Updating the Gieskieng Transmission Line
Not So Fast!
Last month I investigated the capacitive loading of an open-ended transmission line for the purpose of using loading to shorten the size of a Gieskieng antenna and observed an apparent change in the velocity of propagation in the cable with different values of loading reactance. A few days after the publication of this article, I received an e-mail from Steve Berbick, W6SLD. Steve pointed out that there was a fundamental error in my calculations and the apparent velocity change is an artifact of that error. Further, he suggested that the artifact converts my procedure from one to measure the effect of loading to an easy way to determine the actual characteristic impedance of a transmission line. He observed that in a normal line, the velocity of propagation is one of the more constant properties, as it is set by the material electrical properties of the plastic used to construct the line.
I had used the characteristic impedance of the antenna analyzer input, 50 ohms, to normalize the reactance of the loading capacitor at the resonant frequency where the load/line combination is a quarter of a wavelength long. This normalizing introduces a silent new parameter into the equation: the entry point on the Smith Chart where the load ends and the line begins. Instead, I should have used the impedance of the twin-lead, nominally 300 ohms. It is obvious that the phenomenon that we are talking about, the transformation of impedance by a length of transmission line, is not happening at the analyzer terminals. It is happening in the line and so the calculation must use the line Zo. Table 1 is a repeat of last month’s quarter-wave data. The colored parts are calculations and the white parts are the measured data.

The Smith Chart is a device that computes the impedance along a transmission line as defined by the load and distance along the line. It is calibrated in terms of units of fractions of a wavelength of line length (not feet or meters) and units of characteristic impedance of the line, Zo (not measured impedance in ohms). The calculation space on the chart is a half wavelength long since the line characteristics repeat themselves every half wave along the line. All the reactance conditions along a quarter wave transformer are located around a half circumference of the round Smith Chart; all perfectly real (not inductive or capacitive) values of the impedance are located along the diameter that connects the half circumference ends. The center of the circle is the point on the diameter that represents a normalized matched resistive load of 1.0 or Zo/Zo.
The values of the normalized reactance curve around the half-circumference, that is a quarter wave long, is:
-j*tan (electrical degrees from the source to the load)
Since the half circumference (180 physical degrees on the chart) is a quarter wave transformer, the physical degrees are 2x the electrical degrees. For example, the point where the reactance is 1.0, or a value in ohms that is equal to the line impedance Zo, is at 45 electrical degrees or 90 physical degrees around the chart.
Correcting Velocity
In view of Steve’s correction, the velocity of the transmission line is constant with frequency. Resonance is the frequency where the capacitive load is transformed to zero reactance and, with lossless line, zero resistance. When a capacitive load is put on the end of the line, the combination at resonance is composed partly of line and partly of the reactance of the capacitive load at the resonant frequency. The connection point is where the load reactance is equal to the line reactance.
Suppose I have a length of line that is a electrically a quarter of a wave long at a frequency F, which means it is physically 1/4 of the wavelength:
(=300/F meters in free space*the velocity [typically 0.8 in twin lead] meters long)
With no capacitive load, this line is resonant at F and the open end is transformed to a short that is easily found by the antenna analyzer at F. The impedance at the open end of the line is -j*tan(90 degrees), or an infinite impedance. Call its length L meters.
Suppose that I now place a capacitor across the open end of the line and adjust it until the reactance of the capacitor:
(-i/(2*pi*F*C)
Is equal to the value of the characteristic impedance of the line, Zo, or in normalized form, -j1.0.
If I cut the line where this value is found on the Smith Chart, the line will extend 90 physical degrees or 45 electrical degrees around the chart since tan 45 = 1.0. The combination of half the original line plus the capacitor will still be resonant at F. The new length is L/2 meters.
Another Experiment
Now let’s take this combination of line and capacitor that is resonant at F and perform the experiment that I described last month. I connect the load and tune it to the proper C value. Then I tune the analyzer to zero reactance, which occurs at F MHz. I compute that the capacitor has a reactance of Zo ohms (say 300 ohms), and I normalize that value to 1.0 by dividing with the line Zo (assumed to be 300 ohms).
I locate the value of -j1.0 on the Smith chart, and find it is at 0.125 wavelength from the antenna analyzer (zero impedance) end of the line. I then compute that the velocity in the cable is:
[the physical length (=0.8*1/8 wavelength)]/[the electrical length (1/8 wavelength)]
….and find it is 0.8. Big surprise!
Now, for comparison, let me deliberately make an error in the normalizing value. Let’s use, say, 50 ohms. All the measured numbers are the same except that the 300 ohms capacitive reactance now normalizes to 6.0. I look on the Smith Chart and find 6.0 is at 161 physical or 80.5 electrical degrees, or 0.224 wavelengths from the analyzer.
I then compute that the velocity factor in the cable is:
[0.8*1/8 wavelength]/[0.224 wavelength] =0.457!!!
As my first EE boss, Andy Przedpelski, used to say, “there are no miracles! It is doing just what you designed it to do, not what you intended it to do!” Thanks, Steve, for detecting my latest “miracle”.
Steve suggested that this error could be useful in finding the actual line impedance, Zo. Merely take a piece of line, and measure its lowest frequency where an open-ended line section is a quarter wave transformer. Then add capacitive loads and see what velocity factor is computed by going through the above procedure. (The analyzer can be used to measure the capacitive reactance with no line at the resonant frequency, or measure it at a lower frequency and compute the reactance at the resonant frequency).
Turn the Tables
We can set up a table like Table 2 to show the measurements at a number of frequencies by using different capacitors. If the computed velocity changes with frequency then the normalizing is incorrect. Adjust the normalizing value and re-compute until the velocity is unchanged. I did this with the data in Table 1 and found that my twin-lead Zo is 324 ohms, the normalizing value that converts Table 1 into Table 2. Table 3 shows the 3/4 wavelength condition. Note that the length of the line is in meters, which is computed from the wavelength fraction attributed to the line. It is always the same at every frequency.


A frequency error in measurement will also introduce an apparent velocity error. This means that the attempt to do this experiment with a shorted quarter-wave transformer or any multiple of an open half wave will not work. The analyzer cannot measure an impedance greater than 640 ohms. In practice, the closest one can come to 640 is a number like 619 or 591 ohms, and the value is jumps all over the place. The analyzer is using a digital circuit with crude quantification. One can find the value nearest 640 ohms both above and below the resonant frequency of a line that has high impedance at the analyzer. Then find the mean frequency. However, I found that the resulting velocity numbers are almost random numbers. The peak of the resonant impedance is not found by the mean of the measured numbers.
It is best to also set up and measure shorted half and full wave sections and average all the velocities. The averaging procedure is necessary because the open end of the line has a small stray capacitance load due to E fields in space around the ends of the wires. The shorted line is much cleaner.
I have taken data on the shorted and the inductively loaded line in a similar fashion to the capacitive loaded line. The numbers contain all sorts of strange resonances. The inductor used was a large rotary unit commonly used in antenna matching circuits. Many unknown extra loading and resonances may occur due to stray capacitance between the wires of the inductor, connecting wires etc. The inductively loaded half-wave transformer must be fabricated by putting a twin-lead plug on the end and making up several coils on sockets, with a minimum of extraneous wiring. Only then will the data be reliable.
Line Radiation Antennas?
The Gieskieng antenna experiments have been all about combinations of sections of transmission line sometimes loaded with capacitors. Much discussion recently has occurred about certain “antennas” which are basically capacitors such as the EH antenna, the Isotron, etc. Many of these come with instructions that ask that the feed line be at least a quarter wave long! In all these electrically small devices, the main radiator seems to always turn out to be the feed line. So, if you can’t beat line radiation, why not join it: throw away the “antenna” and just use the feed line. My magnetite-loaded monopole is tuned by rolling a coil of the feed line up and down the cable.
So, what could be stealthier than a simple length of line? The line might be terminated with a coil or capacitor, plugged into a “tuner” that consists of a coil of cable with a socket on each end, and tuned with capacitors either across the coil or in series with the shield of the coil and the shield of the “antenna” part. The function of the sockets is to allow access to the shield of the cable without cutting the cable insulation. This procedure would put the tuning indoors and out of the weather instead of outside near the roof. The “antenna” itself is only a cable, and easily hidden. This is obviously an oversimplification of what an antenna does because of many other special considerations, but it’s worth a thought or two, and will be the subject of some future experiments.
Originally posted on the AntennaX Online Magazine by Joel C. Hungerford, KB1EGI
Last Updated : 30th January 2025