Coaxial Cable
formula on coaxial cable, including the skin effect
frequency
inner radius
outer radius
relative dielectric
Power
electric conductivity
loss tangent
wave impedance
\(Z_0=\sqrt{\frac{\mu}{\epsilon_0\epsilon_r}}\)
characteristic impedance
\(Z_c=\frac{V_0}{I_0}= \frac{Z_0 ln(b/a)}{2\pi}\)
Voltage(max)
\(P=\frac{1}{2}V_0 I_0=\frac{1}{2Zc}V_0^2\)
Voltage rms
current(max)
\(I_0=\frac{V_0}{Z_c}\)
Current rms
maximum electric field
\(E_r=\frac{V_0}{\rho ln(b/a)}e^{-j k z}\)
maximum magnet flux density
\( H_\phi=\frac{E_\rho}{Z_0}=\frac{B}{\mu}\)
phase speed
\(v_p=\frac{\omega}{k}=\frac{1}{\sqrt{\epsilon_0 \mu_0 \epsilon_r}}=\frac{c}{\sqrt{\epsilon_r}}\)
single mode band
\( f_c=\frac{c}{\pi(a+b)\sqrt{\epsilon_r}}\)
resistivity
\(\rho=\frac{1}{\sigma}\)
anger frequency
\(\omega=2 \pi f\)
skin depth
\(\delta=\sqrt{\frac{2\rho}{\omega\mu}}\sqrt{\sqrt{1+(\rho\omega\epsilon)^2}+\rho\omega\epsilon}\)
series resistance
\(R_s=\frac{1}{\sigma\delta}\)
series inductance
\(L=\frac{\mu ln(b/a)}{2 \pi}\)
shunt capacitance
\(C=\frac{2\pi\epsilon}{ln(b/a)}\)
series resistance
\(R=\frac{R_s}{2\pi}(\frac{1}{a}+\frac{1}{b})\)
shunt conductance
\(G=\frac{2\pi \omega\epsilon' \tan\delta}{ln(b/a)}\)
propagation constant
\(\gamma=\alpha+j\beta=\sqrt{(R+j\omega L)(G+j\omega C)}\)
characteristic impedance
\(Z=\frac{V_0^+}{I_0^+}=-\frac{V_0^-}{I_0^-}=\frac{R+j\omega L}{jk}=\sqrt{\frac{R+j \omega L}{G+j \omega C}}\)
loss per meter
\(20\log_{10}(e^{-\alpha})\)