Transmission Line Interface

AAplot's Transmission Line interface provides tools for making measurements of the electrical length of a transmission line.




Resonant Frequency Measurement

The Resonant Frequency measurement tool estimates the frequency that a given transmission line appear as an electrical length.

The resonant frequencies are measured in AAplot by observing the reactance of the transmission line when the far end of the line is left open.

Starting at a low frequency near DC, the reactance term that is seen by the antenna analyzer is negative (capacitive). As the frequency is increased, the reactance turns less capacitive, until it becomes zero: this is where the transmission line is 0.25 of a wavelength.

When the frequency is raised further, the reactance again becomes positive (inductive) and eventually decreases again. The point where the reactance is again 0 is where the transmission line is 0.5 of a wavelength. The next point where the reactance crosses 0 correspond to 0.75 wavelength, etc.

AAplot finds where the complex value of the Bilinear transform of the impedance has an argument that is the number of wavelength requested, taking into account the number of times the reactance crosses zero.

With an RG-58 coax cable that is approximately 10.4 meters long electrically, the following figure shows the frequency at which it behaves as an electrical 0.22 wavelength transmission line:



The next figure shows the frequency at which the same cable behaves as an electrical 0.88 wavelength transmission line:



Please note that in general (as seen above), the frequency where a transmission line behaves like a "0.88 wavelength" cable is not four times the frequency when the transmission line behaves as a "0.22 wavelength" cable. The reason for this is the dielectric of a coax cable is dispersive and the velocity factor at one frequency is different from the velocity factor at a different frequency.

Use the 0.88 wavelength setting if you want to measure a line to use as a 0.88 wavelength section, do not measure it for a different frequency and assume that dimensions will scale linearly.

The next tool measures the electrical length of a transmission line for any specified frequency.


Electrical Length Measurement

The Electrical Length Measurement tool estimates the electrical length of a transmission line that is unterminated at the far end. The following figure shows the measured electrical length of the same coax cable that is used above when measured at 31.1 MHz:



The length is shown in both the number of wavelengths and the phase angle in number of degrees.