diff --git a/_psets/5.md b/_psets/5.md new file mode 100644 index 0000000000000000000000000000000000000000..b63f04756efb17fb458985417004086497df22ef --- /dev/null +++ b/_psets/5.md @@ -0,0 +1,66 @@ +--- +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.