Last Week's Question

Increasing the spacing between the two wires in a parallel-wire transmission line,

1. increases the velocity of propagation
2. decreases the velocity of propagation
3. has no effect on the velocity of propagation
4. all of the above

Answer

The correct answer is "c". The velocity of propagation in a transmission line with a homogeneous dielectric is determined by the properties of the dielectric. The equation relating the velocity of propagation to the dielectric properties is $v=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{\mu \epsilon }$}\right.$, where mu is the material's permeability and e is the electric permittivity. The velocity can also be expressed in terms of the inductance and capacitance per unit length, $v=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$\sqrt{LC}$}\right.$. L and C are properties of the conductor geometry, but any change in conductor geometry that increases L (e.g. increasing the spacing between the two conductors) results in a proportional decrease in C. So the product LC is a constant equal to the product με.

It is important to note that, in a non-homogeneous dielectric, changing the spacing between the wires can change the effective dielectric constant. For example in a ribbon cable (or parallel microstrip traces on a circuit board) some of the electric field between the conductors is in the wire insulation (or board dielectric) and some of the field is in air. In this situation, increasing the spacing between conductors can cause a lower percentage of the field to be contained in the dielectric. This will decrease the effectivity permittivity of the transmission line dielectric and increase the velocity of propagation.

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