Tentukan $R$, $L$, $C$, dan $G$ pada kabel koaksial dengan $a = 0,25 \text{ mm}$, $b = 2,50 \text{ mm}$, $c = 3,30 \text{ mm}$, $\epsilon_r = 2,0$, $\mu_r = 1$, $\sigma_c = 1,0 \times 10^7 \text{ S/m}$, $\sigma = 1,0 \times 10^{-5} \text{ S/m}$, dan $f = 300\text{ Mhz}$
Pada frekuensi tinggi ($300 \text{ MHz}$), arus tidak mengalir di seluruh penampang konduktor, melainkan hanya di permukaannya saja. Fenomena ini disebut Skin Effect.
Kita hitung ketebalan kulit
$$\delta = \frac{1}{\sqrt{\pi f \mu_0 \sigma_c}}$$
$$\delta = \frac{1}{\sqrt{3.14 \cdot 3 \times 10^8 \cdot 4\pi \times 10^{-7} \cdot 1.0 \times 10^7}}$$
$$\delta = \frac{1}{\sqrt{1.183 \times 10^{10}}}$$
$$\delta = \frac{1}{1.087 \times 10^5}$$
$$\delta = 9.199 \times 10^{-6}$$
Kita hitung resistansi permukaan
$$R_s = \frac{1}{\sigma_c \delta}$$
$$R_s = \frac{1}{1.0 \times 10^7 \cdot 9.199 \times 10^{-6}}$$
$$R_s = \frac{1}{91.992}$$
$$R_s = 0.01087 \ \Omega$$
Kita hitung logaritma natural perbandingan
$$\ln\left(\frac{b}{a}\right)$$
$$\ln\left(\frac{2.50}{0.25}\right)$$
$$\ln(10)$$
$$2.302$$
(a) Perhitungan Resistansi
$$R = \frac{R_s}{2\pi} \left( \frac{1}{a} + \frac{1}{b} \right)$$
$$R = \frac{0.01087}{2 \cdot 3.14} \cdot \left(\frac{1}{0.00025} + \frac{1}{0.0025} \right)$$
$$R = \frac{0.01087}{6.28} \cdot (4000 + 400)$$
$$R = 0.00173 \cdot 4400$$
$$\mathbf{R = 7.612 \ \Omega/\text{m}}$$
(b) Perhitungan Induktansi
$$L = \frac{\mu_0 \mu_r}{2\pi} \ln\left(\frac{b}{a}\right)$$
$$L = \frac{4\pi \times 10^{-7} \cdot 1}{2\pi} \cdot 2.302$$
$$L = 2 \times 10^{-7} \cdot 2.302$$
$$L = 4.604 \times 10^{-7}$$
$$\mathbf{L = 0.46 \ \mu\text{H/m}}$$
(c) Perhitungan Kapasitansi
$$C = \frac{2\pi \epsilon_0 \epsilon_r}{\ln(b/a)}$$
$$C = \frac{2 \cdot 3.14 \cdot 8.854 \times 10^{-12} \cdot 2.0}{2.302}$$
$$C = \frac{1.112 \times 10^{-10}}{2.302}$$
$$C = 0.483 \times 10^{-10}$$
$$\mathbf{C = 48.3 \text{ pF/m}}$$
(d) Perhitungan Konduktansi
$$G = \frac{2\pi \sigma}{\ln(b/a)}$$
$$G = \frac{2 \cdot 3.14 \cdot 1 \times 10^{-5}}{2.302}$$
$$G = \frac{6.28 \times 10^{-5}}{2.302}$$
$$G = 2.728 \times 10^{-5}$$
$$\mathbf{G = 27.28 \ \mu\text{S/m}}$$
