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#### tenderne

##### Member level 2
importance of length in trasnmission line

Hi All,

I got some confusion about the transimission line,
(1) what is the difference/relationship between 'relative permittivity' and 'effective permittivity'?
(2) is 'permittivity' same as 'dielectric constant'?
(3) what is 'geometry length' and 'electrical length'?
(4) suppose I have 'relative permittivity' and 'geometry length', how to calculate the [Y] matrix of transmission line?
(5) if I have only 'electrical length', then how to get [Y] matrix?

I tried to get some information from RF design books, but nowhere can find any accurate description. I am even more confused by the 'lossy' and 'lossless', 2-port and 4-port representation of transmission line.

Kindly give me some help or just some good reference books. Many thanks in advance.

best regards,
tenderne

y matrix

1. Relative permittivity is usually known as the dielectric constant and describes the actual permittivity divided by permittivity of free space, ε0. In transmission lines and especially microstrip systems, the system doesn't have one physical permittivity. For instance, with a microstrip system, it's typically some dielectric on one side of the copper trace and air or a different dielectric on the other. There are effects like fringing capacitance that affect the transmission line characteristics. Effective permittivity replaces the inhomogeneous system with a single effective dielectric constant so it's easier to analyze/design.

2. Relative permittivity is. For instance, relative permittivity (and dielectric constant) of air is actually 1.0001 or so, but the permittivity is 1.001*ε0.

3. Electrical length describes the delay an electromagnetic signal actually experiences in a system/transmission line. If you have a coaxial line, the geometrical length describes the actual measurable, physical length. However, because of the dielectric in the cable, the delay of the signal will not be the same as if it was transmitted through vacuum. So you take the delay of the signal and convert that to an equivalent length, usually in terms of the wavelength, so you'll typically see transmission lines described as λ/4 long instead of a length in inches.

4 and 5. See Microwave Engineering by Pozar for step-by-step procedures.

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