How to convert inductance value into a equivelent MLIN value at particular frequency

[raju_kambar]

Dear Sir
I want to convert the particular inductance value, suppose L=0.5nH value at a particular frequency of 2GHz to equivalent MLIN value.

As we know length of MLIN line is less than λ/4 short circuited, it acts as a inductive.Similarly length of MLIN line is greater than λ/4 open circuited , it acts as a inductive.
Similarly how to convert the L= 0.5nH or some other inductance value at frequency of interest 2GHz or some other frequency to a equivalent MLIN with width and length.

 

[vfone]

**broken link removed**

 

[raju_kambar]

**broken link removed**

vfone Sir,
Whatever you have shown link, using that link we can inductance by changing MLIN width, length , and thickness. But it not taking interest frequency.But I need to convert the inductance at a particular frequency to MLIN.
I need formula for calculating inductance at a particular frequency convert into a equivalent MLIN. Can you help to convert the inductance at particular frequency into equivalent MLIN

 

[FvM]

The inductance formula linked in post #2 is in fact only valid for short lines l<<λ.

For shorted lossless transmission lines of arbitrary line, the input impedance can be easily calculated referring to Z0, l and λ:

Z1 = j Zo tan(2 pi l/λ)

 

[vfone]

Yes, the equation is valid only for lines << λ. Usually < λ/10
Most of the situations in microwave design we need to design equivalent inductances in microstrip only for very short lines, much shorter than λ.

 

[FvM]

The inductance error of the linear formula for λ/10 is about -15 %, and -3.5 % for λ/20. (x/tan(x))

 

[vfone]

15% is not such bad because anyway microstrip inductance depends by many other factors compared to lumped inductors.
Myself sometimes I prefer using microstrip inductors in RF circuits, and I found that for frequencies in 800MHz to 6GHz range works very well, if you know how to deal with impedances and Q-factors of the circuit.
As a rule in this kind of circuit, always the microstrip inductor must have a lower loaded-Q than the similar lumped inductor.
Motorola, back in '70s and '80s, was one of the first companies that use microstrip inductors on a very large scale in their circuits. I would recommend to any RF engineer to find and look to those old circuits to see what really means RF circuit design.