A Coaxial Line Used as a Tuned CircuitAuthor: R.J.Edwards G4FGQ © 15th April 2005
At HF and above, with a short circuit at one end, a 1/4-wavelength coaxial line can be used as a tuned circuit with a fairly high Q. With a variable capacitor across the open end an adjustable parallel tuned circuit results. Less commonly a series-tuned circuit can be formed depending on application.
For given line dimensions, this program calculates the value of the tuning capacitor needed to resonate the line to a particular frequency. Tuned circuit Q, input impedance, parallel R and X, and other properties of interest of the line itself are also calculated.
Common uses are receiver RF tuned circuits and transmitter tank circuits. Tap down the coaxial inner conductor for a low impedance match to an antenna.
For given conductor diameters, Q increases with resonant frequency. Very high values of Q are obtainable at UHF. At MF, Q values are generally lower than can be realized by conventional coils and capacitors. But in any case the physical length of a line at HF is too long and impractical for ordinary applications. This program is useable for educational purposes from LF to microwaves.
Computed line input resistance at resonance is the same as that of an ordinary parallel LC tuned circuit. Computed line input reactance is that tuned out by the parallel capacitor simultaneously with the input reactance of a transistor or tube used as an RF amplifier of which the tuned circuit forms a part.
Note that as line length nears 1/4-wave, tuning capacitor approaches zero pF. In practice the line will be made somewhat shorter than 1/4-wave to permit the capacitor to be adjusted precisely to resonance. Line length, by itself, is too imprecise for accurate adjustment of resonant frequency.
Dielectric loss in the insulant, especially with air spacing, is very small and is neglected. But it has the effect of reducing Q and input R above 2 or 3 GHz.
Negative capacitor values and Q are incorrect at line lengths greater than 1/4 wavelengths. All other computed data is correct at all line lengths.
Note that as the short-circuited line length and attenuation increases above 13 or 14dB, resonant line input resistance oscillates-about and eventually converges on the line impedance Zo. Zo is almost independent of frequency above LF. For more exact behaviour of coaxial Zo, at VLF down to power frequencies, see program CoaxPair.exe. For balanced-twin and open-wire lines see programs RJELine2 & 3.
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 CoaxTune 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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