## Characteristic Impedance of Transmission Lines

### Characteristic Impedance

Consider an ideal, infinitely long transmission line. Exciting the input of this transmission line with the alternating voltage Vin(t) results in the current Iin(t). The characteristic impedance of this transmission line is given by the equation:

`${Z}_{0}=\frac{{V}_{in}\left(t\right)}{{I}_{in}\left(t\right)}$`

Consider a transmission line of length `L` terminated by load impedance of `ZL`.

The complex propagation constant for this line is given by the equation:

`$\gamma =\left(\alpha +j\beta \right)$`

where ɑ and β are the attenuation and phase constants. The complex characteristic impedance is given by the equation:

`${Z}_{0}={R}_{0}+j{X}_{0}$`

where `R0` and `X0` are the real and imaginary parts, respectively.

The input impedance of the line is given by the equation in:

#### Characteristic Impedances of Microstrip and Coplanar Waveguide Transmission Lines

Create microstrip and coplanar waveguide transmission lines with default properties. Use the `getZ0` from RF PCB Toolbox™ to calculate the characteristic impedance of following transmission lines: