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** HowTo convert lumped elements to Trans.Line?

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Junior Member level 1
Aug 13, 2001
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lumped to distributive convert

Dear all,

I'd like to know what are the methods or tools available to convert lumped elements (inductors) in to distributed transmission lines (high impedance transmission line).

Since there are several inductors in a distributed amplifier, should I convert 1 by 1 or the whole lumped circuit ?

Many thanks in advance for everyone's extended guide.

convert lumped circuit to s parameters

There are approximate equations I cannot rememebr now, but will look it for you next week (I packed everything b/.c I am moving :) ).

The best you can do is to simulate in an RF simulator a piece of ideal inductor with the required inductance you want, and simulate a high Z transmition line (I suggest 90 ohms), with different lengths till you get approximately equal responses (S21, etc..any will do it)..

Experiment with different lenghts. You cannot make the two responses exactly equal, since a trnasmition line will not behave as an inductor at all frequencies...

Good luck...

convert lumped elements to transmission line

Are you trying to replace a physical inductor with a meadnered hi impedance line?
This can be done, equations to calculate this will be highly dependant on the substrate material and obviously the frequency. This is generally done for cost cutting in a design or if you have a resonance problem in the actual component. If you have the space it can become useful, but a good inductor is more than often better.
The simulator method as mentioned is a good one, but you will have to get all the relavent substrate parameters and a good rf model of your inductor. Be aware that you may be making things worse by inserting a long length of line. These can radiate quite hideously, and when looking at the S21 you will see a re-surgence at twice the frequency and so on..


lumped elements how to find line length

You can optimize in MWO2002 Your transmission line parameters to minimize the S-parameters difference (in interesting band) between the corresponding inductors & TL, (if this TL type supported by MWO), or try to do this manually, using the tuning tool. I'm repeatedly have the same problem and I think this is the best solution. Convert formulas may be very approximate and limited in terms of frequency and substrate parameters.

With response,

convert distributed element transmission line

Former suggestions exellent, but you could look in the black bible for microwave design(Microwave filters and impedance matching Matthai,young and Jones), there you have the equation for designing semi lumped low and high pass filters, which are the same topologies as matching networks-filters are actually also matching networks.
Also you can find the equations in Transmissions line design handbook, by Wadell.

good first approximation

A good first approximation is to multiply the line impedance by the tangent of the line length (as long as it is under a quarter wave long, that is 0 degrees to 90 degrees). This will give you the inductive reactance for a shorted line and the capacitive reactance for an open line.

The only problem is that these are narrow band devices. Since the line length (in wavelengths) chages with frequency, so will the reactance. The impedance also varies as the tangent of the length for multiples of quarter wave lengths. Do not make a filter with these expecting to eliminate harmonics of signals. Murphys law will always put a leak in the transmission band at your harmonic.

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