Enter the resistance per unit length, angular frequency, inductance per unit length, conductance per unit length, and capacitance per unit length into the calculator to determine the characteristic impedance.
Transmission Line Formula
The following formula is used to calculate the characteristic impedance (Z0) of a transmission line.
Z0 = sqrt((R + jwL) / (G + jwC))
Variables:
- 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
To calculate the characteristic impedance of a transmission line, add the resistance per unit length to the product of the angular frequency and inductance per unit length, multiplied by the imaginary unit. Similarly, add the conductance per unit length to the product of the angular frequency and capacitance per unit length, multiplied by the imaginary unit. Divide the first result by the second result, and take the square root of the quotient.
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.
How to Calculate Transmission Line?
The following steps outline how to calculate the characteristic impedance (Z0) for a Transmission Line using the given formula:
- First, determine the values of R, w, L, G, and C.
- Next, substitute the values into the formula: Z0 = sqrt((R + jwL) / (G + jwC)).
- Then, simplify the expression inside the square root.
- Finally, calculate the square root of the simplified expression to find the characteristic impedance (Z0).
Example Problem:
Use the following variables as an example problem to test your knowledge:
R = 10 ohms/meter
w = 100 radians/second
L = 0.5 henries/meter
G = 0.2 siemens/meter
C = 0.1 farads/meter
j = imaginary unit
