
### Electrical Length of the line in meters

We can express the physical length of the line in meters. However, in high-frequency electronics (microwave engineering), we usually convert this length to the fraction of a wavelength of a signal that is traveling on the line.

Typically, but not always, $N$ is a fraction, for example, $N=\frac {1}{2}=0.5$, $N=\frac {1}{4}=0.25$ or $N=\frac {1}{8}=0.125$; although it can be any The lenght of the line is then written as

If the physical length of the line is $l=\frac {\lambda }{4}$, we say: This line is quarter-wavelength long at 1GHz, meaning one-quarter of the wavelength fits on the line. We could also say that the line is 7.5cm long, as wavelength is $\lambda =30 \unit {cm}$ at $1$GHz.

When we say quarter-wavelength long, we refer to the lines physical length at a specific frequency.

### Electrical length of the line in degrees

The phase shift between input and output signal on a transmission line is $\Theta =\beta *l$. $beta$ is called the phase constant. It represents the spatial frequency of the signal. $\Theta =\beta *L$ is the phase in degrees or radians (related is a time delay in seconds). $\Theta$ can be, for example $\Theta = 45^0$, $\Theta = 90^0$, $\Theta = 180^0$. $\Theta$ is a function of frequency, because $\beta$ is a function of frequency. If $\Theta = 90^0$, we say: The line is 90 degrees long at 1GHz, meaning the output signal at 1GHz will be shifted for $90^0$ with respect to the input signal. When we say $90^0$, we refer to the lines electrical length, representing the number of degrees that the line introduces between the input and the output signal.