BerandaSainsFisikaElektromagnetika - Gelombang Terpandu - Bagian 2

Elektromagnetika – Gelombang Terpandu – Bagian 2

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

$$G = \frac{2\pi \sigma}{\ln(b/a)}$$

$$G = \frac{2 \cdot 3.14 \cdot 1 \times 10^{-5}}{2.302}$$

$$G = \frac{6.28 \times 10^{-5}}{2.302}$$

$$G = 2.728 \times 10^{-5}$$

$$\mathbf{G = 27.28 \ \mu\text{S/m}}$$

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