- #1
Marcus95
- 50
- 2
Homework Statement
A coaxial transmission line consists of an inner cylindrical conductor of radius a = 1 mm and a
cylindrical outer conductor chosen to make the characteristic impedance 75 ohm. The space
between the conductors is lled with a gas which can stand a maximum eld of 105 V/m
without dielectric breakdown. Estimate the maximum mean radio-frequency power that
can be transmitted along this line into a matching load.
Homework Equations
On transmission line
## Z = \sqrt{L/C} ##
For coaxial with radius a and b:
##C = \frac{2\pi \epsilon \epsilon_0}{ln(b/a)} ##
##L = \frac{\mu_0 ln(b/a)}{2\pi} ##
The Attempt at a Solution
The voltage between the two conductors is by Gauss's law:
## V = \int \boldsymbol{E} \cdot d\boldsymbol{r} = E_0 ln(b/a) ##
hence:
## V_{max} = E_{max} ln(b/a) ##
also:
##Z = \sqrt{\mu / \epsilon \epsilon_0} \frac{ln(b/a)}{2\pi} ##
Using ##P = VI = V^2/Z ## and asuuming ##epsilon \approx 1## gives:
##P_{max} = 0.21 GW##, but the answer is supposed to be 104 W.
What am I doing wrong? Many thanks!