diff --git a/_psets/5.md b/_psets/5.md index cf048e84386da0c0c0830bacf52682b529acca6e..290c523dd9c9376741cae6c5f5e87f8f6f3e85ef 100644 --- a/_psets/5.md +++ b/_psets/5.md @@ -4,6 +4,7 @@ title: Problem Set 5 ## (7.1) +{:.question} 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? @@ -24,8 +25,10 @@ filter for the sorts of noise that can reach the conducting pair, with the cutof determined by the shield's thickness. Grounding it ensures that built up static charge has a place to go, though not all shields are grounded. + ## (7.2) +{:.question} Salt water has a conductivity ∼4 S/m. What is the skin depth at $$10^4$$ Hz? $$ @@ -36,8 +39,10 @@ $$ \end{align*} $$ + ## (7.3) +{:.question} Integrate Poynting’s vector $$P = E \times H$$ to find the power flowing across a cross-sectional slice of a coaxial cable, and relate the answer to the current and voltage in the cable. @@ -68,51 +73,63 @@ $$ so we can write the total power as $$IV$$. + ## (7.4) +{:.question} 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) +{:.question} 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) +{:.question} What is the characteristic impedance? ### (b) +{:.question} What is the velocity? ### (c) +{:.question} 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) +{:.question} 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) +{:.question} For RG58/U, at what frequency does the wavelength become comparable to the diameter? + ## (7.6) +{:.question} CAT6 twisted pair cable used in ethernet networks has a propagation delay of 4.6 ns/m, and an impedance of 100 ohms. ### (a) +{:.question} What is the physical length of a minimum size 64 byte frame? ### (b) +{:.question} 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.