A coaxial cable is a type of electrical cable consisting of a central conductor, an insulating layer, a metallic shield, and an outer insulating layer. It is used to transmit high-frequency signals with low loss and is commonly used in telecommunications, cable television, and internet connections.
The formulas to calculate the impedance, capacitance, inductance, and cutoff frequency of a coaxial cable are:
\[ Z = \frac{138 \log \left( \frac{D}{d} \right)}{\sqrt{pr}} \] \[ \text{Capacitance} = \frac{7.354 \cdot pr}{\log \left( \frac{D}{d} \right)} \text{ pF} \] \[ \text{Inductance} = 140.4 \log \left( \frac{D}{d} \right) \text{ nH} \] \[ \text{Cutoff Frequency} = \frac{11.8}{\sqrt{pr} \cdot \pi \left( \frac{D + d}{2} \right)} \text{ GHz} \]
Where:
Let's assume the following values:
Using the formulas:
\[ Z = \frac{138 \log \left( \frac{10}{2} \right)}{\sqrt{2.2}} = \frac{138 \log (5)}{\sqrt{2.2}} = 149.74 \text{ Ω} \] \[ \text{Capacitance} = \frac{7.354 \cdot 2.2}{\log (5)} = 10.05 \text{ pF} \] \[ \text{Inductance} = 140.4 \log (5) = 225.97 \text{ nH} \] \[ \text{Cutoff Frequency} = \frac{11.8}{\sqrt{2.2} \cdot \pi \left( \frac{10 + 2}{2} \right)} = 0.42 \text{ GHz} \]
The impedance is 149.74 Ω, the capacitance is 10.05 pF, the inductance is 225.97 nH, and the cutoff frequency is 0.42 GHz.