end and 4.5 maters from the shorted end. Table 2 shows that the result has a fair match (swr == 2.6) at 7.7 MHz.

Another connection point was made at the other end of the antenna: 2.77 meters from the short and 4.55 meters from the open end. It tuned to 8 MHz with a SWR of 2.8. Table 3 shows the tuning. It is clear that both antennas are behaving the same with the slight difference in tap points causing a slight difference in resonant frequency.

Both of these antenna connections were measured with the MFJ-249 Analyzer through a 1.8 meter piece of RG-58 with ferrite chokes behind the connectors. The measured values have to be transformed towards the antenna by 1.8/0.66 ==2.77 meters, the electrical length of the cable. This is easily done on the Smith Chart using a ruler and a pair of sharp pointed dividers: after plotting the Real and Imaginary measured impedance at some frequency on the Smith Chart, a radial line from the center is located by putting one divider point at the center and the other on the test result, and laying the ruler alongside the divider points. The ruler intersects a value along the circumference that is the phase angle of that data point in wavelengths, say: 0.352 wavelengths.
The 1.8-meter cable is 0.064 wavelengths long at 7 MHz, so the antenna is at (0.352 – 0.064 == 0.288) wavelengths. The ruler is then laid from the center of the chart to 0.288 wavelengths, and the divider put from the center to the new impedance value on the chart and along the ruler. A circle at the radius of a data point on the Smith Chart goes through every possible impedance that can be found along a cable with a standing wave that includes the data point. The new point on the circle is at the antenna terminals. In tables 2 and 3, the “data angle” column corresponds to the 0.352 number in the example. The cable delay in wavelengths is shown at each frequency and the angle corresponding to the antenna position is the “net” column. The new impedance is shown.
This exercise reveals a problem with the MFJ Analyzer: it measures the size of the real and imaginary components of the impedance, but not the sign! One has to continually stay oriented to the position on the antenna relative to a known point, such as the shorted end. Since travel along the antenna and cable toward the generator (the MFJ analyzer) moves clockwise around the chart, and the first half of the chart starting at the short is capacitive reactance and inductive admittance, the sign of the imaginary term is usually evident. One has to watch out when a series of data points crosses from one half of the chart into the other half and put the minus sign in when appropriate.
Table 4 shows the third harmonic tuning of the twin lead antenna. By this time I had observed the capacitive nature of the antenna at these frequencies and inserted a small inductance (4.25 turns 1 inch in diameter) between the antenna and the center conductor of the cable. The difference made by the coil is clear — it can be tuned to a perfect match at 26.379 MHz with this small coil. Without the coil, the resonance is not very obvious at near 26.7 MHz. The Rn and Xn columns are the normalized values of the impedance, which are the measured values in ohms divided by the 50-ohm impedance of the cable. The Smith Chart is laid out in terms of normalized impedance and admittance.

Tables 5 and 6 show the antenna tuning around 13 MHz with and without the tuning coil. Table 7 summarizes the data transformed back to the antenna. It is not obvious that it can be tuned to 13 MHz until the coil is installed and the analyzer frequency scanned over the band, although the red numbers in the Tables 6 and 7 hints at some kind of resonant phenomenon. The coil size affects both the frequency and size of the lowest SWR value — the numbers shown are at the best SWR.



By the time all this data had been processed, I was going cross-eyed poking at the Smith Chart with little pointy dividers. An easier way was needed to see how things changed as the various dimensions and frequencies were changed. Computers should do this and let people think—thus, a model was needed. I looked all over the Internet for a usable Smith Chart program and found some good sites but no good programs that could construct this antenna.
This antenna is best explained by the computing following steps:
- Compute the admittance seen at the input of a section of transmission line that is shorted at the far end
- Compute the admittance seen at the input of a section of transmission line that is open at the far end
- Add the admittances to get the admittance at the connection point of the antenna
- Convert the admittance found in 3 to the impedance at that point
- Compute the inductance or capacitance which would give a reactance to cancel that found in 4
- Connect the tuning reactance in 5 in series with the impedance of the connection point of 4
The reactive part of this calculation is given by the following formulas. The real, or lossy part that includes radiation resistance and ohmic losses is not known until an antenna is built and measured. But, if they are small, they will not affect the resonance due to the antenna structure very much. Therefore, only the reactive part of the impedance need be computed to shed some light on how the antenna works. The impedance of a lossless line terminated in a short or open circuit is well known and shown below. The formulas associated with the steps are:
1.
Admittance Y = 1/(impedance Z). Z = jZo*tan (2*pi*length/wavelength) Zo =characteristic Z of line
Y = -j/(Zo)*cotan(2*pi*length/wavelength) for a shorted line
2.
Z = -jZo*cotan(2*pi*length/wavelength) for an open line
Y=j/Zo*tan(2*pi*length/wavelength)
3.
Y total = (j/Zo*tan(2*pi*length/wavelength) -j/(Zo)*cotan(2*pi*length/wavelength))
The first term is capacitive—The second term is inductive. The combination is just like a parallel tuned circuit!! It exhibits a net reactance that changes with frequency and goes through zero at resonance.
4.
Y = (a + jb) becomes Z with:
1/Y = (1 + j0)/(a + jb) = (1*a+0*b)/(a^2 + b^2) + j(a*0 -1*b)/(a^2 + b^2)
if losses a = 0
1/Y =0 -j*(1/b)
5.
The impedance of an inductor is Z = jL *(2*pi*frequency)
The impedance of a capacitor is: Z = 1/j*(C*(2*pi*frequency) = -j*1/(C*(2*pi*frequency)
Making it Easier
An interactive spreadsheet calculator (Table 10) was constructed using Microsoft Excel (Ed: if you don’t have MS Excel installed, a free Excel viewer may be downloaded from the Microsoft website, although you won’t be able to run the calculator) to perform the steps described above. Table 8 shows an example of the results. The computation is done for five frequencies – two on each side of a “design frequency” of 13.15 MHz spaced by 100 KHz. The top section is two sided and computes the admittance for a shorted line (the olive part) and an open line (the rust colored part) and combines these admittances in the center of the top section (the blue part). These calculations start with the length of the line, which is magnified by dividing by the velocity of signals in the line. It computes the wavelength at each frequency and arrives at the fraction of a wavelength represented by each line. The admittance is then calculated and combined as shown in the jB column of each section. The user enters velocity, physical length, characteristic impedance of the line used in the antenna and frequency.

The combined admittance is then converted to impedance for each of the five frequencies in the next lower center section (purple part). A negative number here indicates the antenna looks like a capacitor; a positive number indicates an inductor.
In the bottom section on the left, the sheet calculates the reactance in ohms of the combined Z and computes an inductance value to cancel the capacitance Z of the antenna. The purple bar in the lower left group of numbers indicates the design frequency, 13.15 MHz. Column D, labeled Z in this group of numbers, takes the inductance that tunes at the design frequency and computes its impedance at the five frequencies.
In the bottom center section, the sum of the impedance from the inductor and the antenna is computed for each frequency. Note that there is residual impedance above and below the design frequency — capacitive below and inductive above the design frequency.
Table 9 shows the same data at 7.7 MHz, where the antenna is inductive and the tuning is done by a 17 pF capacitor. Again, Table 10 is the interactive spreadsheet calculator. All inputs required are shown in the yellow section in the lower right of the sheet.

The spreadsheet calculator automatically chooses a capacitor or inductor to tune with and rejects the wrong one by printing “false” in the appropriate places.
At this time I know of no way to enter the real part of these impedances. This antenna will act like any of the tuned circuit antennas such as an Isotron — the lowest SWR is at the point on the tuning curve that is nearest to 50 ohms, and not exactly at the resonance point computed above. The real antenna includes all losses, the model does not, and therefore not possible to exactly compute the SWR.
Contrary to what an engineer once told me (“my simulation is better than real life”) this model is intended to convey a simple means of tweaking the parameters to see how the antenna behaves and provide a starting point in an antenna construction. Based on what I have seen, it appears possible to make a multiband version by switching in various tuning reactance’s. The next month I will try to do that and see if it radiates—weather permitting! My antenna support tree has lost its top and four large branches to the storms and 50mph winds this past month! The tree is rapidly becoming my antenna pole!
Originally posted on the AntennaX Online Magazine by Joel C. Hungerford, KB1EGI
Last Updated : 4th January 2025