How to Convert Transimission Line to Equivalent Lumped Element

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Hi,

Below is link talking about the PLL operating at 75GHz: http://cc.ee.ntu.edu.tw/~jrilee/publications/75G_pll_J.pdf

Could any experts explain me how to convert the VCO loaded with lossy transmission line to equivalent VCO loaded with lumped inductor?

I mean, how to calculate the equivalent inductance of the lumped inductor.

I am quite baffled with that.

Thanks a lot.
 

Hi,

If you can get the S-Parameters, I feel that you can get the equivalent lumped result readily.
Second, Matlab RF Toolbox has an example to fit S-Parameters to a lumped network (sum of rational functions).
 

Attached is the math to calculate the loaded impedance, if you know the line impedance Z0 and load ZL.



The difficulty with inductor design at these frequencies is that they get physically small, and it is difficult to achieve good Q factor. My company offers RFIC inductor synthesis software, and I found that many designers prefer transmission line designs above 60GHz.

https://muehlhaus.com/products/rfic-inductor-toolkit-for-ads
 

A spiral, meander, or other shape inductor, on top of lower Q also provides more problems and unknowns at very high frequencies.
A high impedance straight microstrip line is better option than an inductor at those microwave frequencies.
An equation for the inductance of the microstrip inductor that is used for many years by microwave engineers is:

L[nH/mm] = 0.2{ln[l/(w+t)]+1.193+0.2235(w+t)/l}

where l=length of the strip, w=width of the strip, t=thickness of the metal
The above microstrip inductor is without ground plane (or the ground plane is far enough to be ignored). Generally the inductance of the strip line is decreased by the presence of the ground plane.
 
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