Transmission Line Calculator

Formula

The formula to calculate the characteristic impedance (Z0) is:

\[ Z0 = \sqrt{\frac{R + jwL}{G + jwC}} \]

Where:

\( Z0 \) is the characteristic impedance (ohms)
\( R \) is the resistance per unit length (ohms/meter)
\( w \) is the angular frequency (radians/second)
\( L \) is the inductance per unit length (henries/meter)
\( G \) is the conductance per unit length (siemens/meter)
\( C \) is the capacitance per unit length (farads/meter)
\( j \) is the imaginary unit

What is a Transmission Line?

A transmission line is a specialized cable or other structure designed to conduct alternating current of radio frequency, that is, currents with a frequency high enough to have wave properties. It is used for high-frequency signals, typically in the range of 300 MHz to 3 GHz, to minimize losses and distortion. Transmission lines are used for purposes such as connecting radio transmitters and receivers with their antennas, distributing cable television signals, and computer network connections.

Example Calculation

Let's assume the following values:

Resistance per unit length (R) = 50 ohms/meter
Angular Frequency (w) = 2π × 10^9 radians/second
Inductance per unit length (L) = 2 × 10^-7 henries/meter
Conductance per unit length (G) = 1 × 10^-3 siemens/meter
Capacitance per unit length (C) = 1 × 10^-12 farads/meter

Using the formula to calculate the characteristic impedance:

\[ Z0 = \sqrt{\frac{50 + j(2\pi \times 10^9)(2 \times 10^{-7})}{1 \times 10^{-3} + j(2\pi \times 10^9)(1 \times 10^{-12})}} \]

The Characteristic Impedance (Z0) is approximately 50 ohms.