An open-ended quarter-wavelength, air-spaced, parallel-wire transmission line is found to(adsbygoogle = window.adsbygoogle || []).push({});

be in resonance with an oscillator when its length is 0.25 m. When a capacitance of 1 pF

is connected across the open end, it is found that the length of the line must be reduced

to 0.125 m to obtain resonance. Show that the characteristic impedance of the line is

approximately 530 *Ohms

[Remember that, using V proportional to exp(i(kz-wt)) the impedance of a capacitor is i/wc]

The main problem here is I don't really understand the question!!! Can someone explain what it actually means/wants me to do? It's the found to be in resonance part that I don't get - does it mean is impedance matched to?

I think that the two circumstances will give me two equations which should be easier enough to manipulate to find the characteristic impedance.

For a quarter wavelength line Zin/Z = Z/Zt where Zin is the input impedance, Z the characteristic impedance and Zt the terminating impedance.

For an open circuited line Zin/Z = -jcot(ka) where j is the imaginary unit, and a the length of the line

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# Homework Help: Quarter Wavelength Transmission Line

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