Why is Electrical length greater than physical length?

[shopi Ram]

I have few ques regarding the electrical length of a transmission lines
1) What is a electrical length and how does it differ from physical length?
2) Why is the electrical length greater than the physical length?
3) Why is electrical length of a transmission line greater than free space?

pls help me find ans


Thanks
shopi

 

[Darkcrusher]

Hi!

An electrical length is a length refered to the wavelength. Suppose your frequency is 100MHz therefore your free wavelength is 3 meters. Mostly the transmission line is built from dielectric material which causes the wavelength to be shorter. Suppose your transmission line is a commercial coax, your wavelength IN the coax would be 2 meters instead of 3.

Next If you use a physical length of...

0 meters, your electrical length is 0 degrees
1 meter, your electrical length is 180 degrees
2 meter, your electrical length is 360 degrees

Its importance lies into frequency independed calculations.

Hope this helps!

 

[WimRFP]

The clue is in the propagation speed. In free space a line with le = 1m would introduce a delay of td = 1/c0 = 3.333ns.

When, due to dielectric material (as in a coaxial transmission line), the propagation speed is less (about 0.66*c0), this line (with physical length of 1m) would show a delay of.

Td = 1/(0.66*c0) = 5.05ns.

This is more, so electrically spoken; this line appears to be longer.

Based on le = td*c0, the dielectrically filled line has an electrical length of:

el.le=td*c0 = 5.05n*3e8 = 1.52m.

So electrical length is the physical length of a line with propagation speed c0 that behaves the same as the actual line.

Note that unterminated lines have somewhat more electrical length, even when corrected for the propagation speed of the actual line. This is because of the capacitive fringing at the unterminated end.

If you express the electrical length in wavelength, you can say
electrical length = (physical length)/(wavelength IN trans.line)

Also here the line may appear longer due to fringe effects.