What is electrical length used for?

in terms of transmission lines, is the electrical length always calculed with frequency in units of (MHz) ?

What is electrical length used ?

Electrical length is expressed in terms of wavelength λ. Usually the unit is λ, like 1λ, 3.4λ etc. Note that electrical length is therefore defined for a given frequency.
When transmission line is considered, usually guided wavelength λ is considered (not a free space wavelength).

Regards,
jerzyg

In an simulation program, an ideal electrical length is given as a number of degrees of phase and the frequency that the phase is measured at. Such as "45 degrees at 2 GHz". That assumes that the dielectric constant is 1.0 and that the electrical length varies linearly with frequency.

However, since air dielectrics are seldom encountered in a circuit design, a lot of programs allow you to define electrical length as a physical length and a dielectric constant. Such as "0.1 meter and an effective dielectric constant of Er=4.5". That, once again, assumes that the electrical length varies linearly with frequency.

That is about it. In one of the most common media, microstrip, the electrical length does NOT vary lineary with frequency (called dispersion). So when you enter a length of a microstrip line, and the substrate dielectric constant, the program computes an effective dielectric constant, and thus an electrical length, that is a function of Physical length, substrate dielectric constant, and frequency.

Hi, i will explain in mathematics.

Electrical length = BL

Where L = physical length (m), and

B= 2*pi/λ
= 2*pi*f / v
= ω √ue

where pi=3.142, λ=wavelength(m), f=frequency (Hz), v=velocity guided (m/s)

and
1/(√ue) = v
1/(√uoe)=c (speed of light free space)
c/(√urer)=v

and
uo*ur= u and eo*er=e

e=Permitivity
u=Permeability
er=relative permitivity
ur=relative permeability
eo=Permitivity in freespace (constant)
uo=Permeability in freespace (constant)

I hope i don't confuse you. But do correct me if you found any error in my explaination. Thanks.

Added after 1 hours 39 minutes:

Correction:
1/(√uoeo)=c (speed of light free space)

very sorry for the mistake

Electrical length are in unit length.
It can be in meter, mm, inches, or mils.

Skip all the calculation of c, λ, μ, ρ... we have a simple formula:

in air, εr=1,
Electrical Length= 2.95"/ (F (GHz) or 2.95"/(1000 X F (MHz))
=74.93mm/ F (GHz) or 74.93mm"/(1000 X F (MHz))

Added after 2 hours 24 minutes:

Correction:

The above calculation is for a quater-wave length (λ/4). Full wave length (λ) is 4 times of that numbers.

Krytar

hi

i agree with the above and wish to add that the environment that the condouctor ii in affects its EL

regards

if the electrical length of a cable is its length measured in wavelengths (λ) and is related to the frequency of the wave and the velocity with which it propagates along the transmission line, what do you think of the following formula :

Electrical length = length of the line / λ
Electrical length = (length of the line)(frequency)/velocity propagation

looks like Jerzyg definition, looks ok ?

Hi,

Usually when people refer electrical length, it can expressed either in degree or in wavelength..

For example,

f * λ = v
one wavelength =λ = 2*pi = 360°
becos B*L= (2*pi/λ)*λ=360°

quarter wavelength = λ/4 is also = 90°
becos B*L = (2*pi/λ)*λ/4 = pi/2 =90°

half wavelength = λ/2 is also = 180°
becos B*L = (2*pi/λ)*λ/2 = pi =180°

and so on... [/i]