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

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raju_kambar

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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 said:
**broken link removed**
Click to expand...

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
 

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