# 物理代写|电动力学代写electromagnetism代考|PHYS3040

## 物理代写|电动力学代写electromagnetism代考|TWIN FEEDER

Let us now consider twin feeder. This type of cable is usually air spaced and so the shunt resistance is zero. (If air conducted electricity, our electricity bills would be even higher than now!) So, air-spaced twin feeder only has the series resistance of the conductors. Thus,
$$R=\frac{l}{\sigma A} \Omega$$
or
$$R^{\prime}=\frac{l}{\sigma A} \Omega \mathrm{m}^{-1}$$
Of course, if the twin feeder were not air spaced but surrounded by a lossy dielectric, the shunt resistance would be given by
$$R=\frac{\ln \left(\frac{d-a}{a}\right)}{\pi \sigma \times \text { length }} \Omega$$
where we have made use of our new relationship Equation (4.23).

## 物理代写|电动力学代写electromagnetism代考|MiCrostrip Lines

We seldom need to consider the shunt resistance of a length of microstrip. This is because printed circuit boards are usually made of PTFE or Teflon, $\sigma \approx 10^{-16} \mathrm{~S} \mathrm{~m}^{-1}$, and this makes them very poor conductors. Instead, the voltage drop along a length of track is very important.

The metallization on printed circuit boards usually has a uniform cross-sectional area, and so the resistance of a length of track is given hy
$$R=\frac{l}{\sigma A} \Omega$$
where A is the cross-sectional area of the track. As copper is usually used on pcbs, the resistance per $\mathrm{cm}$ is
\begin{aligned} R^{\prime} &=\frac{1}{58 \times 10^8 \times w \times t} \ &=\frac{1.7 \times 10^{-10}}{w \times t} \Omega \mathrm{cm}^{-1} \end{aligned}
where $w$ is the width of the track, and $t$ is the thickness of the metalization.

## 物理代写|电动力学代写electromagnetism代考|TWIN FEEDER

$$R=\frac{l}{\sigma A} \Omega$$

$$R^{\prime}=\frac{l}{\sigma A} \Omega \mathrm{m}^{-1}$$

$$R=\frac{\ln \left(\frac{d-a}{a}\right)}{\pi \sigma \times \text { length }} \Omega$$

## 物理代写|电动力学代写electromagnetism代考|MiCrostrip Lines

$$R=\frac{l}{\sigma A} \Omega$$

$$R^{\prime}=\frac{1}{58 \times 10^8 \times w \times t} \quad=\frac{1.7 \times 10^{-10}}{w \times t} \Omega \mathrm{cm}^{-1}$$

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