The Input Impedance of a Coaxial Transmission Line Terminated with a LoadAuthor: R.J.Edwards G4FGQ © 3rd April 2006
This program is a companion to Line-Zin which deals with balanced-pair lines.
The input impedance of a transmission line is often needed. Much experience is required just to guess what it might be. This program accurately calculates it.
The load impedance, R+jX, can be anywhere between a short circuit and a virtual open circuit. Input impedance is calculated in the same series R+jX form.
The reactive component of Zinput, depending on its sign, is also given in the form of microhenrys or picofarads. It is sometimes useful to know this.
The program can be used to assist with design of transmission line impedance-matching transformers when one or both of the terminations are complex.
The reflection coefficient and SWR on the line are also calculated. This data can be used in further investigations.
Note how line loss increases when high standing waves are present on the line.
Inner conductor diameter is needed in order to calculate attenuation.
As frequency decreases line Zo has an increasing negative angle. When the line attenuation exceeds 40 dB this is indicated by a negative value of input reactance. At high attenuation the input impedance converges on line Zo.
Note that when the line is terminated with its exact Zo = Ro + jXo, the SWR and reflection coefficient respectively become 1-to-1 and zero for all line lengths
This increasing negative angle of Zo with decreasing frequency is a property of all transmission lines. At low audio and power frequencies the angle of Zo of coaxial cables approaches -45 degrees.
The Smith Chart assumes Zo of transmission lines to be purely resistive at all frequencies. The Chart becomes inaccurate at MF and useless at VLF.
Even at 1.9 MHz, using the Smith Chart to design quarter-wave matching transformers can cause serious errors. This program accurately takes the angle of Zo and line loss into account.
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 Input_Z 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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