Updating the Gieskieng Transmission Line - II
Last month I described the effect of using a loading capacitor to lower the resonant frequency of a quarter wave open-ended line section. The capacitor can be considered as a variation of the line’s open end. The line transforms its impedance into a short circuit at resonance. In a similar way of thinking, an inductor can be considered a variation of a short circuit. An inductor, too, can be used to lower the resonant frequency of a half wave section. The half wave section transforms the inductive reactance into a short circuit at resonance. Since the antenna analyzer cannot measure high impedance, only transformations into a short can be measured accurately using my MFJ analyzer. Placing a capacitor across the exact center of an inductively loaded half wave section uses both a quarter wave and a half wave effect at the same time. With the correct inductive input and a coupling link to the drive cable, the 8.94-meter length of twin-lead can be tuned from below 3.5 MHz to above 7.4 MHz.
I think of the situation this way: start with a half wave piece of twin-lead with the far end shorted and the near end connected to the analyzer. The short is a coil with an inductance of zero and a reactance of zero. Imagine the short twisted into a few turns of a coil. Now the half wave line is terminated with a small inductive reactance, which appears after being transformed by the line to be a small lengthening of the twin-lead.
The reactance has a value:
X = j*2*pi*F*L
where F is the new resonant frequency of the “lengthened” combination of twin-lead and inductance, and L is the inductance. If L is increased to a very large value, the reactance approaches infinity, or an open circuit. At this value, the cable part of the combination is transforming an open circuit into a short; it is a quarter wave transformer, and the resonant frequency is half the original, unloaded frequency. Further increasing the L value gives very little change in length. To continue lowering the resonant frequency, one must add a capacitor at the point along the half wave twin-lead past where the impedance is infinite – exactly in the center when there is no loading.
Figure 1: Combining an inductively loaded line and a
capacitively loaded line to lower frequency of resonance

If X is correctly normalized by dividing it by the impedance of the cable, then the normalized reactance is equal to the tangent of the wavelength fraction that is represented by the twin-lead length at the new, lowered resonant frequency (the twin-lead started out being a half wavelength long with a short at the far end, and becomes a smaller fraction of wavelength of the lowered resonant frequency as L increases). The rest of the “lengthened “ twin-lead is the equivalent length at F of the reactance X. Since we know the combination is equal to a half wavelength transformer, then (1 – atan(cable length in wavelengths)) is the equivalent length due to X. For a half wave section, (one minus (the cable length in meters/ wavelength of the resonant frequency in meters)) is also the equivalent length of X. These two ways to compute the angle at the point where the L is connected can be compared to check the normalized impedance of the twin-lead.
Table 1 shows the results of loading 8.94 meters of twin-lead with various values of inductance. The coils were old-fashioned plug-in coils with 5 pins, such as we “old timers” once used for regenerative receivers, etc. Using the plug in coils with a socket soldered to the end of the twin-lead eliminated extraneous lengths of connecting wire and capacitance between leads while allowing an easy change among inductors of known values. Another socket was fashioned with short leads to connect to the antenna analyzer to measure each inductor.

The first column of Table 1 is the inductor value, with the zero value being a short. The second column is the resonant frequency found. The results are grouped according to the number of half wavelengths of twin-lead associated with the resonance. The third and fourth columns are the value of impedance found at resonance. The exact resonance, where the reactive term equals zero, was very tricky to set. The fifth column shows the wavelength in free space of the resonant frequency. The sixth column shows the number of half wavelengths the coil/ twin-lead combination represents. The next two columns show the reactance of each inductor and the value after normalization by the cable impedance, 250 ohms, shown in the green section above the Table. The last two columns show the part of the combination length that is represented by the cable, calculated indirectly from the tangent of the normalized reactance and directly from the ratio of the electrical cable length divided by the wavelength. It is evident that the two ways to compute the cable part track well, even though the assumed Zo of the twin-lead is lower than expected.
Table 1 shows another interesting characteristic: the amount in MHz that the spread of inductance values lowers the resonant frequency of the half wave transformer is constant, independent of the total number of half wavelengths involved! The change is about 6 MHz for a change of L from zero to 22 uH.
I observed that for the half wavelength transformer, both ends have a zero-impedance level. I tried two ways to connect the ends together to make a loop, with the analyzer connected across the twin-lead. One way is to connect the end of the each twin-lead wire to the other end of the same wire — I called this the parallel connection. The other way was to connect each wire to the opposite end of the other wire. I called this the Mobius strip connection, which makes a two-turn coil or full wave transformer out of the twin-lead. (The Mobius strip twin-lead has only one surface! Try it: With the ends connected to make a loop, hold it flat on the corner of a table and draw a line on the twin-lead insulation by sliding it under the pen. After the junction slides under the pen twice, you will meet the line again. It is on both “sides” of the twin-lead even though you didn’t pick the pen up and turn over the line.)
The parallel connection of the loop was most interesting — it gave good resonant low impedance points at 1, 2, 3, and 4 half-wave frequencies; but only the lowest, half-wave frequency also achieved near-zero ohm real impedance values at the drive point when connected in a loop. Figure 2 shows the connection diagram. I decided to drive the combination by a link coil on the plug in coil form, which allows better balance for the drive to the twin-lead, and to look only at the half wavelength “lengthened by a load” case. The object of all this is, after all, to find a way to shrink the antenna for the longer wavelengths, such as 160, 80, and 40 meters.

A tuning capacitor was connected exactly opposite the inductor drive and twin-lead ends in the loop by sticking two pins through the wires and connecting the 300 pF tuning capacitor with a geared down knob across the twin-lead. Thus, I got both loading styles working at once. Table 2 shows all the resonant frequencies for various combinations of L and C. The original inductor values used in Table 1 are included, along with two new values that I made in order to achieve a tuning that would go from below 80 meters to above 40 meters.

To show that the twin-lead is very much affecting the tuning, Table 3 shows the resonant frequency of each L and C combination connected with zero length leads. Table 4 shows the fraction of the L-C alone resonant frequencies achieved by separating them with the twin-lead loop.


Table 5 shows the impedance at resonance of the system as seen by the analyzer through the link. At the resonant frequency, the matching was very good; at all other frequencies the analyzer measured about 1 ohm – the d-c resistance of the link! Evidently the current through the inductor-load is a good way to drive this antenna system. These values are easily adjusted for a given inductor load by changing the number of turns in the link.

We Can Shrink – Can We Radiate?
The twin-lead loop with both L and C loading offers a way to get significant reduction in antenna size with understandable and stable electrical characteristics. This loop has a diameter of 2.4 meters, yet it tunes easily to 80 and 40 meters with a 2.17 uH coil and it tunes into 160 meters with a 22 uH coil. The remaining question must be answered — will it radiate? If so, is it the antenna or the drive cable? I’ve tried many resonant circuits that don’t radiate! These questions will be the subject of further experiments
Originally posted on the AntennaX Online Magazine by Joel C. Hungerford, KB1EGI
Last Updated : 31th January 2025