- #1
nathangrand
- 40
- 0
An open-ended quarter-wavelength, air-spaced, parallel-wire transmission line is found to
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
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