RF Design: Electrical length

Sooner or later, the design engineer who is working in microwave or high frequency electronics, is going to come up against the concept of electrical length. In order to understand this concept lets work out the following arithmetic:

1.0 The wave number or phase constant = β = 2π/λ

For those unfamiliar with this, we recommend looking up the description of this quantity in the SPG blog at (http://signalpro-ain.blogspot.com/).

2.0 The electrical length is defined by θ = βl where l = physical length

3.0 θ = βl = (l/ λ) *360 degrees

Here λ is the wavelength of the signal in the applicable dielectric ( or sometimes called the guide wavelength).

4.0 For a frequencies in Ghz, this becomes: [360 * fGhz * l(cm) * √εeff]/30 cm


In this case frequency is in Ghz, physical length is in centimeters.

For example:

Let frequency be 1 Ghz.
Let λ = 0.8 λ(air) or √εeff = 1.25
Let l = 0.1 meters = 0.1E2 centimeters

Then :

θ = [360* 1*0.1E2*1.25]/30 degrees

θ = 150 degrees