5.md

title: Problem Set 5

(7.1)

Cables designed to carry signals with minimum pickup of interference often consist of a twisted pair of conductors surrounded by a grounded shield. Why the twist? Why the shield?

(7.2)

Salt water has a conductivity ∼4 S/m. What is the skin depth at 10^4 Hz?

(7.3)

Integrate Poynting’s vector P = E \times H to find the power flowing across a cross-sectional slice of a coaxial cable, and relate the answer to the current and voltage in the cable.

(7.4)

Find the characteristic impedance and signal velocity for a transmission line consisting of two parallel strips with a width w and a separation h (Figure 7.4). You can ignore fringing fields by assuming that they are sections of conductors infinitely wide.

(7.5)

The most common coaxial cable, RG58/U, has a dielectric with a relative permittivity of 2.26, an inner radius of 0.406 mm, and an outer radius of 1.48 mm.

(a)

What is the characteristic impedance?

(b)

What is the velocity?

(c)

If a computer has a clock speed of 1 ns, how long can a length of RG58/U be and still deliver a pulse within one clock cycle?

(d)

It is often desirable to use thinner coaxial cable to minimize size or weight but still match the impedance of RG58/U (to minimize reflections). If such a cable has an outer diameter of 30 mils (a mil is a thousandth of an inch), what is the inner diameter?

(e)

For RG58/U, at what frequency does the wavelength become comparable to the diameter?

(7.6)

CAT6 twisted pair cable used in ethernet networks has a propagation delay of 4.6 ns/m, and an impedance of 100 ohms.

(a)

What is the physical length of a minimum size 64 byte frame?

(b)

Now consider what would happen if a “T” connector was used to connect one CAT6 cable to two other ones. Estimate the reflection coefficient for a signal arriving at the T.