Last Week's Question
The characteristic impedance of a coaxial transmission line with an air dielectric is,
- less than 1 ohm
- between 20 and 100 ohms
- about 377 ohms
- greater than 100,000 ohms
The best answer to the question above is "b". The formula for the characteristic impedance of a low-loss coaxial cable is Z0 = η/(2π) ln(router/rinner), where η is the intrinsic impedance of the dielectric and router and rinner are the outer and inner conductor radii, respectively. Theoretically, the characteristic impedance can take on any arbitrarily low or arbitrarily high value. As a practical matter though, any air-dielectric coaxial cable with reasonably low losses and reasonable flexibility will have a characteristic impedance between 20 and 100 ohms.
The characteristic impedance of a transmission line is the ratio of the voltage to the current in a wave traveling in one direction down the line. In low-loss cables, it's approximately equal to the square root of the ratio of the inductance per unit length to the capacitance per unit length.
The resistance of the conductors for a given length of coaxial cable may be less than 1 ohm, but conductor resistance has very little impact on the characteristic impedance. The resistance between the conductors (across the dielectric) for a given length of coaxial cable may be greater than 100,000 ohms, but this resistance also has very little impact on the characteristic impedance.
The ratio of the electric field strength to the magnetic field strength in a coaxial cable is equal to the intrinsic impedance of the dielectric. In a cable with an air dielectric, this is approximately 377 ohms, but this is not the characteristic impedance. The intrinsic impedance of a dielectric material and the characteristic impedance of a transmission line are two very different things.