Calculate Line Characteristics from Open & Closed Impedance MeasurementsAuthor: R.J.Edwards G4FGQ © 4th January 2001
Input impedance measurements on a transmission line with the remote end open-circuit and then with the remote end short-circuit provide enough information from which to calculate the line's impedance Zo, the angle of Zo and overall attenuation in dBs. When line length is known the inductance, capacitance, conductor resistance and conductance of the insulating material per unit length can also be calculated together with propagation velocity.
This program performs the necessary calculations. Accuracy of results depends only on the measuring accuracy of Zoc = Roc+jXoc, Zsc = Rsc+jXsc, and length.
However, an inherent ambiguity must be resolved regarding the number of whole 1/2-wavelengths contained in the line length. Depending on the unknown velocity of propagation, different numbers of 1/2-waves will result in the same measured values of Zoc and Zsc. So in addition to the basic input data, the program asks for an estimate of the velocity factor to assist with selection of the correct number of whole 1/2-wavelengths. Sensible computed values of R,L,C,G per unit length and computed VF will indicate whether the correct choice has been made. But beware - measuring errors may confuse the best choice of velocity factor.
The most difficult line characteristics to determine accurately are conductor resistance and dielectric conductance (leakance). Both contribute to line loss which is itself small and prone to error. Separation of the two effects needs very precise measurements. Measuring errors may result in either value having an impossible -ve sign. However, other computed data may be accurate enough.
At 10 Mhz and below, the angle of Zo of all types of line is almost invariably -ve. Exceptions occur only in the unlikely event of dielectric loss exceeding conductor loss. Be very suspicious of +ve Zo angles and check measurements, measuring instruments and measurement method. When the Zo angle is positive it is likely, but not certain, one of the other computed parameters is in error.
Other obvious symptoms of measuring error, or of incorrect estimate of VF, are computed VF greater than unity, or -ve values of VF, inductance or capacitance.
A simple, accurate method of determining propagation velocity is to search for the lowest frequency at which a sharp minimum occurs in the o/c input impedance response. At that frequency the line is 1/4-wavelength long. At the next higher frequency of a sharp minimum the line is 3/4-wavelengths long, etc, etc.
However, accuracy of the important line characteristics, Zo and attenuation, is not impaired even by a large error in estimating electrical line length.
Some Comments on Accuracy
Measured input data to this program will often have been obtained on a length of unknown transmission line in order to calculate its primary characteristics: R,L,C,G or its secondary characteristics: Zo, dBs, VF. If measurements are accurate enough, all these values can be obtained from just 6 input measurements: Roc, Xoc, Rsc, Xsc, line length, frequency.
The relationship between program input and output is complex. If a random set of data is input it is virtually impossible computed output data will apply to any real transmission line. Unless measured values on a real line are precise and accurate, the more sensitive output data will be very unreliable.
For greater reliability when investigating an unknown line it is necessary to take into account conductor diameters. On short lines conductor resistance and attenuation can be more accurately calculated from dimensions than from transmission measurements. When that uncertainty has been eliminated the electrical measurement data can be refined to provide more accurate information on other less sensitive line parameters.
At HF, dielectric conductance and the associated loss is almost always much smaller than conductor resistance loss. So large errors in G can be tolerated.
To avoid extremes of input impedance which may be outside the range of a bridge do not measure Zoc and Zsc at frequencies where the line is an integral number quarterwaves in length. Best frequencies when making measurements on relatively short lines are where line length is roughly 1/8th, 3/8ths, 5/8ths-wavelengths long, etc.
On these lengths both Xoc and Xsc are of the same order of magnitude as Zo and well inside the range of a bridge. Xoc and Xsc always have opposite signs.
At HF, when a line is less than 1/4-wave long, Xoc always has a negative sign and Xsc always has a positive sign. Signs alternate for every length increase of 1/4-wavelength.
Run this Program from the Web or Download and Run
it from Your Computer
This program is self-contained and ready to use. It does not require installation. Click this link Zoc_Zsc then click Open to run from the web or Save to save the program to your hard drive. If you save it to your hard drive, double-click the file name from Windows Explorer (Right-click Start then left-click Explore to start Windows Explorer) and it will run.
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